Help:Displaying a formula

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aria-controls="toc-Use_of_HTML_templates-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Use of HTML templates subsection</span> </button> <ul id="toc-Use_of_HTML_templates-sublist" class="vector-toc-list"> <li id="toc-HTML_entities" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#HTML_entities"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>HTML entities</span> </div> </a> <ul id="toc-HTML_entities-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Superscripts_and_subscripts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Superscripts_and_subscripts"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Superscripts and subscripts</span> </div> </a> <ul id="toc-Superscripts_and_subscripts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spacing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spacing"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Spacing</span> </div> </a> <ul id="toc-Spacing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-More" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#More"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>More</span> </div> </a> <ul id="toc-More-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-LaTeX_basics" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#LaTeX_basics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>LaTeX basics</span> </div> </a> <button aria-controls="toc-LaTeX_basics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle LaTeX basics subsection</span> </button> <ul id="toc-LaTeX_basics-sublist" class="vector-toc-list"> <li id="toc-LaTeX_commands" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#LaTeX_commands"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>LaTeX commands</span> </div> </a> <ul id="toc-LaTeX_commands-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Special_characters" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Special_characters"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Special characters</span> </div> </a> <ul id="toc-Special_characters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spaces" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spaces"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Spaces</span> </div> </a> <ul id="toc-Spaces-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-LaTeX_environments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#LaTeX_environments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>LaTeX environments</span> </div> </a> <ul id="toc-LaTeX_environments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rendering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rendering"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Rendering</span> </div> </a> <ul id="toc-Rendering-sublist" class="vector-toc-list"> <li id="toc-Force-rerendering_of_formulas" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Force-rerendering_of_formulas"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5.1</span> <span>Force-rerendering of formulas</span> </div> </a> <ul id="toc-Force-rerendering_of_formulas-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Formatting_using_LaTeX" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Formatting_using_LaTeX"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Formatting using LaTeX</span> </div> </a> <button aria-controls="toc-Formatting_using_LaTeX-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Formatting using LaTeX subsection</span> </button> <ul id="toc-Formatting_using_LaTeX-sublist" class="vector-toc-list"> <li id="toc-Functions,_symbols,_special_characters" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Functions,_symbols,_special_characters"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Functions, symbols, special characters</span> </div> </a> <ul id="toc-Functions,_symbols,_special_characters-sublist" class="vector-toc-list"> <li id="toc-Accents_and_diacritics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Accents_and_diacritics"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.1</span> <span>Accents and diacritics</span> </div> </a> <ul id="toc-Accents_and_diacritics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Standard_numerical_functions" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Standard_numerical_functions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.2</span> <span>Standard numerical functions</span> </div> </a> <ul id="toc-Standard_numerical_functions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bounds" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Bounds"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.3</span> <span>Bounds</span> </div> </a> <ul id="toc-Bounds-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Projections" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Projections"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.4</span> <span>Projections</span> </div> </a> <ul id="toc-Projections-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Differentials_and_derivatives" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Differentials_and_derivatives"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.5</span> <span>Differentials and derivatives</span> </div> </a> <ul id="toc-Differentials_and_derivatives-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Letter-like_symbols_or_constants" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Letter-like_symbols_or_constants"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.6</span> <span>Letter-like symbols or constants</span> </div> </a> <ul id="toc-Letter-like_symbols_or_constants-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modular_arithmetic" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Modular_arithmetic"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.7</span> <span>Modular arithmetic</span> </div> </a> <ul id="toc-Modular_arithmetic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Radicals" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Radicals"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.8</span> <span>Radicals</span> </div> </a> <ul id="toc-Radicals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Operators" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Operators"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.9</span> <span>Operators</span> </div> </a> <ul id="toc-Operators-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sets" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Sets"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.10</span> <span>Sets</span> </div> </a> <ul id="toc-Sets-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relations" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Relations"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.11</span> <span>Relations</span> </div> </a> <ul id="toc-Relations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometric" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Geometric"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.12</span> <span>Geometric</span> </div> </a> <ul id="toc-Geometric-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Logic" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Logic"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.13</span> <span>Logic</span> </div> </a> <ul id="toc-Logic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Arrows" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Arrows"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.14</span> <span>Arrows</span> </div> </a> <ul id="toc-Arrows-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Special" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Special"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.15</span> <span>Special</span> </div> </a> <ul id="toc-Special-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Unsorted_(new_stuff)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Unsorted_(new_stuff)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.16</span> <span>Unsorted (new stuff)</span> </div> </a> <ul id="toc-Unsorted_(new_stuff)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Larger_expressions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Larger_expressions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Larger expressions</span> </div> </a> <ul id="toc-Larger_expressions-sublist" class="vector-toc-list"> <li id="toc-Subscripts,_superscripts,_integrals" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Subscripts,_superscripts,_integrals"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2.1</span> <span>Subscripts, superscripts, integrals</span> </div> </a> <ul id="toc-Subscripts,_superscripts,_integrals-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Fractions,_matrices,_multilines" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fractions,_matrices,_multilines"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Fractions, matrices, multilines</span> </div> </a> <ul id="toc-Fractions,_matrices,_multilines-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Parenthesizing_big_expressions,_brackets,_bars" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Parenthesizing_big_expressions,_brackets,_bars"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Parenthesizing big expressions, brackets, bars</span> </div> </a> <ul id="toc-Parenthesizing_big_expressions,_brackets,_bars-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Display_attribute" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Display_attribute"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Display attribute</span> </div> </a> <ul id="toc-Display_attribute-sublist" class="vector-toc-list"> <li id="toc-Inline" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Inline"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5.1</span> <span>Inline</span> </div> </a> <ul id="toc-Inline-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Block" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Block"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5.2</span> <span>Block</span> </div> </a> <ul id="toc-Block-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Not_specified" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Not_specified"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5.3</span> <span>Not specified</span> </div> </a> <ul id="toc-Not_specified-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Equation_numbering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Equation_numbering"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Equation numbering</span> </div> </a> <ul id="toc-Equation_numbering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Alphabets_and_typefaces" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Alphabets_and_typefaces"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.7</span> <span>Alphabets and typefaces</span> </div> </a> <ul id="toc-Alphabets_and_typefaces-sublist" class="vector-toc-list"> <li id="toc-Mixed_text_faces" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Mixed_text_faces"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.7.1</span> <span>Mixed text faces</span> </div> </a> <ul id="toc-Mixed_text_faces-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Color" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Color"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.8</span> <span>Color</span> </div> </a> <ul id="toc-Color-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formatting_issues" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formatting_issues"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.9</span> <span>Formatting issues</span> </div> </a> <ul id="toc-Formatting_issues-sublist" class="vector-toc-list"> <li id="toc-Spacing_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Spacing_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.9.1</span> <span>Spacing</span> </div> </a> <ul id="toc-Spacing_2-sublist" class="vector-toc-list"> <li id="toc-Empty_horizontal_or_vertical_spacing" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Empty_horizontal_or_vertical_spacing"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.9.1.1</span> <span>Empty horizontal or vertical spacing</span> </div> </a> <ul id="toc-Empty_horizontal_or_vertical_spacing-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Alignment_with_normal_text_flow" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Alignment_with_normal_text_flow"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.9.2</span> <span>Alignment with normal text flow</span> </div> </a> <ul id="toc-Alignment_with_normal_text_flow-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Unimplemented_elements_and_workarounds" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Unimplemented_elements_and_workarounds"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10</span> <span>Unimplemented elements and workarounds</span> </div> </a> <ul id="toc-Unimplemented_elements_and_workarounds-sublist" class="vector-toc-list"> <li id="toc-Special_integral_operators" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Special_integral_operators"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.1</span> <span>Special integral operators</span> </div> </a> <ul id="toc-Special_integral_operators-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-\oiint_and_\oiiint" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#\oiint_and_\oiiint"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.2</span> <span><span>\oiint</span> and <span>\oiiint</span></span> </div> </a> <ul id="toc-\oiint_and_\oiiint-sublist" class="vector-toc-list"> <li id="toc-\oiint_and_\oiiint_as_PNG_images" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#\oiint_and_\oiiint_as_PNG_images"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.2.1</span> <span><span>\oiint</span> and <span>\oiiint</span> as PNG images</span> </div> </a> <ul id="toc-\oiint_and_\oiiint_as_PNG_images-sublist" class="vector-toc-list"> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-5"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.2.1.1</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Oriented_\oiint_and_\oiiint_as_PNG_images" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Oriented_\oiint_and_\oiiint_as_PNG_images"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.2.2</span> <span>Oriented <span>\oiint</span> and <span>\oiiint</span> as PNG images</span> </div> </a> <ul id="toc-Oriented_\oiint_and_\oiiint_as_PNG_images-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Arc_notation_\overarc" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Arc_notation_\overarc"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.3</span> <span>Arc notation <span>\overarc</span></span> </div> </a> <ul id="toc-Arc_notation_\overarc-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Triple_dot_\dddot" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Triple_dot_\dddot"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.4</span> <span>Triple dot <span>\dddot</span></span> </div> </a> <ul id="toc-Triple_dot_\dddot-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Starred_operatorname_\operatorname*" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Starred_operatorname_\operatorname*"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.5</span> <span>Starred operatorname <span>\operatorname*</span></span> </div> </a> <ul id="toc-Starred_operatorname_\operatorname*-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Strikethrough" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Strikethrough"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.6</span> <span>Strikethrough</span> </div> </a> <ul id="toc-Strikethrough-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formatting_in_\text" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Formatting_in_\text"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.7</span> <span>Formatting in \text</span> </div> </a> <ul id="toc-Formatting_in_\text-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Automatic_line-breaking" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Automatic_line-breaking"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.10.8</span> <span>Automatic line-breaking</span> </div> </a> <ul id="toc-Automatic_line-breaking-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Syntax_to_avoid" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Syntax_to_avoid"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.11</span> <span>Syntax to avoid</span> </div> </a> <ul id="toc-Syntax_to_avoid-sublist" class="vector-toc-list"> <li id="toc-Unicode_characters" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Unicode_characters"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.11.1</span> <span>Unicode characters</span> </div> </a> <ul id="toc-Unicode_characters-sublist" class="vector-toc-list"> <li id="toc-Invisible_Unicode_characters" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Invisible_Unicode_characters"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.11.1.1</span> <span>Invisible Unicode characters</span> </div> </a> <ul id="toc-Invisible_Unicode_characters-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Deprecated_syntax" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Deprecated_syntax"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.11.2</span> <span>Deprecated syntax</span> </div> </a> <ul id="toc-Deprecated_syntax-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Chemistry" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Chemistry"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Chemistry</span> </div> </a> <button aria-controls="toc-Chemistry-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Chemistry subsection</span> </button> <ul id="toc-Chemistry-sublist" class="vector-toc-list"> <li id="toc-Molecular_and_condensed_formula" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Molecular_and_condensed_formula"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Molecular and condensed formula</span> </div> </a> <ul id="toc-Molecular_and_condensed_formula-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bonds" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bonds"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Bonds</span> </div> </a> <ul id="toc-Bonds-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Charges" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Charges"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Charges</span> </div> </a> <ul id="toc-Charges-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Addition_compounds_and_stoichiometric_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Addition_compounds_and_stoichiometric_numbers"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Addition compounds and stoichiometric numbers</span> </div> </a> <ul id="toc-Addition_compounds_and_stoichiometric_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wiki_linking" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Wiki_linking"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Wiki linking</span> </div> </a> <ul id="toc-Wiki_linking-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-(Italic)_Math" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#(Italic)_Math"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6</span> <span>(Italic) Math</span> </div> </a> <ul id="toc-(Italic)_Math-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Oxidation_states" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Oxidation_states"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.7</span> <span>Oxidation states</span> </div> </a> <ul id="toc-Oxidation_states-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Greek_characters" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Greek_characters"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.8</span> <span>Greek characters</span> </div> </a> <ul id="toc-Greek_characters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Isotopes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Isotopes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.9</span> <span>Isotopes</span> </div> </a> <ul id="toc-Isotopes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-States" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#States"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.10</span> <span>States</span> </div> </a> <ul id="toc-States-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Precipitate_and_gas_formation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Precipitate_and_gas_formation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.11</span> <span>Precipitate and gas formation</span> </div> </a> <ul id="toc-Precipitate_and_gas_formation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reaction_arrows" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reaction_arrows"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.12</span> <span>Reaction arrows</span> </div> </a> <ul id="toc-Reaction_arrows-sublist" class="vector-toc-list"> <li id="toc-Comparison_of_arrow_symbols" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Comparison_of_arrow_symbols"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.12.1</span> <span>Comparison of arrow symbols</span> </div> </a> <ul id="toc-Comparison_of_arrow_symbols-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_examples_using_ordinary_LaTeX_tags" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Further_examples_using_ordinary_LaTeX_tags"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.13</span> <span>Further examples using ordinary LaTeX tags</span> </div> </a> <ul id="toc-Further_examples_using_ordinary_LaTeX_tags-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Commutative_diagrams" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Commutative_diagrams"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Commutative diagrams</span> </div> </a> <button aria-controls="toc-Commutative_diagrams-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Commutative diagrams subsection</span> </button> <ul id="toc-Commutative_diagrams-sublist" class="vector-toc-list"> <li id="toc-1_step_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#1_step_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>1 step method</span> </div> </a> <ul id="toc-1_step_method-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-3_step_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#3_step_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>3 step method</span> </div> </a> <ul id="toc-3_step_method-sublist" class="vector-toc-list"> <li id="toc-Diagrams_in_TeX" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Diagrams_in_TeX"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.1</span> <span>Diagrams in TeX</span> </div> </a> <ul id="toc-Diagrams_in_TeX-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Convert_to_SVG" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Convert_to_SVG"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.2</span> <span>Convert to SVG</span> </div> </a> <ul id="toc-Convert_to_SVG-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Upload_the_file" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Upload_the_file"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.3</span> <span>Upload the file</span> </div> </a> <ul id="toc-Upload_the_file-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Examples_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.4</span> <span>Examples</span> </div> </a> <ul id="toc-Examples_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Semantics_and_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Semantics_and_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Semantics and links</span> </div> </a> <ul id="toc-Semantics_and_links-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples_of_implemented_TeX_formulas" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Examples_of_implemented_TeX_formulas"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Examples of implemented TeX formulas</span> </div> </a> <button aria-controls="toc-Examples_of_implemented_TeX_formulas-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Examples of implemented TeX formulas subsection</span> </button> <ul id="toc-Examples_of_implemented_TeX_formulas-sublist" class="vector-toc-list"> <li id="toc-Quadratic_polynomial" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quadratic_polynomial"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Quadratic polynomial</span> </div> </a> <ul id="toc-Quadratic_polynomial-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quadratic_formula" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quadratic_formula"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Quadratic formula</span> </div> </a> <ul id="toc-Quadratic_formula-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tall_parentheses_and_fractions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tall_parentheses_and_fractions"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.3</span> <span>Tall parentheses and fractions</span> </div> </a> <ul id="toc-Tall_parentheses_and_fractions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Integrals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Integrals"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.4</span> <span>Integrals</span> </div> </a> <ul id="toc-Integrals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Matrices_and_determinants" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Matrices_and_determinants"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.5</span> <span>Matrices and determinants</span> </div> </a> <ul id="toc-Matrices_and_determinants-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Summation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Summation"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.6</span> <span>Summation</span> </div> </a> <ul id="toc-Summation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Differential_equation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Differential_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.7</span> <span>Differential equation</span> </div> </a> <ul id="toc-Differential_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complex_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complex_numbers"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.8</span> <span>Complex numbers</span> </div> </a> <ul id="toc-Complex_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limits" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Limits"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.9</span> <span>Limits</span> </div> </a> <ul id="toc-Limits-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Integral_equation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Integral_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.10</span> <span>Integral equation</span> </div> </a> <ul id="toc-Integral_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Example" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Example"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.11</span> <span>Example</span> </div> </a> <ul id="toc-Example-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Continuation_and_cases" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Continuation_and_cases"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.12</span> <span>Continuation and cases</span> </div> </a> <ul id="toc-Continuation_and_cases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Prefixed_subscript" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Prefixed_subscript"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.13</span> <span>Prefixed subscript</span> </div> </a> <ul id="toc-Prefixed_subscript-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fraction_and_small_fraction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fraction_and_small_fraction"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.14</span> <span>Fraction and small fraction</span> </div> </a> <ul id="toc-Fraction_and_small_fraction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Area_of_a_quadrilateral" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Area_of_a_quadrilateral"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.15</span> <span>Area of a quadrilateral</span> </div> </a> <ul id="toc-Area_of_a_quadrilateral-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Volume_of_a_sphere-stand" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Volume_of_a_sphere-stand"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.16</span> <span>Volume of a sphere-stand</span> </div> </a> <ul id="toc-Volume_of_a_sphere-stand-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Multiple_equations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Multiple_equations"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.17</span> <span>Multiple equations</span> </div> </a> <ul id="toc-Multiple_equations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.1</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.2</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown 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class="mw-page-title-namespace">Help</span><span class="mw-page-title-separator">:</span><span class="mw-page-title-main">Displaying a formula</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 53 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-53" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">53 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%B9%D8%AF%D8%A9:%D8%B9%D8%B1%D8%B6_%D8%B5%D9%8A%D8%BA%D8%A9_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9" title="مساعدة:عرض صيغة رياضية – Arabic" lang="ar" hreflang="ar" data-title="مساعدة:عرض صيغة رياضية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Vikipediya:Formullar" title="Vikipediya:Formullar – Azerbaijani" lang="az" hreflang="az" data-title="Vikipediya:Formullar" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Wantuan:Math" title="Wantuan:Math – Balinese" lang="ban" hreflang="ban" data-title="Wantuan:Math" data-language-autonym="Basa Bali" data-language-local-name="Balinese" class="interlanguage-link-target"><span>Basa Bali</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%BE%E0%A6%B9%E0%A6%BE%E0%A6%AF%E0%A7%8D%E0%A6%AF:%E0%A6%97%E0%A6%BE%E0%A6%A3%E0%A6%BF%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A7%82%E0%A6%A4%E0%A7%8D%E0%A6%B0" title="সাহায্য:গাণিতিক সূত্র – Bangla" lang="bn" hreflang="bn" data-title="সাহায্য:গাণিতিক সূত্র" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0%D0%BB%D0%B0%D1%80" title="Википедия:Формулалар – Bashkir" lang="ba" hreflang="ba" data-title="Википедия:Формулалар" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D1%8D%D0%B4%D1%8B%D1%8F:TeX" title="Вікіпэдыя:TeX – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Вікіпэдыя:TeX" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A3%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B8" title="Уикипедия:Формули – Bulgarian" lang="bg" hreflang="bg" data-title="Уикипедия:Формули" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Ajuda:F%C3%B3rmula" title="Ajuda:Fórmula – Catalan" lang="ca" hreflang="ca" data-title="Ajuda:Fórmula" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/N%C3%A1pov%C4%9Bda:Matematick%C3%A9_vzorce" title="Nápověda:Matematické vzorce – Czech" lang="cs" hreflang="cs" data-title="Nápověda:Matematické vzorce" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hj%C3%A6lp:Formatering_med_opm%C3%A6rkningskoder" title="Hjælp:Formatering med opmærkningskoder – Danish" lang="da" hreflang="da" data-title="Hjælp:Formatering med opmærkningskoder" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hilfe:TeX" title="Hilfe:TeX – German" lang="de" hreflang="de" data-title="Hilfe:TeX" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Juhend:Matemaatiliste_valemite_kirjutamine" title="Juhend:Matemaatiliste valemite kirjutamine – Estonian" lang="et" hreflang="et" data-title="Juhend:Matemaatiliste valemite kirjutamine" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%92%CE%BF%CE%AE%CE%B8%CE%B5%CE%B9%CE%B1:TeX_%CE%B5%CE%BA%CF%84%CE%B5%CE%BD%CF%8E%CF%82" title="Βοήθεια:TeX εκτενώς – Greek" lang="el" hreflang="el" data-title="Βοήθεια:TeX εκτενώς" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ayuda:Uso_de_LaTeX" title="Ayuda:Uso de LaTeX – Spanish" lang="es" hreflang="es" data-title="Ayuda:Uso de LaTeX" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Helpo:TEX_en_Vikipedio" title="Helpo:TEX en Vikipedio – Esperanto" lang="eo" hreflang="eo" data-title="Helpo:TEX en Vikipedio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Laguntza:Adierazpen_sinboliko_fisiko-matematikoak_idazteko_gida" title="Laguntza:Adierazpen sinboliko fisiko-matematikoak idazteko gida – Basque" lang="eu" hreflang="eu" data-title="Laguntza:Adierazpen sinboliko fisiko-matematikoak idazteko gida" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%D9%87%D9%86%D9%85%D8%A7:%D9%81%D8%B1%D9%85%D9%88%D9%84%E2%80%8C%D9%86%D9%88%DB%8C%D8%B3%DB%8C" title="راهنما:فرمول‌نویسی – Persian" lang="fa" hreflang="fa" data-title="راهنما:فرمول‌نویسی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Aide:Formules_TeX" title="Aide:Formules TeX – French" lang="fr" hreflang="fr" data-title="Aide:Formules TeX" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Wikipedia:Etiquetas_TeX" title="Wikipedia:Etiquetas TeX – Galician" lang="gl" hreflang="gl" data-title="Wikipedia:Etiquetas TeX" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%84%ED%82%A4%EB%B0%B1%EA%B3%BC:TeX_%EB%AC%B8%EB%B2%95" title="위키백과:TeX 문법 – Korean" lang="ko" hreflang="ko" data-title="위키백과:TeX 문법" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%95%D5%A3%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6:%D4%B2%D5%A1%D5%B6%D5%A1%D5%B1%D6%87%D5%A5%D6%80" title="Օգնություն:Բանաձևեր – Armenian" lang="hy" hreflang="hy" data-title="Օգնություն:Բանաձևեր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Wikipedija:Formule" title="Wikipedija:Formule – Croatian" lang="hr" hreflang="hr" data-title="Wikipedija:Formule" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bantuan:Menampilkan_rumus" title="Bantuan:Menampilkan rumus – Indonesian" lang="id" hreflang="id" data-title="Bantuan:Menampilkan rumus" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Wikipedia:Formulas_TeX" title="Wikipedia:Formulas TeX – Interlingua" lang="ia" hreflang="ia" data-title="Wikipedia:Formulas TeX" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Aiuto:Formule_matematiche_TeX" title="Aiuto:Formule matematiche TeX – Italian" lang="it" hreflang="it" data-title="Aiuto:Formule matematiche TeX" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%A0%D7%95%D7%A1%D7%97%D7%90%D7%95%D7%AA" title="עזרה:נוסחאות – Hebrew" lang="he" hreflang="he" data-title="עזרה:נוסחאות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Pitulung:Rumus" title="Pitulung:Rumus – Javanese" lang="jv" hreflang="jv" data-title="Pitulung:Rumus" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%95%E1%83%98%E1%83%99%E1%83%98%E1%83%9E%E1%83%94%E1%83%93%E1%83%98%E1%83%90:%E1%83%A4%E1%83%9D%E1%83%A0%E1%83%9B%E1%83%A3%E1%83%9A%E1%83%94%E1%83%91%E1%83%98" title="ვიკიპედია:ფორმულები – Georgian" lang="ka" hreflang="ka" data-title="ვიკიპედია:ფორმულები" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Pagalba:Lyg%C4%8Di%C5%B3_%C4%AFk%C4%97limas_bei_redagavimas" title="Pagalba:Lygčių įkėlimas bei redagavimas – Lithuanian" lang="lt" hreflang="lt" data-title="Pagalba:Lygčių įkėlimas bei redagavimas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Wikip%C3%A9dia:K%C3%A9pletle%C3%ADr%C3%B3_nyelv" title="Wikipédia:Képletleíró nyelv – Hungarian" lang="hu" hreflang="hu" data-title="Wikipédia:Képletleíró nyelv" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D0%B0:TeX_markup" title="Википедиа:TeX markup – Mongolian" lang="mn" hreflang="mn" data-title="Википедиа:TeX markup" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%80%E1%80%B0%E1%80%A1%E1%80%8A%E1%80%AE:Displaying_a_formula" title="အကူအညီ:Displaying a formula – Burmese" lang="my" hreflang="my" data-title="အကူအညီ:Displaying a formula" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Help:TeX_in_Wikipedia" title="Help:TeX in Wikipedia – Dutch" lang="nl" hreflang="nl" data-title="Help:TeX in Wikipedia" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/Wikipedia:TeX%E3%81%AB%E9%96%A2%E3%81%99%E3%82%8B%E7%96%91%E5%95%8F%E8%B3%AA%E5%95%8F" title="Wikipedia:TeXに関する疑問質問 – Japanese" lang="ja" hreflang="ja" data-title="Wikipedia:TeXに関する疑問質問" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Hjelp:Vise_en_formel" title="Hjelp:Vise en formel – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Hjelp:Vise en formel" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%87%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%99:%E1%9E%9A%E1%9E%BC%E1%9E%94%E1%9E%98%E1%9E%93%E1%9F%92%E1%9E%8F" title="ជំនួយ:រូបមន្ត – Khmer" lang="km" hreflang="km" data-title="ជំនួយ:រូបមន្ត" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pomoc:Wzory" title="Pomoc:Wzory – Polish" lang="pl" hreflang="pl" data-title="Pomoc:Wzory" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ajuda:Guia_de_edi%C3%A7%C3%A3o/F%C3%B3rmulas_TeX" title="Ajuda:Guia de edição/Fórmulas TeX – Portuguese" lang="pt" hreflang="pt" data-title="Ajuda:Guia de edição/Fórmulas TeX" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Ajutor:Formatul_TeX" title="Ajutor:Formatul TeX – Romanian" lang="ro" hreflang="ro" data-title="Ajutor:Formatul TeX" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D1%8B" title="Википедия:Формулы – Russian" lang="ru" hreflang="ru" data-title="Википедия:Формулы" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Ndihm%C3%AB:TeX" title="Ndihmë:TeX – Albanian" lang="sq" hreflang="sq" data-title="Ndihmë:TeX" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Pomoc:Matematick%C3%A9_vzorce" title="Pomoc:Matematické vzorce – Slovak" lang="sk" hreflang="sk" data-title="Pomoc:Matematické vzorce" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Wikipedija:TeXov_zapis" title="Wikipedija:TeXov zapis – Slovenian" lang="sl" hreflang="sl" data-title="Wikipedija:TeXov zapis" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BC%D0%BE%D1%9B:%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B5" title="Помоћ:Формуле – Serbian" lang="sr" hreflang="sr" data-title="Помоћ:Формуле" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Ohje:Kaavat" title="Ohje:Kaavat – Finnish" lang="fi" hreflang="fi" data-title="Ohje:Kaavat" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Wikipedia:Matematiska_uttryck" title="Wikipedia:Matematiska uttryck – Swedish" lang="sv" hreflang="sv" data-title="Wikipedia:Matematiska uttryck" data-language-autonym="Svenska" data-language-local-name="Swedish" 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For other uses, see <a href="/wiki/Wikipedia:MATH_(disambiguation)" class="mw-disambig" title="Wikipedia:MATH (disambiguation)">WP:MATH (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1238436933">.mw-parser-output .ombox{margin:4px 0;border-collapse:collapse;border:1px solid #a2a9b1;background-color:var(--background-color-neutral-subtle,#f8f9fa);box-sizing:border-box;color:var(--color-base,#202122)}.mw-parser-output .ombox.mbox-small{font-size:88%;line-height:1.25em}.mw-parser-output .ombox-speedy{border:2px solid #b32424;background-color:#fee7e6}.mw-parser-output .ombox-delete{border:2px solid #b32424}.mw-parser-output .ombox-content{border:1px solid #f28500}.mw-parser-output .ombox-style{border:1px solid #fc3}.mw-parser-output .ombox-move{border:1px solid #9932cc}.mw-parser-output .ombox-protection{border:2px solid #a2a9b1}.mw-parser-output .ombox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .ombox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .ombox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .ombox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ombox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .ombox{margin:4px 10%}.mw-parser-output .ombox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}body.skin--responsive .mw-parser-output table.ombox img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .ombox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ombox-speedy{background-color:#310402}}</style><table class="plainlinks ombox ombox-notice" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Twemoji_1f527.svg/30px-Twemoji_1f527.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Twemoji_1f527.svg/45px-Twemoji_1f527.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Twemoji_1f527.svg/60px-Twemoji_1f527.svg.png 2x" data-file-width="512" data-file-height="512"/></span></span></td><td class="mbox-text"><div style="padding-top: 6px; padding-bottom: 5px;"><b>This help page is a <a href="/wiki/Wikipedia:Project_namespace#Wikipedia_how-to_and_information_pages" title="Wikipedia:Project namespace">how-to guide</a>.</b><br/><div style="font-size: 90%;">It explains concepts or processes used by the Wikipedia community. It is not one of <a href="/wiki/Wikipedia:Policies_and_guidelines" title="Wikipedia:Policies and guidelines">Wikipedia's policies or guidelines</a>, and may reflect varying levels of <a href="/wiki/Wikipedia:Consensus" title="Wikipedia:Consensus">consensus</a>.</div></div></td><td class="mbox-imageright"><style data-mw-deduplicate="TemplateStyles:r1252059228">.mw-parser-output .module-shortcutboxplain{float:right;margin:0 0 0 1em;border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-base,#fff);padding:0.3em 0.6em 0.2em 0.6em;text-align:center;font-size:85%}.mw-parser-output .module-shortcutboxleft{float:left;margin:0 1em 0 0}.mw-parser-output .module-shortcutlist{display:inline-block;border-bottom:1px solid var(--border-color-base,#a2a9b1);margin-bottom:0.2em}.mw-parser-output .module-shortcutboxplain ul{font-weight:bold}.mw-parser-output .module-shortcutanchordiv{position:relative;top:-3em}.mw-parser-output li .module-shortcutanchordiv{float:right}.mw-parser-output .mbox-imageright .module-shortcutboxplain{padding:0.4em 1em 0.4em 1em;line-height:1.3;margin:0}</style><div class="module-shortcutanchordiv"><span id="WP:FORMULA"></span><span id="WP:MATH"></span><span id="WP:MATHS"></span><span id="WP:LATEX"></span></div><div class="module-shortcutboxplain noprint" role="note"><div class="module-shortcutlist"><a href="/wiki/Wikipedia:Shortcut" title="Wikipedia:Shortcut">Shortcuts</a></div><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:FORMULA&redirect=no">WP:FORMULA</a></span></li><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:MATH&redirect=no">WP:MATH</a></span></li><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:MATHS&redirect=no">WP:MATHS</a></span></li><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:LATEX&redirect=no">WP:LATEX</a></span></li></ul></div></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Editing_a_formula_using_VisualEditor.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Editing_a_formula_using_VisualEditor.png/220px-Editing_a_formula_using_VisualEditor.png" decoding="async" width="220" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Editing_a_formula_using_VisualEditor.png/330px-Editing_a_formula_using_VisualEditor.png 1.5x, //upload.wikimedia.org/wikipedia/commons/9/98/Editing_a_formula_using_VisualEditor.png 2x" data-file-width="413" data-file-height="382"/></a><figcaption>This screenshot shows the formula <span class="texhtml"><i>E</i> = <i>mc</i><sup><small>2</small></sup></span> being edited using <a href="/wiki/VisualEditor" title="VisualEditor">VisualEditor</a>. The window is opened by typing "<math>" in VisualEditor. The visual editor shows a button that allows to choose one of three offered modes to display a formula.</figcaption></figure> <p>There are three methods for displaying formulas in Wikipedia: raw <a href="/wiki/HTML" title="HTML">HTML</a>, HTML with <a href="/wiki/Template:Math_templates" title="Template:Math templates">math templates</a> (abbreviated here as <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span>), and a subset of <a href="/wiki/LaTeX" title="LaTeX">LaTeX</a> implemented with the <a href="/wiki/HTML_markup" class="mw-redirect" title="HTML markup">HTML markup</a> <code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr"><span class="p"><</span><span class="nt">math</span><span class="p">></</span><span class="nt">math</span><span class="p">></span></code> (referred to as <i>LaTeX</i> in this article). Each method has some advantages and some disadvantages, which have evolved over time with improvements of <a href="/wiki/MediaWiki" title="MediaWiki">MediaWiki</a>. The manual of style <a href="/wiki/MOS:MATH" class="mw-redirect" title="MOS:MATH">MOS:MATH</a> has not always evolved accordingly. So the how-to recommendations that appear below may differ from those of the manual of style. In this case, they express a <a href="/wiki/Wikipedia:CONSENSUS" class="mw-redirect" title="Wikipedia:CONSENSUS">consensus</a> resulting of the practice of most experienced members of <a href="/wiki/Wikipedia:WikiProject_Mathematics" title="Wikipedia:WikiProject Mathematics">WikiProject Mathematics</a> and many discussions at <a href="/wiki/Wikipedia_talk:WikiProject_Mathematics" title="Wikipedia talk:WikiProject Mathematics">Wikipedia talk:WikiProject Mathematics</a>. </p><p>For example, the famous <a href="/wiki/Einstein_formula" class="mw-redirect" title="Einstein formula">Einstein formula</a> can be entered in raw HTML as <code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">nowrap</span><span class="p">|</span><span class="ge">''E''</span> <span class="p">{{</span><span class="nf">=</span><span class="p">}}</span> <span class="ge">''mc''</span><span class="p"><</span><span class="nt">sup</span><span class="p">></span>2<span class="p"></</span><span class="nt">sup</span><span class="p">>}}</span></code>, which is rendered as <span class="nowrap"><i>E</i> = <i>mc</i><sup>2</sup></span> (the template <span class="nowrap">{{</span><a href="/wiki/Template:Nowrap" title="Template:Nowrap">nowrap</a><span class="nowrap">}}</span> is here only for avoiding a line break inside the formula). With <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span>, it can be entered as <code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">math</span><span class="p">|</span><span class="ge">''E''</span> <span class="p">{{</span><span class="nf">=</span><span class="p">}}</span> <span class="ge">''mc''</span><span class="p">{{</span><span class="nt">sup</span><span class="p">|</span>2<span class="p">}}}}</span></code>, which is rendered as <span class="texhtml"><i>E</i> = <i>mc</i><sup>2</sup></span>. With LaTeX, it is entered as <code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr"><span class="p"><</span><span class="nt">math</span><span class="p">></span>E=mc^2<span class="p"></</span><span class="nt">math</span><span class="p">></span></code>, and rendered as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=mc^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=mc^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f73dbd37a0cac34406ee89057fa1b36a1e6a18e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.976ex; height:2.676ex;" alt="{\displaystyle E=mc^{2}}"/></span>. </p> <meta property="mw:PageProp/toc"/> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Use_of_raw_HTML" data-mw-thread-id="h-Use_of_raw_HTML"><span data-mw-comment-start="" id="h-Use_of_raw_HTML"></span>Use of raw HTML<span data-mw-comment-end="h-Use_of_raw_HTML"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=1" title="Edit section: Use of raw HTML"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Variable names and many symbols look very different with raw HTML and the other display methods. This may be confusing in the common case where several methods are used in the same article. Moreover, mathematicians who are used to reading and writing texts written with <a href="/wiki/LaTeX" title="LaTeX">LaTeX</a> often find the raw HTML rendering awful. </p><p>So, raw HTML should normally not be used for new content. However, raw HTML is still present in many mathematical articles. It is generally a good practice to convert it to <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> format, but coherency must be respected; that is, such a conversion must be done in a whole article, or at least in a whole section. Moreover, such a conversion must be identified as such in the edit summary, and making other changes in the same edit should be avoided. This is for helping other users to identify changes that are possibly controversial (the "diff" of a conversion may be very large, and may hide other changes). </p><p>Converting raw HTML to <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> is rather simple: when the formula is enclosed with <span class="nowrap">{{</span><a href="/wiki/Template:Nowrap" title="Template:Nowrap">nowrap</a><span class="nowrap">}}</span>, it suffices to change "nowrap" into "math". However, if the formula contains an equal sign, one has to add <code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr">1=</code> just before the formula for avoiding confusion with the template syntax; for example, <code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">math</span><span class="p">|</span><span class="nl">1</span><span class="o">=</span><span class="ge">''E''</span> = <span class="ge">''mc''</span><span class="p">{{</span><span class="nt">sup</span><span class="p">|</span>2<span class="p">}}}}</span></code>. Also, vertical bars, if any, must either be replaced with <code>{{<a href="/wiki/Template:!" title="Template:!">!</a>}}</code> or avoided by using <code>{{<a href="/wiki/Template:Abs" class="mw-redirect" title="Template:Abs">abs</a>}}</code>. </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="LaTeX_vs._{{math}}" data-mw-thread-id="h-LaTeX_vs._{{math}}"><span id="LaTeX_vs._.7B.7Bmath.7D.7D"></span><span data-mw-comment-start="" id="h-LaTeX_vs._{{math}}"></span>LaTeX vs. {{math}}<span data-mw-comment-end="h-LaTeX_vs._{{math}}"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=2" title="Edit section: LaTeX vs. {{math}}"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="LaTeX_vs._math_template"></span> </p><p>These two ways of writing mathematical formulas each have their advantages and disadvantages. They are both accepted by the manual of style <a href="/wiki/MOS:MATH" class="mw-redirect" title="MOS:MATH">MOS:MATH</a>. The rendering of variable names is very similar. Having a variable name displayed in the same paragraph with <code>{{<a href="/wiki/Template:Math" title="Template:Math">math</a>}}</code> and <code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr"><span class="p"><</span><span class="nt">math</span><span class="p">></span></code> is generally not a problem. </p><p>The disadvantages of LaTeX are the following: On some browser configurations, LaTeX inline formulas appear with a slight vertical misalignment, or with a font size that may be slightly different from that of the surrounding text. This is not a problem with a block displayed formula, and also typically not with inline formulas that exceed the normal line height marginally (for example formulas with subscripts and superscripts). The use of LaTeX in a <a href="/wiki/Wikipedia:Piped_link" title="Wikipedia:Piped link">piped link</a> or in a section heading does not appear in blue in the linked text or the table of content. Moreover, links to section headings containing LaTeX formulas do not always work as expected. Finally, having many LaTeX formulas may significantly increase the processing time of a page. LaTeX formulas should be avoided in image captions or footnotes, because when the image is clicked for a larger display or a footnote is selected on a mobile device, LaTeX in the caption or footnote will not render. </p><p>Disadvantages of <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> include that not all formulas can be displayed, and while it may be possible to display a complicated formula with <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span>, it may be poorly rendered. Except for the most common symbols such as letters, numerals, and basic punctuation, rendering of <a href="/wiki/Unicode" title="Unicode">Unicode</a> mathematical symbols can be inconsistent in size or alignment where fallback fonts do not match, and some readers may not have any font which includes certain uncommon symbols. Spaces within a formula must be directly managed (for example by including explicit <a href="/wiki/Hair_space" class="mw-redirect" title="Hair space">hair</a> or <a href="/wiki/Thin_space" title="Thin space">thin spaces</a>). Variable names must be italicized explicitly, and superscripts and subscripts must use an explicit tag or template. Except for short formulas, the source of a formula typically has more markup overhead and can be difficult to read. </p><p>The common practice of most members of <a href="/wiki/Wikipedia:WPM" class="mw-redirect" title="Wikipedia:WPM">WikiProject mathematics</a> is the following: </p> <ul><li>Use of <span class="nowrap">{{</span><a href="/wiki/Template:Mvar" title="Template:Mvar">mvar</a><span class="nowrap">}}</span> and <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> for isolated variables and <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> for simple inline formulas; or alternately the use of LaTeX for these purposes (optionally using the <span class="nowrap">{{</span><a href="/wiki/Template:Tmath" title="Template:Tmath">tmath</a><span class="nowrap">}}</span> template), especially on articles with many complex formulas or where rendering seems inconsistent</li> <li>Use of <span class="nowrap">{{</span><a href="/wiki/Template:Mvar" title="Template:Mvar">mvar</a><span class="nowrap">}}</span> and <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> for formulas in image captions, even if the rendering is mediocre</li> <li>Use of LaTeX for separately displayed formulas and more complicated inline formulas</li> <li>Use of LaTeX for formulas involving symbols that are not regularly rendered in Unicode (see <a href="/wiki/MOS:BBB" class="mw-redirect" title="MOS:BBB">MOS:BBB</a>)</li> <li>Avoid formulas in section headings, and when this is necessary, use raw HTML (see <a href="/wiki/Finite_field" title="Finite field">Finite field</a> for an example)</li></ul> <p>The choice between <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> and LaTeX depends on the editor. Converting a page from one format to another must be done with stronger reasons than editor preference. </p> <div class="mw-heading mw-heading3"><h3 id="Display_format_of_LaTeX" data-mw-thread-id="h-Display_format_of_LaTeX-LaTeX_vs._{{math}}"><span data-mw-comment-start="" id="h-Display_format_of_LaTeX-LaTeX_vs._{{math}}"></span>Display format of LaTeX<span data-mw-comment-end="h-Display_format_of_LaTeX-LaTeX_vs._{{math}}"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=3" title="Edit section: Display format of LaTeX"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>By default SVG images with non-visible <a href="/wiki/MathML" title="MathML">MathML</a> are generated. The text-only form of the LaTeX can be set via <a href="/wiki/Help:Preferences" title="Help:Preferences">user preferences</a> at <a href="/wiki/Special:Preferences#mw-prefsection-rendering" title="Special:Preferences">My Preferences – Appearance – Math</a>. </p><p>The hidden MathML can be used by screen readers and other assistive technology. To display the MathML in Firefox: </p> <ul><li>Install the <a rel="nofollow" class="external text" href="https://addons.mozilla.org/en-US/firefox/addon/native-mathml/">Native MathML</a> extension</li> <li>Or copy <a rel="nofollow" class="external text" href="https://github.com/fred-wang/webextension-native-mathml/blob/master/content-scripts/mediawiki.css">its CSS rules</a> to your Wikipedia <a href="/wiki/Help:User_style" title="Help:User style">user stylesheet</a>.</li></ul> <p>In either case, you must have fonts that support MathML (<a rel="nofollow" class="external text" href="https://developer.mozilla.org/en-US/docs/Mozilla/MathML_Project/Fonts">see developer.mozilla.org</a>) installed on your system. For copy-paste support in Firefox, you can also install <a rel="nofollow" class="external text" href="https://addons.mozilla.org/en-US/firefox/addon/mathml-copy/">MathML Copy</a>. </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Use_of_HTML_templates" data-mw-thread-id="h-Use_of_HTML_templates"><span data-mw-comment-start="" id="h-Use_of_HTML_templates"></span>Use of HTML templates<span data-mw-comment-end="h-Use_of_HTML_templates"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=4" title="Edit section: Use of HTML templates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:MATHSYMBOL"></span></div><div class="module-shortcutboxplain noprint" role="note"><div class="module-shortcutlist"><a href="/wiki/Wikipedia:Shortcut" title="Wikipedia:Shortcut">Shortcut</a></div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:MATHSYMBOL&redirect=no">WP:MATHSYMBOL</a></span></li></ul></div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Wikipedia:Rendering_math" title="Wikipedia:Rendering math">Wikipedia:Rendering math</a></div> <p>TeX markup is not the only way to render mathematical formulas. For simple inline formulas, the template <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> and its associated templates are often preferred. The following comparison table shows that similar results can be achieved with the two methods. See also <a href="/wiki/Help:Special_characters" title="Help:Special characters">Help:Special characters</a>. </p> <table class="wikitable"> <tbody><tr> <th>TeX syntax </th> <th>TeX rendering </th> <td rowspan="5"> </td> <th>HTML syntax </th> <th>HTML rendering </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\alpha</span></math></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">math</span><span class="p">|</span><span class="ge">''</span><span class="ni">&alpha;</span><span class="ge">''</span><span class="p">}}</span></code> or <code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">mvar</span><span class="p">|</span><span class="ni">&alpha;</span><span class="p">}}</span></code> </td> <td><span class="texhtml"><i>α</i></span> or <span class="texhtml mvar" style="font-style:italic;">α</span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math>f(x) = x<span class="nb">^</span>2</math></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84ddac4ae10b1aa4a11741c79771a583419fb1fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.9ex; height:3.176ex;" alt="{\displaystyle f(x)=x^{2}}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">math</span><span class="p">|</span><span class="nl">1</span><span class="o">=</span><span class="ge">''f''</span>(<span class="ge">''x''</span>) = <span class="ge">''x''</span><span class="p"><</span><span class="nt">sup</span><span class="p">></span>2<span class="p"></</span><span class="nt">sup</span><span class="p">>}}</span></code> </td> <td><span class="texhtml"><i>f</i>(<i>x</i>) = <i>x</i><sup>2</sup></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\{</span>1,e,<span class="k">\pi\}</span></math></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{1,e,\pi \}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mi>e</mi> <mo>,</mo> <mi>π</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{1,e,\pi \}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1d815f10d5905c898266e8a03b19b421155536" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.971ex; height:2.843ex;" alt="{\displaystyle \{1,e,\pi \}}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">math</span><span class="p">|{{</span><span class="nt">mset</span><span class="p">|</span>1, <span class="ge">''e''</span>, <span class="ge">''</span><span class="ni">&pi;</span><span class="ge">''</span><span class="p">}}}}</span></code> </td> <td><span class="texhtml">{1, <i>e</i>, <i>π</i>}</span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math>|z| <span class="k">\leq</span> 2</math></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |z|\leq 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>≤</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |z|\leq 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/519593b209744218518efb60d8b8a00e3e5ef863" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.643ex; height:2.843ex;" alt="{\displaystyle |z|\leq 2}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">math</span><span class="p">|{{</span><span class="nt">abs</span><span class="p">|</span><span class="ge">''z''</span><span class="p">}}</span> <span class="ni">&le;</span> 2<span class="p">}}</span></code> </td> <td><span class="texhtml">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"><i>z</i></span>| ≤ 2</span> </td></tr> </tbody></table> <p>Here is a summary of the mathematical templates: </p> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r886049405">.mw-parser-output .noitalic{font-style:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049405"></div><div role="navigation" class="navbox" aria-labelledby="Math_templates285" style="padding:3px"><table class="nowraplinks hlist mw-collapsible expanded navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Math_templates" title="Template:Math templates"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Math_templates" title="Template talk:Math templates"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Math_templates" title="Special:EditPage/Template:Math templates"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Math_templates285" style="font-size:114%;margin:0 4em">Math templates</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="*Functions_*Numeral_systems285" style="font-size:114%;margin:0 4em"> <ul><li>Functions</li> <li>Numeral systems</li></ul> </div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;font-size:110%;"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Functions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Template:Elementary_arithmetic" title="Template:Elementary arithmetic">elementary arithmetic</a></li> <li><a href="/wiki/Template:Precision" title="Template:Precision">precision</a></li> <li><a href="/wiki/Template:Val" title="Template:Val">val</a> (value formatting)</li> <li><a href="/wiki/Template:Percentage" title="Template:Percentage">percentage</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Numeral systems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>{{<a href="/wiki/Module:BaseConvert" title="Module:BaseConvert">#invoke:BaseConvert</a>|<i>X</i>to<i>Y</i>}}</li> <li><a href="/wiki/Template:Binary" title="Template:Binary">binary</a></li> <li><a href="/wiki/Template:Decimal2Base" title="Template:Decimal2Base">decimal2Base</a></li> <li><a href="/wiki/Template:Hex2dec" title="Template:Hex2dec">hex2dec</a></li> <li><a href="/wiki/Template:Hexadecimal" title="Template:Hexadecimal">hexadecimal</a></li> <li><a href="/wiki/Template:Octal" title="Template:Octal">octal</a></li> <li><a href="/wiki/Template:Quaternary" title="Template:Quaternary">quaternary</a></li> <li><a href="/wiki/Template:Rn" title="Template:Rn">rn</a></li> <li><a href="/wiki/Template:Roman" title="Template:Roman">roman</a></li> <li><a href="/wiki/Template:Ternary" title="Template:Ternary">ternary</a></li> <li><a href="/wiki/Template:Vigesimal" title="Template:Vigesimal">vigesimal</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Conversions285" style="font-size:114%;margin:0 4em">Conversions</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;font-size:110%;"><div style="padding:0 0.25em"><table style="margin:0 auto 0;text-align:left;"><tbody><tr style="vertical-align:top"><td> <table style="padding-right:2.5em;"><tbody><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Convert" title="Template:Convert">convert</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> many units (see: <a href="/wiki/Template:Convert/list_of_units" title="Template:Convert/list of units">list</a>)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Cvt" class="mw-redirect" title="Template:Cvt">cvt</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> abbreviated <span class="nowrap">{{</span><a href="/wiki/Template:Convert" title="Template:Convert">convert</a><span class="nowrap">}}</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Convinfobox" title="Template:Convinfobox">convinfobox</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <span class="nowrap">{{</span><a href="/wiki/Template:Convert" title="Template:Convert">convert</a><span class="nowrap">}}</span> for infoboxes</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Bbl_to_t" title="Template:Bbl to t">bbl to t</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> barrels of oil to tonnes</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Long_ton" title="Template:Long ton">long ton</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> long hundredweights, quarters and pounds to kilograms;<br/>long tons and hundredweights to pounds and metric tons</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Miles-chains" title="Template:Miles-chains">miles-chains</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> miles and chains to kilometres linking "chains"</td></tr></tbody></table></td><td> <table><tbody><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Decdeg" title="Template:Decdeg">decdeg</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> degrees, minutes, and seconds to <a href="/wiki/Decimal_degrees" title="Decimal degrees">decimal degrees</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Deg2DMS" title="Template:Deg2DMS">deg2dms</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> decimal degrees to degrees, minutes, and seconds</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Deg2HMS" title="Template:Deg2HMS">deg2hms</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> decimal degrees to <a href="/wiki/Hour_angle" title="Hour angle">hour angle</a> (in hours, minutes, and seconds)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:HMS2Deg" title="Template:HMS2Deg">hms2deg</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <a href="/wiki/Hour_angle" title="Hour angle">hour angle</a> (in hours, minutes, and seconds) to decimal degrees</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Inflation" title="Template:Inflation">inflation</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> calculate inflation of Consumer Price Index-related prices</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Pop_density" title="Template:Pop density">pop density</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> population density in an area</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Track_gauge" title="Template:Track gauge">track gauge</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> railway track gauges</td></tr></tbody></table></td></tr></tbody></table></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible uncollapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Notation_and_formatting285" style="font-size:114%;margin:0 4em">Notation and <a href="/wiki/Category:Mathematical_formatting_templates" title="Category:Mathematical formatting templates">formatting</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;font-size:110%;"><div style="padding:0 0.25em"><table style="margin:0 auto 0;text-align:left;"><tbody><tr style="vertical-align:top"><td> <table style="padding-right:2.5em;"><tbody><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Bigmath" title="Template:Bigmath">bigmath</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> bigger font to match <span class="noitalic"><a href="/wiki/TeX" title="TeX">TeX</a></span> <span class="noitalic"><samp>\displaystyle</samp></span> (standalone formulas only)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <ul><li><a href="/wiki/Template:Bra-ket" title="Template:Bra-ket">bra-ket</a></li> <li><a href="/wiki/Template:Braket" title="Template:Braket">braket</a></li> <li><a href="/wiki/Template:Bra" class="mw-redirect" title="Template:Bra">bra</a></li> <li><a href="/wiki/Template:Ket" class="mw-redirect" title="Template:Ket">ket</a></li></ul></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">bra–ket notation</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Ceil" title="Template:Ceil">ceil</a>, <a href="/wiki/Template:Floor" title="Template:Floor">floor</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> calculations <a href="https://www.mediawiki.org/wiki/Help:Extension:ParserFunctions##expr" class="extiw" title="mw:Help:Extension:ParserFunctions">:mw:Help:#expr</a>; formatting indicators <span class="noitalic">⌈3.14⌉</span>, <span class="noitalic"><span style="font-size:1em">⌊</span>3.14<span style="font-size:1em">⌋</span></span> (no calculation performed)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Fraction" title="Template:Fraction">fraction</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> slant fractions <span class="frac"><span class="num">3</span>⁄<span class="den">5</span></span> (not for maths/science articles; use <i>standing</i> or upright fractions <span class="noitalic"><code>{{<a href="/wiki/Template:Sfrac" title="Template:Sfrac">sfrac</a>}}</code></span> instead)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Intmath" title="Template:Intmath">intmath</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <a href="/wiki/Integral_symbol" title="Integral symbol">integral symbols</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <li><a href="/wiki/Template:Langle" title="Template:Langle">langle</a></li> <li><a href="/wiki/Template:Rangle" title="Template:Rangle">rangle</a></li> <li><a href="/wiki/Template:Angle_bracket" title="Template:Angle bracket">angbr</a></li></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <a href="/wiki/Bracket#Angular_brackets" title="Bracket">angular brackets</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <li><a href="/wiki/Template:Ldelim" title="Template:Ldelim">ldelim</a></li> <li><a href="/wiki/Template:Rdelim" title="Template:Rdelim">rdelim</a></li></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> multiline delimiters (2–5 lines inclusive)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Abs" class="mw-redirect" title="Template:Abs">abs</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> absolute values (paired vertical lines)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Math" title="Template:Math">math</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> short text-based formulas</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Mathcal" title="Template:Mathcal">mathcal</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> [mathematical] calligraphic font; alternative to <span class="noitalic"><a href="/wiki/LaTeX" title="LaTeX">LaTeX</a></span> <span class="noitalic"><samp>\mathcal{...}</samp></span></td></tr></tbody></table></td><td> <table><tbody><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Mvar" title="Template:Mvar">mvar</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> individual italicized maths variables in normal text</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <li><a href="/wiki/Template:Overline" title="Template:Overline">overline</a></li> <li><a href="/wiki/Template:Underline" title="Template:Underline">underline</a></li></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> a line set above/below a sequence of characters</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Overarc" title="Template:Overarc">overarc</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> an arc set above a sequence of characters</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <li><a href="/wiki/Template:Overset" title="Template:Overset">overset</a></li> <li><a href="/wiki/Template:Underset" title="Template:Underset">underset</a></li></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> arbitrary characters/diacritics set above/below one another</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Pars" title="Template:Pars">pars</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> parentheses that can be resized <span class="noitalic"><span class="texhtml"><span style="font-size:150;">(</span><span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"><span style="font-size:120%">∑</span></span><span style="font-size:150;">)</span></span></span></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Sfrac" title="Template:Sfrac">sfrac</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> "standing" or upright fractions <span class="sfrac">⁠<span class="tion"><span class="num">3</span><span class="sr-only">/</span><span class="den">5</span></span>⁠</span> (use in maths/science articles instead of<span class="noitalic"><code>{{<a href="/wiki/Template:Fraction" title="Template:Fraction">fraction</a>}}</code></span>)</td></tr><tr style="vertical-align:top"><td style="vertical-align:middle;text-align:right;padding-right:1.0em;"> <li><a href="/wiki/Template:Sub" title="Template:Sub">sub</a></li> <li><a href="/wiki/Template:Sup" title="Template:Sup">sup</a></li> <li><a href="/wiki/Template:Su" title="Template:Su">su</a></li></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> subscripts and superscripts</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Tmath" title="Template:Tmath">tmath</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> Wrap <span class="noitalic"><a href="/wiki/TeX" title="TeX">TeX</a></span> in <span class="noitalic"><math></span> tags</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Tombstone" title="Template:Tombstone">tombstone</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> symbol indicating the <a href="/wiki/Tombstone_(typography)" title="Tombstone (typography)">end of a proof</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Val" title="Template:Val">val</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> measurement values, uncertainties and units</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/Template:Vec" class="mw-redirect" title="Template:Vec">vec</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> various overarrows, underarrows, etc.</td></tr></tbody></table></td></tr></tbody></table></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="*Boxes_*Tags_*Notices285" style="font-size:114%;margin:0 4em"> <li>Boxes</li> <li>Tags</li> <li>Notices</li> </div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;font-size:110%;"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;background:transparent;color:inherit;"><div style="padding:0px"><table class="navbox-columns-table" style="border-spacing: 0px; text-align:left;width:100%;"><tbody><tr><td class="navbox-abovebelow" style="font-weight:bold;">Boxes</td><td class="navbox-abovebelow" style="border-left:2px solid #fdfdfd;font-weight:bold;">Tags</td></tr><tr style="vertical-align:top"><td class="navbox-list" style="padding:0px;text-align:center;width:10em;"><div> <ul><li><a href="/wiki/Template:Arithmetic_operations" title="Template:Arithmetic operations">arithmetic operations</a></li> <li><a href="/wiki/Template:Calculus" title="Template:Calculus">calculus</a></li> <li><a href="/wiki/Template:Infobox_mathematical_function" title="Template:Infobox mathematical function">Infobox mathematical function</a></li> <li><a href="/wiki/Template:Functions" title="Template:Functions">functions</a></li></ul> </div></td><td class="navbox-list" style="border-left:2px solid #fdfdfd;padding:0px;text-align:center;width:10em;"><div> <ul><li><a href="/wiki/Template:Metricate" title="Template:Metricate">metricate</a></li> <li><a href="/wiki/Template:Undue_precision" title="Template:Undue precision">undue precision</a></li> <li><a href="/wiki/Template:Units_attention" title="Template:Units attention">units attention</a></li></ul> </div></td></tr></tbody></table></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185"/></span></span> <a href="/wiki/Category:Mathematics_templates" title="Category:Mathematics templates">Category</a></li> <li><a href="/wiki/Module:Math" title="Module:Math">Module:Math</a></li></ul> </div></td></tr></tbody></table></div> <p>Care should be taken when writing sets within <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span>, as braces, equal signs, and vertical bars can conflict with template syntax. The <span class="nowrap">{{</span><a href="/wiki/Template:Mset" title="Template:Mset">mset</a><span class="nowrap">}}</span> template is available for braces, as shown in the example above. Likewise, <span class="nowrap">{{</span><a href="/wiki/Template:Abs" class="mw-redirect" title="Template:Abs">abs</a><span class="nowrap">}}</span> encloses its parameter inside vertical bars to help with the pipe character conflicting with template syntax. For a single vertical bar, use <code>{{<a href="/wiki/Template:!" title="Template:!">!</a>}}</code>, and for an equal sign, use <code>{{<a href="/wiki/Template:%3D" title="Template:=">=</a>}}</code>. </p> <div class="mw-heading mw-heading3"><h3 id="HTML_entities" data-mw-thread-id="h-HTML_entities-Use_of_HTML_templates"><span data-mw-comment-start="" id="h-HTML_entities-Use_of_HTML_templates"></span>HTML entities<span data-mw-comment-end="h-HTML_entities-Use_of_HTML_templates"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=5" title="Edit section: HTML entities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Though <a href="/wiki/Unicode" title="Unicode">Unicode</a> characters are generally preferred, sometimes <a href="/wiki/HTML_entities" class="mw-redirect" title="HTML entities">HTML entities</a> are needed to avoid problems with wiki syntax or confusion with other characters: </p> <table style="text-align:center;"><tbody><tr style="vertical-align:top"><td class="unicode"> <</td><td class="unicode"> ></td><td class="unicode"> −</td><td class="unicode"> •</td><td class="unicode">′</td><td class="unicode"> ″</td><td class="unicode"> ⋅</td><td class="unicode"> ·</td><td class="unicode"> –</td><td class="unicode"> —</td></tr><tr style="vertical-align:top"><td class="mw-code"> &lt;</td><td class="mw-code"> &gt;</td><td class="mw-code"> &minus;</td><td class="mw-code"> &bull;</td><td class="mw-code"> &prime;</td><td class="mw-code"> &Prime;</td><td class="mw-code"> &sdot;</td><td class="mw-code"> &middot;</td><td class="mw-code"> &ndash;</td><td class="mw-code"> &mdash;</td></tr></tbody></table> <p>In the table below, the codes on the left produce the symbols on the right, but these symbols can also be entered directly in the wikitext either by typing them if they are available on the keyboard, by copy-pasting them, or by using menus below the edit windows. (When editing any Wikipedia page in a desktop web browser, use the "Insert" pulldown menu immediately below the article text, or the "Special characters" menu immediately above the article text.) Normally, lowercase Greek letters should be entered in italics, that is, enclosed between two single quotes (<code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="ge">''</span></code>). </p> <table class="wikitable" border="1"> <tbody><tr> <th>HTML syntax </th> <th>Rendering </th></tr> <tr style="vertical-align:middle;"> <td> <pre>&alpha; &beta; &gamma; &delta; &epsilon; &zeta; &eta; &theta; &iota; &kappa; &lambda; &mu; &nu; &xi; &omicron; &pi; &rho; &sigma; &sigmaf; &tau; &upsilon; &phi; &chi; &psi; &omega;</pre> </td> <td> <p>α β γ δ ε ζ<br/>η θ ι κ λ μ ν<br/>ξ ο π ρ σ ς<br/>τ υ φ χ ψ ω<br/> </p> </td></tr> <tr style="vertical-align:middle;"> <td> <pre>&Gamma; &Delta; &Theta; &Lambda; &Xi; &Pi; &Sigma; &Phi; &Psi; &Omega;</pre> </td> <td> <p>Γ Δ Θ Λ Ξ Π<br/>Σ Φ Ψ Ω </p> </td></tr> <tr style="vertical-align:middle;"> <td><pre>&int; &sum; &prod; &minus; &plusmn; &infin; &asymp; &prop; = &equiv; &ne; &le; &ge; &times; &middot; &sdot; &divide; &part; &prime; &Prime; &nabla; &permil; &deg; &there4; &empty;</pre> </td> <td> <p>∫ ∑ ∏ − ± ∞<br/>≈ ∝ = ≡ ≠ ≤ ≥<br/>× · ⋅ ÷ ∂ ′ ″<br/>∇ ‰ ° ∴ ∅ </p> </td></tr> <tr style="vertical-align:middle;"> <td><pre>&isin; &notin; &cap; &cup; &sub; &sup; &sube; &supe; &not; &and; &or; &exist; &forall; &rArr; &hArr; &rarr; &harr; &uarr; &darr; &alefsym; - &ndash; &mdash;</pre> </td> <td> <p>∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇<br/>¬ ∧ ∨ ∃ ∀<br/>⇒ ⇔ → ↔ ↑ ↓<br/>ℵ - – — </p> </td></tr> </tbody></table> <div class="mw-heading mw-heading3"><h3 id="Superscripts_and_subscripts" data-mw-thread-id="h-Superscripts_and_subscripts-Use_of_HTML_templates"><span data-mw-comment-start="" id="h-Superscripts_and_subscripts-Use_of_HTML_templates"></span>Superscripts and subscripts<span data-mw-comment-end="h-Superscripts_and_subscripts-Use_of_HTML_templates"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=6" title="Edit section: Superscripts and subscripts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table style="text-align:center;"><tbody><tr style="vertical-align:top"><td class="unicode">x<sup>2</sup></td><td class="unicode"> x<sub>3</sub></td><td class="unicode"> x<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sub></span></span></td></tr><tr style="vertical-align:top"><td class="mw-code">x<sup>2</sup></td><td class="mw-code">x<sub>3</sub></td><td class="mw-code">x{{su|b=1|p=2|lh=1}}</td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Spacing" data-mw-thread-id="h-Spacing-Use_of_HTML_templates"><span data-mw-comment-start="" id="h-Spacing-Use_of_HTML_templates"></span>Spacing<span data-mw-comment-end="h-Spacing-Use_of_HTML_templates"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=7" title="Edit section: Spacing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>To avoid line-wrapping in the middle of a formula, use <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span>. If necessary, a <a href="/wiki/Non-breaking_space" title="Non-breaking space">non-breaking space</a> ( ) can be inserted with "&nbsp;". When an inline formula is long enough, it can be helpful to allow it to break across lines. Whether using LaTeX or templates, split the formula at each acceptable breakpoint into separate <code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math></span></code> tags or <span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">math</a><span class="nowrap">}}</span> templates with any binary relations or operators and intermediate whitespace included at the trailing rather than leading end of a part. </p><p>Typically <a href="/wiki/Whitespace_character" title="Whitespace character">whitespace</a> should be a regular space ( ) or none at all. In rare circumstances, such as where one character overlaps another due to one being in italics, a thin space can be added with <span class="nowrap">{{</span><a href="/wiki/Template:Thin_space" title="Template:Thin space">thin space</a><span class="nowrap">}}</span>. </p> <div class="mw-heading mw-heading3"><h3 id="More" data-mw-thread-id="h-More-Use_of_HTML_templates"><span data-mw-comment-start="" id="h-More-Use_of_HTML_templates"></span>More<span data-mw-comment-end="h-More-Use_of_HTML_templates"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=8" title="Edit section: More"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For more on Wikipedia howtos and math style guidelines: </p> <ul><li><a href="/wiki/MOS:FRAC" class="mw-redirect" title="MOS:FRAC">MOS:FRAC</a> for how to input fractions in various circumstances</li> <li><a href="/wiki/MOS:RADICAL" class="mw-redirect" title="MOS:RADICAL">MOS:RADICAL</a> for how to square and other roots in various circumstances</li> <li>Per <a href="/wiki/MOS:ELLIPSIS" class="mw-redirect" title="MOS:ELLIPSIS">MOS:ELLIPSIS</a>, "..." (three ASCII periods) is used instead of "…" (single character)</li> <li><a href="/wiki/Arrow_(symbol)#Arrows_in_Unicode" title="Arrow (symbol)">Arrow (symbol) § Arrows in Unicode</a></li> <li><a href="/wiki/Mathematical_operators_and_symbols_in_Unicode" title="Mathematical operators and symbols in Unicode">Mathematical operators and symbols in Unicode</a></li> <li><a href="/wiki/Wikipedia:Manual_of_Style_(mathematics)" class="mw-redirect" title="Wikipedia:Manual of Style (mathematics)">Wikipedia:Manual of Style (mathematics)</a></li></ul> <p>For more on special characters: </p> <ul><li><a rel="nofollow" class="external text" href="http://www.unicode.org/charts/charindex.html">Unicode character name index</a> can be used to find the Unicode number of a character.</li> <li><a rel="nofollow" class="external text" href="http://www.w3.org">W3C</a> list of MathML characters indexed by <a rel="nofollow" class="external text" href="http://www.w3.org/TR/MathML2/bycodes.html">code</a> or <a rel="nofollow" class="external text" href="http://www.w3.org/TR/MathML2/byalpha.html">name</a></li> <li><a href="/wiki/List_of_XML_and_HTML_character_entity_references" title="List of XML and HTML character entity references">List of XML and HTML character entity references</a> – includes all named entities</li> <li><a href="/wiki/Glossary_of_mathematical_symbols" title="Glossary of mathematical symbols">Glossary of mathematical symbols</a></li></ul> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="LaTeX_basics" data-mw-thread-id="h-LaTeX_basics"><span data-mw-comment-start="" id="h-LaTeX_basics"></span>LaTeX basics<span data-mw-comment-end="h-LaTeX_basics"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=9" title="Edit section: LaTeX basics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Math markup goes inside <code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math></span>...<span class="nt"></math></span></code>. Chemistry markup goes inside <code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math</span><span class="w"> </span><span class="err">chem</span><span class="nt">></span>...<span class="nt"></math></span></code> or <code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><chem></span>...<span class="nt"></chem></span></code>. <code>{{tmath|...}}</code> can be used in place of <code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math></span>...<span class="nt"></math></span></code> to avoid line wrapping of adjacent text (with caveats). All these tags use TeX. </p><p>The TeX code has to be put literally: MediaWiki templates, predefined templates, and parameters cannot be used within math tags: pairs of double braces are ignored and "#" gives an error message. However, math tags work in the then and else part of #if, etc. See <a href="https://meta.wikimedia.org/wiki/Template:Demo_of_attempt_to_use_parameters_within_TeX" class="extiw" title="m:Template:Demo of attempt to use parameters within TeX">m:Template:Demo of attempt to use parameters within TeX</a> <span style="font-size:85%;">(<a href="https://meta.wikimedia.org/wiki/Special:Whatlinkshere/Template:Demo_of_attempt_to_use_parameters_within_TeX" class="extiw" title="m:Special:Whatlinkshere/Template:Demo of attempt to use parameters within TeX">backlinks</a> <a class="external text" href="https://meta.wikimedia.org/wiki/Template:Demo_of_attempt_to_use_parameters_within_TeX?action=edit">edit</a>)</span> for more information. </p><p>The now deprecated tag <code><ce></code> was considered too ambiguous, and it has been replaced by <code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr"><span class="p"><</span><span class="nt">chem</span><span class="p">></span></code>.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="LaTeX_commands" data-mw-thread-id="h-LaTeX_commands-LaTeX_basics"><span data-mw-comment-start="" id="h-LaTeX_commands-LaTeX_basics"></span>LaTeX commands<span data-mw-comment-end="h-LaTeX_commands-LaTeX_basics"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=10" title="Edit section: LaTeX commands"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>LaTeX commands are case-sensitive, and take one of the following two formats: </p> <ul><li>They start with a backslash <code>\</code> and then have a name consisting of letters only. Command names are terminated by a space, a number or any other "non-letter" character.</li> <li>They consist of a backslash <code>\</code> and exactly one non-letter.</li></ul> <p>Some commands need an <a href="/wiki/Argument" title="Argument">argument</a>, which has to be given between curly braces <code>{}</code> after the command name. Some commands support optional <a href="/wiki/Parameter" title="Parameter">parameters</a>, which are added after the command name in square brackets <code>[]</code>. The general syntax is: </p> <pre>\commandname[option1,option2,...]{argument1}{argument2}... </pre> <div class="mw-heading mw-heading3"><h3 id="Special_characters" data-mw-thread-id="h-Special_characters-LaTeX_basics"><span data-mw-comment-start="" id="h-Special_characters-LaTeX_basics"></span>Special characters<span data-mw-comment-end="h-Special_characters-LaTeX_basics"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=11" title="Edit section: Special characters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following symbols are reserved characters that either have a special meaning under LaTeX or are unavailable in all the fonts. If you enter them directly in your text, they will normally not render, but rather do things you did not intend. </p> <pre># $ % ^ & _ { } ~ \ </pre> <p>These characters can be entered by prefixing the escape character backslash <code>\</code> or using special sequences: </p> <pre>\# \$ \% ^\wedge \& \_ \{ \} \sim \backslash </pre> <p>yielding: </p> <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \#\$\%^{\wedge }\&\_\{\}\sim \backslash }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">#</mi> <mi mathvariant="normal">$</mi> <msup> <mi mathvariant="normal">%</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∧</mo> </mrow> </msup> <mi mathvariant="normal">&</mi> <mi mathvariant="normal">_</mi> <mo fence="false" stretchy="false">{</mo> <mo fence="false" stretchy="false">}</mo> <mo>∼</mo> <mi class="MJX-variant" mathvariant="normal">∖</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \#\$\%^{\wedge }\&\_\{\}\sim \backslash }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afcc308375673656e2d3697545923acc16c5050e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.919ex; height:3.009ex;" alt="{\displaystyle \#\$\%^{\wedge }\&\_\{\}\sim \backslash }"/></span></div> <p>The backslash character <code>\</code> can <i>not</i> be entered by adding another backslash in front of it (<code>\\</code>); this sequence is used for line breaking. For introducing a backslash in math mode, you can use <code>\backslash</code> instead which gives <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \backslash }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant" mathvariant="normal">∖</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \backslash }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e865e5b244a7a5d4fdf7a95fe4cea6d25e581ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.162ex; height:2.843ex;" alt="{\displaystyle \backslash }"/></span>. </p><p>The command <code>\tilde</code> produces a tilde which is placed over the next letter. For example, <code>\tilde{a}</code> gives <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3788241de82e20f20362a4496c4ed7d7dc265e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:2.176ex;" alt="{\displaystyle {\tilde {a}}}"/></span>. To produce just a tilde character ~, use <code>\tilde{\ }</code> which gives <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {\ }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mtext> </mtext> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {\ }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/592caf438a7c622a41cb5c9d013e218293a166d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.162ex; height:1.843ex;" alt="{\displaystyle {\tilde {\ }}}"/></span>, placing a ~ over an empty box. Alternatively <code>\sim</code> produces <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sim }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∼</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sim }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afcc42adfcfdc24d5c4c474869e5d8eaa78d1173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.307ex; margin-bottom: -0.478ex; width:1.808ex; height:1.343ex;" alt="{\displaystyle \sim }"/></span>, a large centred ~ which may be more appropriate in some situations. </p><p>The command <code>\hat</code> produces a hat over the next character, for example <code>\hat{o}</code> produces <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {o}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>o</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {o}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b295806edcacca7a1a28fceb6ef9aa231462446" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.292ex; height:2.176ex;" alt="{\displaystyle {\hat {o}}}"/></span>. For a stretchable version, use <code>\widehat{abc}</code> giving <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\widehat {abc}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> <mo>^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\widehat {abc}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82214aa4dad2bab45f4fe13bf571e38040d7aedd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-left: -0.008ex; margin-right: -0.007ex; width:3.37ex; height:3.009ex;" alt="{\displaystyle {\widehat {abc}}}"/></span>. The wedge <code>\wedge</code> is normally used as a mathematical operator <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"/></span>. The sequence <code>{}^\wedge</code> produces <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {}^{\wedge }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∧</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {}^{\wedge }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f13777cdecbade34cc52674ca97b7fda3cf0e792" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.329ex; height:2.343ex;" alt="{\displaystyle {}^{\wedge }}"/></span> the best equivalent to the ASCII <a href="/wiki/Caret" title="Caret">caret</a> ^ character. </p> <div class="mw-heading mw-heading3"><h3 id="Spaces" data-mw-thread-id="h-Spaces-LaTeX_basics"><span data-mw-comment-start="" id="h-Spaces-LaTeX_basics"></span>Spaces<span data-mw-comment-end="h-Spaces-LaTeX_basics"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=12" title="Edit section: Spaces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>"Whitespace" characters, such as blank or tab, are treated uniformly as "space" by LaTeX. Several consecutive <a href="/wiki/Whitespace_character" title="Whitespace character">whitespace characters</a> are treated as one "space". See <a href="#Spacing">below</a> for commands that produces spaces of different size. </p> <div class="mw-heading mw-heading3"><h3 id="LaTeX_environments" data-mw-thread-id="h-LaTeX_environments-LaTeX_basics"><span data-mw-comment-start="" id="h-LaTeX_environments-LaTeX_basics"></span>LaTeX environments<span data-mw-comment-end="h-LaTeX_environments-LaTeX_basics"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=13" title="Edit section: LaTeX environments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Environments</i> in LaTeX have a role that is quite similar to commands, but they usually have effect on a wider part of formula. Their syntax is: </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span> <span class="k">\begin</span><span class="nb">{</span>environmentname<span class="nb">}</span> text to be influenced <span class="k">\end</span><span class="nb">{</span>environmentname<span class="nb">}</span> </pre></div> <p>Environments supported by Wikipedia include <i>matrix</i>, <i>align</i>, etc. See <a href="#Fractions,_matrices,_multilines">below</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Rendering" data-mw-thread-id="h-Rendering-LaTeX_basics"><span data-mw-comment-start="" id="h-Rendering-LaTeX_basics"></span>Rendering<span data-mw-comment-end="h-Rendering-LaTeX_basics"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=14" title="Edit section: Rendering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The font sizes and types are independent of browser settings or CSS. Font sizes and types will often deviate from what HTML renders. Vertical alignment with the surrounding text can also be a problem; a work-around is described in the <a class="mw-selflink-fragment" href="#Alignment_with_normal_text_flow">"Alignment with normal text flow"</a> section below. The <a href="/wiki/Help:User_style#CSS_selectors" title="Help:User style">CSS selector</a> of the images is <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">img.tex</code>. </p><p>Apart from function and operator names, as is customary in mathematics, variables and letters are in italics; digits are not. For other text, (like variable labels) to avoid being rendered in italics like variables, use <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span></code> or <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathrm</span></code> (formerly <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\rm</span></code>). You can also define new function names using <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\operatorname</span><span class="nb">{</span>...<span class="nb">}</span></code>. For example, <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>abc<span class="nb">}</span></code> gives <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{abc}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>abc</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{abc}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebb2fb4d7d22c7708b767b37ebc096fac3c8e705" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.487ex; height:2.176ex;" alt="{\displaystyle {\text{abc}}}"/></span>. <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\operatorname</span><span class="nb">{</span>...<span class="nb">}</span></code> provides spacing before and after the operator name when appropriate, as when <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a<span class="k">\operatorname</span><span class="nb">{</span>sn<span class="nb">}</span>b</code> is rendered as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\operatorname {sn} b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>sn</mi> <mo>⁡</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\operatorname {sn} b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ce90737da8a43025489d6a313e2b8dd30452100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.21ex; height:2.176ex;" alt="{\displaystyle a\operatorname {sn} b}"/></span> (with space to the left and right of "sn") and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a<span class="k">\operatorname</span><span class="nb">{</span>sn<span class="nb">}</span>(b+c)</code> as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\operatorname {sn} (b+c)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>sn</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\operatorname {sn} (b+c)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b347e875930d785e5681533baeaa822669fed6cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.48ex; height:2.843ex;" alt="{\displaystyle a\operatorname {sn} (b+c)}"/></span> (with space to the left and not to the right). LaTeX's starred version, <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\operatorname*</span></code> is not supported, but a workaround is to add <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\limits</span></code> instead. For example, <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\operatorname</span><span class="nb">{</span>sn<span class="nb">}_{</span>b>c<span class="nb">}</span>(b+c) <span class="k">\qquad</span> <span class="k">\operatorname</span><span class="nb">{</span>sn<span class="nb">}</span><span class="k">\limits</span><span class="nb">_{</span>b>c<span class="nb">}</span>(b+c)</code> renders as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {sn} _{b>c}(b+c)\qquad \operatorname {sn} \limits _{b>c}(b+c)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>sn</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mo>></mo> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mspace width="2em"></mspace> <msub> <mi>sn</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mo>></mo> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {sn} _{b>c}(b+c)\qquad \operatorname {sn} \limits _{b>c}(b+c)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa0e54a51b696222a304c7f0bdb925364b949f1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.614ex; height:2.843ex;" alt="{\displaystyle \operatorname {sn} _{b>c}(b+c)\qquad \operatorname {sn} \limits _{b>c}(b+c)}"/></span>.</dd></dl> <p>LaTeX does not have full support for Unicode characters, and not all characters render. Most Latin characters with accents render correctly. However some do not, in particular those that include multiple diacritics (e.g. with Latin letters used in Vietnamese) or that cannot be precomposed into a single character (such as the uppercase Latin letter W with ring), or that use other diacritics (like the ogonek or the double grave accent, used in Central European languages like Polish, or the horn attached above some vowels in Vietnamese), or other modified letter forms (used in IPA notations, or African languages, or in medieval texts), some digram ligatures (like Ĳ in Dutch), or Latin letters borrowed from Greek, or small capitals, as well as superscripts and subscript letters. For example, <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>ð<span class="nb">}</span></code> and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>þ<span class="nb">}</span></code> (used in Icelandic) will give errors. </p><p>The normal way of entering quotation marks in text mode (two back ticks for the left and two apostrophes for the right), such as <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>a ``quoted'' word<span class="nb">}</span></code> will not work correctly. As a workaround, you can use the Unicode left and right quotation mark characters, which are available from the "Symbols" dropdown panel beneath the editor: <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>a “quoted” word<span class="nb">}</span></code>. </p> <div class="mw-heading mw-heading4"><h4 id="Force-rerendering_of_formulas" data-mw-thread-id="h-Force-rerendering_of_formulas-Rendering"><span data-mw-comment-start="" id="h-Force-rerendering_of_formulas-Rendering"></span>Force-rerendering of formulas<span data-mw-comment-end="h-Force-rerendering_of_formulas-Rendering"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=15" title="Edit section: Force-rerendering of formulas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MediaWiki stores rendered formulas in a <a href="/wiki/Web_cache" title="Web cache">cache</a> so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables <code>action=purge&mathpurge=true</code>. Imagine for example there is a wrong rendered formula in the article <a href="/wiki/Integral" title="Integral">Integral</a>. To force the re-rendering of this formula you need to open the URL <code><a class="external free" href="https://en.wikipedia.org/w/index.php?title=Integral&action=purge&mathpurge=true">https://en.wikipedia.org/w/index.php?title=Integral&action=purge&mathpurge=true</a></code> </p><p>Afterwards you need to <a href="/wiki/Wikipedia:Bypass_your_cache" title="Wikipedia:Bypass your cache">bypass your browser cache</a> so that the new created images of the formulas are actually downloaded. </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Formatting_using_LaTeX" data-mw-thread-id="h-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Formatting_using_LaTeX"></span>Formatting using LaTeX<span data-mw-comment-end="h-Formatting_using_LaTeX"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=16" title="Edit section: Formatting using LaTeX"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Functions,_symbols,_special_characters" data-mw-thread-id="h-Functions,_symbols,_special_characters-Formatting_using_LaTeX"><span id="Functions.2C_symbols.2C_special_characters"></span><span data-mw-comment-start="" id="h-Functions,_symbols,_special_characters-Formatting_using_LaTeX"></span>Functions, symbols, special characters<span data-mw-comment-end="h-Functions,_symbols,_special_characters-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=17" title="Edit section: Functions, symbols, special characters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Accents_and_diacritics" data-mw-thread-id="h-Accents_and_diacritics-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Accents_and_diacritics-Functions,_symbols,_special_characters"></span>Accents and diacritics<span data-mw-comment-end="h-Accents_and_diacritics-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=18" title="Edit section: Accents and diacritics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\dot{a}, \ddot{a}, \acute{a}, \grave{a}</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>¨</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>´</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>`</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37bf3791d84c05002894371ec3d5ec406ff8404e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.021ex; height:2.676ex;" alt="{\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\check{a}, \breve{a}, \tilde{a}, \bar{a}</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">ˇ</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>˘</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a086a5b4d09eba6b78e971fe6525f7898212bb23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.021ex; height:2.676ex;" alt="{\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\hat{a}, \widehat{a}, \vec{a}</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>^</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b40619f86cda7ea21ef19ea05b3879f534d26f53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.82ex; height:2.676ex;" alt="{\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}}"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Standard_numerical_functions" data-mw-thread-id="h-Standard_numerical_functions-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Standard_numerical_functions-Functions,_symbols,_special_characters"></span>Standard numerical functions<span data-mw-comment-end="h-Standard_numerical_functions-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=19" title="Edit section: Standard numerical functions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\exp_a b = a^b, \exp b = e^b, 10^m</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>exp</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mi>b</mi> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> <mo>,</mo> <mi>exp</mi> <mo>⁡</mo> <mi>b</mi> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> <mo>,</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11b5fbb640ca24f99050dd3acfc5aeead355316b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.429ex; height:3.176ex;" alt="{\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\ln c = \log c, \lg d = \log_{10} d</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ln c=\log c,\lg d=\log _{10}d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mi>c</mi> <mo>=</mo> <mi>log</mi> <mo>⁡</mo> <mi>c</mi> <mo>,</mo> <mi>lg</mi> <mo>⁡</mo> <mi>d</mi> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln c=\log c,\lg d=\log _{10}d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f196240fa2757adbfa2209bb4c0832a5212472e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.793ex; height:2.676ex;" alt="{\displaystyle \ln c=\log c,\lg d=\log _{10}d}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\sin a, \cos b, \tan c, \cot d, \sec f, \csc g</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin a,\cos b,\tan c,\cot d,\sec f,\csc g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>a</mi> <mo>,</mo> <mi>cos</mi> <mo>⁡</mo> <mi>b</mi> <mo>,</mo> <mi>tan</mi> <mo>⁡</mo> <mi>c</mi> <mo>,</mo> <mi>cot</mi> <mo>⁡</mo> <mi>d</mi> <mo>,</mo> <mi>sec</mi> <mo>⁡</mo> <mi>f</mi> <mo>,</mo> <mi>csc</mi> <mo>⁡</mo> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin a,\cos b,\tan c,\cot d,\sec f,\csc g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca85f31a33eeea28e93fd2ce81a3282949100028" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:32.725ex; height:2.509ex;" alt="{\displaystyle \sin a,\cos b,\tan c,\cot d,\sec f,\csc g}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\arcsin h, \arccos i, \arctan j</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \arcsin h,\arccos i,\arctan j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>arcsin</mi> <mo>⁡</mo> <mi>h</mi> <mo>,</mo> <mi>arccos</mi> <mo>⁡</mo> <mi>i</mi> <mo>,</mo> <mi>arctan</mi> <mo>⁡</mo> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \arcsin h,\arccos i,\arctan j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef94f7e8a6241d4633a85ca7a371b3712fd4b6cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.974ex; height:2.509ex;" alt="{\displaystyle \arcsin h,\arccos i,\arctan j}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\sinh k, \cosh l, \tanh m, \coth n</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sinh k,\cosh l,\tanh m,\coth n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sinh</mi> <mo>⁡</mo> <mi>k</mi> <mo>,</mo> <mi>cosh</mi> <mo>⁡</mo> <mi>l</mi> <mo>,</mo> <mi>tanh</mi> <mo>⁡</mo> <mi>m</mi> <mo>,</mo> <mi>coth</mi> <mo>⁡</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sinh k,\cosh l,\tanh m,\coth n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/464517423fe5bd75bf7c4061a3fc8c9acfcd0275" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.586ex; height:2.509ex;" alt="{\displaystyle \sinh k,\cosh l,\tanh m,\coth n}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sh</mi> <mo>⁡</mo> <mi>k</mi> <mo>,</mo> <mi>ch</mi> <mo>⁡</mo> <mi>l</mi> <mo>,</mo> <mi>th</mi> <mo>⁡</mo> <mi>m</mi> <mo>,</mo> <mi>coth</mi> <mo>⁡</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e778ce57d124a98770a6fb055238388ece8cd7ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.113ex; height:2.509ex;" alt="{\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>argsh</mi> <mo>⁡</mo> <mi>o</mi> <mo>,</mo> <mi>argch</mi> <mo>⁡</mo> <mi>p</mi> <mo>,</mo> <mi>argth</mi> <mo>⁡</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af2ef185d1cb07fa52bcba056b9dde30d5b45f20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.036ex; height:2.509ex;" alt="{\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\sgn r, \left\vert s \right\vert</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {sgn} r,\left\vert s\right\vert }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sgn</mi> <mo>⁡</mo> <mi>r</mi> <mo>,</mo> <mrow> <mo>|</mo> <mi>s</mi> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {sgn} r,\left\vert s\right\vert }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b15ef2a6a7b35cd3065344e88dbf137923fdd17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.225ex; height:2.843ex;" alt="{\displaystyle \operatorname {sgn} r,\left\vert s\right\vert }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\min(x,y), \max(x,y)</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \min(x,y),\max(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">min</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mo movablelimits="true" form="prefix">max</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \min(x,y),\max(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c4c8c94e5d6cd2f050819f44b23ae3009886030" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.892ex; height:2.843ex;" alt="{\displaystyle \min(x,y),\max(x,y)}"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Bounds" data-mw-thread-id="h-Bounds-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Bounds-Functions,_symbols,_special_characters"></span>Bounds<span data-mw-comment-end="h-Bounds-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=20" title="Edit section: Bounds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\min x, \max y, \inf s, \sup t</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \min x,\max y,\inf s,\sup t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">min</mo> <mi>x</mi> <mo>,</mo> <mo movablelimits="true" form="prefix">max</mo> <mi>y</mi> <mo>,</mo> <mo movablelimits="true" form="prefix">inf</mo> <mi>s</mi> <mo>,</mo> <mo movablelimits="true" form="prefix">sup</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \min x,\max y,\inf s,\sup t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a066fe3e8e77118343833371aa3a4981ffe5feab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.419ex; height:2.509ex;" alt="{\displaystyle \min x,\max y,\inf s,\sup t}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\lim u, \liminf v, \limsup w</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim u,\liminf v,\limsup w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">lim</mo> <mi>u</mi> <mo>,</mo> <mo movablelimits="true" form="prefix">lim inf</mo> <mi>v</mi> <mo>,</mo> <mo movablelimits="true" form="prefix">lim sup</mo> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim u,\liminf v,\limsup w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d64be545eeab1dd4944757be8334ac37bca20137" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.968ex; height:2.509ex;" alt="{\displaystyle \lim u,\liminf v,\limsup w}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\dim p, \deg q, \det m, \ker\phi</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \dim p,\deg q,\det m,\ker \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>dim</mi> <mo>⁡</mo> <mi>p</mi> <mo>,</mo> <mi>deg</mi> <mo>⁡</mo> <mi>q</mi> <mo>,</mo> <mo movablelimits="true" form="prefix">det</mo> <mi>m</mi> <mo>,</mo> <mi>ker</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \dim p,\deg q,\det m,\ker \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fde2537af3f9807e0682220b6762ddeff9a80d1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.079ex; height:2.509ex;" alt="{\displaystyle \dim p,\deg q,\det m,\ker \phi }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\injlim, \varinjlim, \projlim, \varprojlim</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \injlim ,\varinjlim ,\projlim ,\varprojlim }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">inj lim</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-OP"> <munder> <mi>lim</mi> <mo>→</mo> </munder> </mrow> <mo>,</mo> <mo movablelimits="true" form="prefix">proj lim</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-OP"> <munder> <mi>lim</mi> <mo>←</mo> </munder> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \injlim ,\varinjlim ,\projlim ,\varprojlim }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ef2b239b322d66e4666ff7e5cd1de40bae2140d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.637ex; margin-bottom: -0.367ex; width:23.851ex; height:3.843ex;" alt="{\displaystyle \injlim ,\varinjlim ,\projlim ,\varprojlim }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Projections" data-mw-thread-id="h-Projections-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Projections-Functions,_symbols,_special_characters"></span>Projections<span data-mw-comment-end="h-Projections-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=21" title="Edit section: Projections"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Pr j, \hom l, \lVert z \rVert, \arg z</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">Pr</mo> <mi>j</mi> <mo>,</mo> <mi>hom</mi> <mo>⁡</mo> <mi>l</mi> <mo>,</mo> <mo fence="false" stretchy="false">‖</mo> <mi>z</mi> <mo fence="false" stretchy="false">‖</mo> <mo>,</mo> <mi>arg</mi> <mo>⁡</mo> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a54d0f05875de37ef810a43a6aed8fea426d3871" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.537ex; height:2.843ex;" alt="{\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z}"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Differentials_and_derivatives" data-mw-thread-id="h-Differentials_and_derivatives-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Differentials_and_derivatives-Functions,_symbols,_special_characters"></span>Differentials and derivatives<span data-mw-comment-end="h-Differentials_and_derivatives-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=22" title="Edit section: Differentials and derivatives"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">dt, <span class="k">\mathrm</span><span class="nb">{</span>d<span class="nb">}</span>t, <span class="k">\partial</span> t, <span class="k">\nabla\psi</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dt,\mathrm {d} t,\partial t,\nabla \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>t</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mo>,</mo> <mi mathvariant="normal">∂</mi> <mi>t</mi> <mo>,</mo> <mi mathvariant="normal">∇</mi> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dt,\mathrm {d} t,\partial t,\nabla \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/648ccde6ebee0c1aabb69c7105a5d3b23f29fefe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.896ex; height:2.509ex;" alt="{\displaystyle dt,\mathrm {d} t,\partial t,\nabla \psi }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">dy/dx, <span class="k">\mathrm</span><span class="nb">{</span>d<span class="nb">}</span>y/<span class="k">\mathrm</span><span class="nb">{</span>d<span class="nb">}</span>x, <span class="k">\frac</span><span class="nb">{</span>dy<span class="nb">}{</span>dx<span class="nb">}</span>, <span class="k">\frac</span><span class="nb">{</span><span class="k">\mathrm</span><span class="nb">{</span>d<span class="nb">}</span>y<span class="nb">}{</span><span class="k">\mathrm</span><span class="nb">{</span>d<span class="nb">}</span>x<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dy/dx,\mathrm {d} y/\mathrm {d} x,{\frac {dy}{dx}},{\frac {\mathrm {d} y}{\mathrm {d} x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>x</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>y</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dy/dx,\mathrm {d} y/\mathrm {d} x,{\frac {dy}{dx}},{\frac {\mathrm {d} y}{\mathrm {d} x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f62d96b9dc4cb3fc19a81cb178ba987383b8fc07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:22.254ex; height:5.509ex;" alt="{\displaystyle dy/dx,\mathrm {d} y/\mathrm {d} x,{\frac {dy}{dx}},{\frac {\mathrm {d} y}{\mathrm {d} x}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\frac</span><span class="nb">{</span><span class="k">\partial</span><span class="nb">^</span>2<span class="nb">}{</span><span class="k">\partial</span> x<span class="nb">_</span>1<span class="k">\partial</span> x<span class="nb">_</span>2<span class="nb">}</span>y, <span class="k">\left</span>.<span class="k">\frac</span><span class="nb">{</span><span class="k">\partial</span><span class="nb">^</span>3 f<span class="nb">}{</span><span class="k">\partial</span><span class="nb">^</span>2 x <span class="k">\partial</span> y<span class="nb">}</span><span class="k">\right\vert</span><span class="nb">_{</span>p<span class="nb">_</span>0<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial ^{2}}{\partial x_{1}\partial x_{2}}}y,\left.{\frac {\partial ^{3}f}{\partial ^{2}x\partial y}}\right\vert _{p_{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi mathvariant="normal">∂</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mi>y</mi> <mo>,</mo> <msub> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>f</mi> </mrow> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>x</mi> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial ^{2}}{\partial x_{1}\partial x_{2}}}y,\left.{\frac {\partial ^{3}f}{\partial ^{2}x\partial y}}\right\vert _{p_{0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66ef74e66f0602a73b6a51609239600fa13d9242" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:20.004ex; height:7.009ex;" alt="{\displaystyle {\frac {\partial ^{2}}{\partial x_{1}\partial x_{2}}}y,\left.{\frac {\partial ^{3}f}{\partial ^{2}x\partial y}}\right\vert _{p_{0}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\prime</span>, <span class="k">\backprime</span>, f<span class="nb">^</span><span class="k">\prime</span>, f', f'', f<span class="nb">^{</span>(3)<span class="nb">}</span>, <span class="k">\dot</span> y, <span class="k">\ddot</span> y</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \prime ,\backprime ,f^{\prime },f',f'',f^{(3)}\!,{\dot {y}},{\ddot {y}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant" mathvariant="normal">′</mi> <mo>,</mo> <mi class="MJX-variant">‵</mi> <mo>,</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>,</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>,</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mspace width="negativethinmathspace"></mspace> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>y</mi> <mo>¨</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \prime ,\backprime ,f^{\prime },f',f'',f^{(3)}\!,{\dot {y}},{\ddot {y}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10f33d6a2fc3ea7ecd6a6ab3f214b973cbf51210" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.857ex; height:3.176ex;" alt="{\displaystyle \prime ,\backprime ,f^{\prime },f',f'',f^{(3)}\!,{\dot {y}},{\ddot {y}}}"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Letter-like_symbols_or_constants" data-mw-thread-id="h-Letter-like_symbols_or_constants-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Letter-like_symbols_or_constants-Functions,_symbols,_special_characters"></span>Letter-like symbols or constants<span data-mw-comment-end="h-Letter-like_symbols_or_constants-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=23" title="Edit section: Letter-like symbols or constants"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar, \N, \R, \Z, \C, \Q</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar ,\mathbb {N} ,\mathbb {R} ,\mathbb {Z} ,\mathbb {C} ,\mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> <mo>,</mo> <mi mathvariant="normal">ℵ</mi> <mo>,</mo> <mi>∁</mi> <mo>,</mo> <mo>∍</mo> <mo>,</mo> <mi mathvariant="normal">ð</mi> <mo>,</mo> <mi>Ⅎ</mi> <mo>,</mo> <mi class="MJX-variant">ℏ</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar ,\mathbb {N} ,\mathbb {R} ,\mathbb {Z} ,\mathbb {C} ,\mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b2f50bc4e68001130db04960121ed3bdf3182b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:29.562ex; height:2.843ex;" alt="{\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar ,\mathbb {N} ,\mathbb {R} ,\mathbb {Z} ,\mathbb {C} ,\mathbb {Q} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS ,\S ,\P ,\mathrm {\AA} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">ℑ</mi> <mo>,</mo> <mi>ı</mi> <mo>,</mo> <mi>ȷ</mi> <mo>,</mo> <mi mathvariant="double-struck">k</mi> <mo>,</mo> <mi>ℓ</mi> <mo>,</mo> <mi>℧</mi> <mo>,</mo> <mi mathvariant="normal">℘</mi> <mo>,</mo> <mi mathvariant="normal">ℜ</mi> <mo>,</mo> <mi mathvariant="normal">Ⓢ</mi> <mo>,</mo> <mi mathvariant="normal">§</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>¶</mo> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>Å</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS ,\S ,\P ,\mathrm {\AA} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce44a8fb6e6ffd2df0eff8d100845716456c1c15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:27.916ex; height:3.343ex;" alt="{\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS ,\S ,\P ,\mathrm {\AA} }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Modular_arithmetic" data-mw-thread-id="h-Modular_arithmetic-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Modular_arithmetic-Functions,_symbols,_special_characters"></span>Modular arithmetic<span data-mw-comment-end="h-Modular_arithmetic-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=24" title="Edit section: Modular arithmetic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">s_k \equiv 0 \pmod{m}</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{k}\equiv 0{\pmod {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>≡</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em"></mspace> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em"></mspace> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{k}\equiv 0{\pmod {m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41d0f4469bd12dd0351cdfa3d3c0001c1c78b861" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.165ex; height:2.843ex;" alt="{\displaystyle s_{k}\equiv 0{\pmod {m}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">a \bmod b</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a{\bmod {b}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo lspace="thickmathspace" rspace="thickmathspace">mod</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a{\bmod {b}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a4080e7a1a76ffc9ccfeecbb0fc726890100d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.909ex; height:2.176ex;" alt="{\displaystyle a{\bmod {b}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\gcd(m, n), \operatorname{lcm}(m, n)</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">gcd</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>lcm</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cf97978556fdc8d6799ba5795ad4668fed38507" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.693ex; height:2.843ex;" alt="{\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\mid, \nmid, \shortmid, \nshortmid</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">∣</mo> <mo>,</mo> <mo>∤</mo> <mo>,</mo> <mo class="MJX-variant">∣</mo> <mo>,</mo> <mo class="MJX-variant">∤</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/394de3a70825dbb8065fa2d1979533c84a7ef0f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.042ex; width:5.471ex; height:2.843ex;" alt="{\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Radicals" data-mw-thread-id="h-Radicals-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Radicals-Functions,_symbols,_special_characters"></span>Radicals<span data-mw-comment-end="h-Radicals-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=25" title="Edit section: Radicals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\surd, \sqrt{2}, \sqrt[n]{2}, \sqrt[3]{\frac{x^3+y^3}{2}}</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \surd ,{\sqrt {2}},{\sqrt[{n}]{2}},{\sqrt[{3}]{\frac {x^{3}+y^{3}}{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">√</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </mroot> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mfrac> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \surd ,{\sqrt {2}},{\sqrt[{n}]{2}},{\sqrt[{3}]{\frac {x^{3}+y^{3}}{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb2f06b0dec0a42806cf1378d9e9b64f10574c1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:21.833ex; height:6.176ex;" alt="{\displaystyle \surd ,{\sqrt {2}},{\sqrt[{n}]{2}},{\sqrt[{3}]{\frac {x^{3}+y^{3}}{2}}}}"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Operators" data-mw-thread-id="h-Operators-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Operators-Functions,_symbols,_special_characters"></span>Operators<span data-mw-comment-end="h-Operators-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=26" title="Edit section: Operators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">+, -, \pm, \mp, \dotplus</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +,-,\pm ,\mp ,\dotplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mo>,</mo> <mo>−</mo> <mo>,</mo> <mo>±</mo> <mo>,</mo> <mo>∓</mo> <mo>,</mo> <mo>∔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +,-,\pm ,\mp ,\dotplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b751e798e6815814aa6611662e14e35711478885" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.176ex; height:2.676ex;" alt="{\displaystyle +,-,\pm ,\mp ,\dotplus }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\times, \div, \divideontimes, /, \backslash</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \times ,\div ,\divideontimes ,/,\backslash }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> <mo>,</mo> <mo>÷</mo> <mo>,</mo> <mo>⋇</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo>,</mo> <mi class="MJX-variant" mathvariant="normal">∖</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times ,\div ,\divideontimes ,/,\backslash }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f608cc43585a02c5bfbd799724a7612038c8546" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.885ex; height:2.843ex;" alt="{\displaystyle \times ,\div ,\divideontimes ,/,\backslash }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\cdot, * \ast, \star, \circ, \bullet</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⋅</mo> <mo>,</mo> <mo>∗</mo> <mo>∗</mo> <mo>,</mo> <mo>⋆</mo> <mo>,</mo> <mo>∘</mo> <mo>,</mo> <mo>∙</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a051f627a43121ff0b4407b4d40813fb9681a6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.595ex; height:2.009ex;" alt="{\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\boxplus, \boxminus, \boxtimes, \boxdot</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊞</mo> <mo>,</mo> <mo>⊟</mo> <mo>,</mo> <mo>⊠</mo> <mo>,</mo> <mo>⊡</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54cc82316b9966e992a5d50ed17a43ff1748bc5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.334ex; height:2.509ex;" alt="{\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\oplus, \ominus, \otimes, \oslash, \odot</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> <mo>,</mo> <mo>⊖</mo> <mo>,</mo> <mo>⊗</mo> <mo>,</mo> <mo>⊘</mo> <mo>,</mo> <mo>⊙</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cce4064a84d81cd73a90b1927329b26e2d186028" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.176ex; height:2.343ex;" alt="{\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\circleddash, \circledcirc, \circledast</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \circleddash ,\circledcirc ,\circledast }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊝</mo> <mo>,</mo> <mo>⊚</mo> <mo>,</mo> <mo>⊛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \circleddash ,\circledcirc ,\circledast }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a7e3536edcca44038580d683e397b522518c62b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.492ex; height:2.343ex;" alt="{\displaystyle \circleddash ,\circledcirc ,\circledast }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\bigoplus, \bigotimes, \bigodot</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bigoplus ,\bigotimes ,\bigodot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⨁</mo> <mo>,</mo> <mo>⨂</mo> <mo>,</mo> <mo>⨀</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigoplus ,\bigotimes ,\bigodot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/009d5fb8fdc7140d48c30a37af236409fab9a37c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:12.6ex; height:3.843ex;" alt="{\displaystyle \bigoplus ,\bigotimes ,\bigodot }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Sets" data-mw-thread-id="h-Sets-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Sets-Functions,_symbols,_special_characters"></span>Sets<span data-mw-comment-end="h-Sets-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=27" title="Edit section: Sets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\{ \}, \O \empty \emptyset, \varnothing</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{\},\emptyset \emptyset \emptyset ,\varnothing }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> <mi mathvariant="normal">∅</mi> <mi mathvariant="normal">∅</mi> <mi mathvariant="normal">∅</mi> <mo>,</mo> <mi class="MJX-variant">∅</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{\},\emptyset \emptyset \emptyset ,\varnothing }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfaab369d5007e0b585c4309bcae62b861000448" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.688ex; height:2.843ex;" alt="{\displaystyle \{\},\emptyset \emptyset \emptyset ,\varnothing }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\in, \notin \not\in, \ni, \not\ni</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \in ,\notin \not \in ,\ni ,\not \ni }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∈</mo> <mo>,</mo> <mo>∉∉</mo> <mo>,</mo> <mo>∋</mo> <mo>,</mo> <mo>∌</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \in ,\notin \not \in ,\ni ,\not \ni }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68a219a3866204d7cb67fee3a71403961030ecb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.855ex; height:2.676ex;" alt="{\displaystyle \in ,\notin \not \in ,\ni ,\not \ni }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\cap, \Cap, \sqcap, \bigcap</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap ,\Cap ,\sqcap ,\bigcap }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mo>,</mo> <mo>⋒</mo> <mo>,</mo> <mo>⊓</mo> <mo>,</mo> <mo>⋂</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap ,\Cap ,\sqcap ,\bigcap }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31e4276fc0e1d550d5a69dbdfd47c95c5ee4e255" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:10.334ex; height:3.843ex;" alt="{\displaystyle \cap ,\Cap ,\sqcap ,\bigcap }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∪</mo> <mo>,</mo> <mo>⋓</mo> <mo>,</mo> <mo>⊔</mo> <mo>,</mo> <mo>⋃</mo> <mo>,</mo> <mo>⨆</mo> <mo>,</mo> <mo>⊎</mo> <mo>,</mo> <mo>⨄</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d31e97cbca58d6df8f72d1aae409ad58252d330e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:20.15ex; height:3.843ex;" alt="{\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\setminus, \smallsetminus, \times</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \setminus ,\smallsetminus ,\times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo class="MJX-variant">∖</mo> <mo>,</mo> <mo>∖</mo> <mo>,</mo> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \setminus ,\smallsetminus ,\times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fda6ef321f4ecefa3987074e9ea335c7518052ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.847ex; height:2.843ex;" alt="{\displaystyle \setminus ,\smallsetminus ,\times }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\subset, \Subset, \sqsubset</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \subset ,\Subset ,\sqsubset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊂</mo> <mo>,</mo> <mo>⋐</mo> <mo>,</mo> <mo>⊏</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \subset ,\Subset ,\sqsubset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71cbdb9c08169bfeb828ef6d8c80a1ffb47a6aa7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.492ex; height:2.176ex;" alt="{\displaystyle \subset ,\Subset ,\sqsubset }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\supset, \Supset, \sqsupset</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \supset ,\Supset ,\sqsupset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊃</mo> <mo>,</mo> <mo>⋑</mo> <mo>,</mo> <mo>⊐</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \supset ,\Supset ,\sqsupset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12effa4ca3363ccdd168d9779ab9a969e6788838" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.492ex; height:2.176ex;" alt="{\displaystyle \supset ,\Supset ,\sqsupset }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊆</mo> <mo>,</mo> <mo>⊈</mo> <mo>,</mo> <mo>⊊</mo> <mo>,</mo> <mo class="MJX-variant">⊊</mo> <mo>,</mo> <mo>⊑</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2df25d7316aa18529b02f3da24b1edb838c97145" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.176ex; height:3.176ex;" alt="{\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊇</mo> <mo>,</mo> <mo>⊉</mo> <mo>,</mo> <mo>⊋</mo> <mo>,</mo> <mo class="MJX-variant">⊋</mo> <mo>,</mo> <mo>⊒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bed14d214c6c1dd79ce26c63402c62e11aadcd43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.176ex; height:3.176ex;" alt="{\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⫅</mo> <mo>,</mo> <mo class="MJX-variant">⊈</mo> <mo>,</mo> <mo>⫋</mo> <mo>,</mo> <mo class="MJX-variant">⫋</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a643f43a163a25fd47d5e5eeefb8be279a600cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.334ex; height:3.343ex;" alt="{\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⫆</mo> <mo>,</mo> <mo class="MJX-variant">⊉</mo> <mo>,</mo> <mo>⫌</mo> <mo>,</mo> <mo class="MJX-variant">⫌</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5e8ec9a50166918315d633bca588fc6166904ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.334ex; height:3.343ex;" alt="{\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Relations" data-mw-thread-id="h-Relations-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Relations-Functions,_symbols,_special_characters"></span>Relations<span data-mw-comment-end="h-Relations-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=28" title="Edit section: Relations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">=, \ne, \neq, \equiv, \not\equiv</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mo>,</mo> <mo>≠</mo> <mo>,</mo> <mo>≠</mo> <mo>,</mo> <mo>≡</mo> <mo>,</mo> <mo>≢</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce6328306dafedabab239cf95e32b71c47f09040" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.178ex; height:2.676ex;" alt="{\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\doteq, \doteqdot,</code> <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\overset{\underset{\mathrm{def}}{}}{=},</code> <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">:=</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \doteq ,\doteqdot ,{\overset {\underset {\mathrm {def} }{}}{=}},:=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≐</mo> <mo>,</mo> <mo>≑</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>=</mo> <munder> <mrow></mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </munder> </mover> </mrow> <mo>,</mo> <mo>:=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \doteq ,\doteqdot ,{\overset {\underset {\mathrm {def} }{}}{=}},:=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/155040ee3a72b39db2a03c5dab0f70cf738a21f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.004ex; height:3.676ex;" alt="{\displaystyle \doteq ,\doteqdot ,{\overset {\underset {\mathrm {def} }{}}{=}},:=}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq ,\eqsim ,\cong ,\ncong }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∼</mo> <mo>,</mo> <mo>≁</mo> <mo>,</mo> <mo>∽</mo> <mo>,</mo> <mo class="MJX-variant">∼</mo> <mo>,</mo> <mo>≃</mo> <mo>,</mo> <mo>⋍</mo> <mo>,</mo> <mo>≂</mo> <mo>,</mo> <mo>≅</mo> <mo>,</mo> <mo>≆</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq ,\eqsim ,\cong ,\ncong }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/533b5e3434e963dd4c1a9cfe5639486311b3de03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.545ex; height:2.509ex;" alt="{\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq ,\eqsim ,\cong ,\ncong }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≈</mo> <mo>,</mo> <mo class="MJX-variant">≈</mo> <mo>,</mo> <mo>≊</mo> <mo>,</mo> <mo>≍</mo> <mo>,</mo> <mo>∝</mo> <mo>,</mo> <mo>∝</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04d429463aa7b4b5a5f7d9f9c9dd7c41c518c2e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.019ex; height:2.343ex;" alt="{\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr"><, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo><</mo> <mo>,</mo> <mo>≮</mo> <mo>,</mo> <mo>≪</mo> <mo>,</mo> <mo>≪̸</mo> <mo>,</mo> <mo>⋘</mo> <mo>,</mo> <mo>⋘̸</mo> <mo>,</mo> <mo>⋖</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e2e20408f43d9175cd7a08edf9c82a2483c8989" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.472ex; height:2.676ex;" alt="{\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle >,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>></mo> <mo>,</mo> <mo>≯</mo> <mo>,</mo> <mo>≫</mo> <mo>,</mo> <mo>≫̸</mo> <mo>,</mo> <mo>⋙</mo> <mo>,</mo> <mo>⋙̸</mo> <mo>,</mo> <mo>⋗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle >,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/672238d9fea0ab0a1254de8b3c2b51539919d04f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.472ex; height:2.676ex;" alt="{\displaystyle >,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≤</mo> <mo>,</mo> <mo>≤</mo> <mo>,</mo> <mo>⪇</mo> <mo>,</mo> <mo>≦</mo> <mo>,</mo> <mo>≰</mo> <mo>,</mo> <mo class="MJX-variant">≰</mo> <mo>,</mo> <mo>≨</mo> <mo>,</mo> <mo class="MJX-variant">≨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8482931cd57dd323576140ee6fbfdf28af4de77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:21.703ex; height:3.509ex;" alt="{\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≥</mo> <mo>,</mo> <mo>≥</mo> <mo>,</mo> <mo>⪈</mo> <mo>,</mo> <mo>≧</mo> <mo>,</mo> <mo>≱</mo> <mo>,</mo> <mo class="MJX-variant">≱</mo> <mo>,</mo> <mo>≩</mo> <mo>,</mo> <mo class="MJX-variant">≩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18a05195616ce8872fe2ab2cc7785f776ee1b8ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:21.703ex; height:3.509ex;" alt="{\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≶</mo> <mo>,</mo> <mo>⋚</mo> <mo>,</mo> <mo>⪋</mo> <mo>,</mo> <mo>≷</mo> <mo>,</mo> <mo>⋛</mo> <mo>,</mo> <mo>⪌</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfcae2a0fe0fc08fa0999d89d5da261670c53ba4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:16.019ex; height:3.843ex;" alt="{\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\leqslant, \nleqslant, \eqslantless</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leqslant ,\nleqslant ,\eqslantless }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⩽</mo> <mo>,</mo> <mo class="MJX-variant">⪇</mo> <mo>,</mo> <mo>⪕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leqslant ,\nleqslant ,\eqslantless }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c3793bb61383708f8b4e4594aa2898bc7bf7c5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.492ex; height:3.176ex;" alt="{\displaystyle \leqslant ,\nleqslant ,\eqslantless }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\geqslant, \ngeqslant, \eqslantgtr</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⩾</mo> <mo>,</mo> <mo class="MJX-variant">⪈</mo> <mo>,</mo> <mo>⪖</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e31b779738312ff472261d3aeac6dbc375e1c8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.492ex; height:3.176ex;" alt="{\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\lesssim, \lnsim, \lessapprox, \lnapprox</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≲</mo> <mo>,</mo> <mo>⋦</mo> <mo>,</mo> <mo>⪅</mo> <mo>,</mo> <mo>⪉</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab89fc9772dcb32cb5e873b4921a7ed2fcf9c030" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.334ex; height:3.176ex;" alt="{\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\gtrsim, \gnsim, \gtrapprox, \gnapprox</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≳</mo> <mo>,</mo> <mo>⋧</mo> <mo>,</mo> <mo>⪆</mo> <mo>,</mo> <mo>⪊</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae55eff5bc3d073b379730898e625add5afa7bdd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.334ex; height:3.176ex;" alt="{\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\prec, \nprec, \preceq, \npreceq, \precneqq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≺</mo> <mo>,</mo> <mo>⊀</mo> <mo>,</mo> <mo>⪯</mo> <mo>,</mo> <mo class="MJX-variant">⋠</mo> <mo>,</mo> <mo>⪵</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cd5dc52fd5439409ab9665aaf45d006cd9e88a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.176ex; height:3.176ex;" alt="{\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\succ, \nsucc, \succeq, \nsucceq, \succneqq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≻</mo> <mo>,</mo> <mo>⊁</mo> <mo>,</mo> <mo>⪰</mo> <mo>,</mo> <mo class="MJX-variant">⋡</mo> <mo>,</mo> <mo>⪶</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24f0255e7127ae3976d5f08dc7a4849b846b345c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.176ex; height:3.176ex;" alt="{\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\preccurlyeq, \curlyeqprec</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \preccurlyeq ,\curlyeqprec }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≼</mo> <mo>,</mo> <mo>⋞</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \preccurlyeq ,\curlyeqprec }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e49ab8b9c850c9d91d1d6d9dab7670acb8902d3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.65ex; height:2.676ex;" alt="{\displaystyle \preccurlyeq ,\curlyeqprec }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\succcurlyeq, \curlyeqsucc</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \succcurlyeq ,\curlyeqsucc }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≽</mo> <mo>,</mo> <mo>⋟</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \succcurlyeq ,\curlyeqsucc }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf63b71ba56a8ae161511baf448f6876e2afe357" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.65ex; height:2.676ex;" alt="{\displaystyle \succcurlyeq ,\curlyeqsucc }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\precsim, \precnsim, \precapprox, \precnapprox</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≾</mo> <mo>,</mo> <mo>⋨</mo> <mo>,</mo> <mo>⪷</mo> <mo>,</mo> <mo>⪹</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e82e1d0783bb43574548510bfe1bf68d62fcd5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.334ex; height:3.176ex;" alt="{\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\succsim, \succnsim, \succapprox, \succnapprox</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≿</mo> <mo>,</mo> <mo>⋩</mo> <mo>,</mo> <mo>⪸</mo> <mo>,</mo> <mo>⪺</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d8f909063920cb7c07a6d7dbe3143e071f840ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.334ex; height:3.176ex;" alt="{\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Geometric" data-mw-thread-id="h-Geometric-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Geometric-Functions,_symbols,_special_characters"></span>Geometric<span data-mw-comment-end="h-Geometric-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=29" title="Edit section: Geometric"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\parallel, \nparallel, \shortparallel, \nshortparallel</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">∥</mo> <mo>,</mo> <mo>∦</mo> <mo>,</mo> <mo class="MJX-variant">∥</mo> <mo>,</mo> <mo class="MJX-variant">∦</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/736c39359b32e4f49ea55439e582c0179af1c7a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.042ex; width:7.278ex; height:2.843ex;" alt="{\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\perp, \angle, \sphericalangle, \measuredangle, 45^\circ</code> for degrees </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \perp ,\angle ,\sphericalangle ,\measuredangle ,45^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊥</mo> <mo>,</mo> <mi mathvariant="normal">∠</mi> <mo>,</mo> <mi>∢</mi> <mo>,</mo> <mi>∡</mi> <mo>,</mo> <msup> <mn>45</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \perp ,\angle ,\sphericalangle ,\measuredangle ,45^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2a19bc814cbb393e1b0715309a443cbb133ca7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.357ex; height:2.676ex;" alt="{\displaystyle \perp ,\angle ,\sphericalangle ,\measuredangle ,45^{\circ }}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Box, \square, \blacksquare, \diamond, \Diamond, \lozenge, \blacklozenge, \bigstar</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Box ,\square ,\blacksquare ,\diamond ,\Diamond ,\lozenge ,\blacklozenge ,\bigstar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>◻</mi> <mo>,</mo> <mi>◻</mi> <mo>,</mo> <mi>◼</mi> <mo>,</mo> <mo>⋄</mo> <mo>,</mo> <mi>◊</mi> <mo>,</mo> <mi>◊</mi> <mo>,</mo> <mi>⧫</mi> <mo>,</mo> <mi>★</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Box ,\square ,\blacksquare ,\diamond ,\Diamond ,\lozenge ,\blacklozenge ,\bigstar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15b565fd5be0c719c902ac53d588bd2dfc9f12c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.669ex; height:2.509ex;" alt="{\displaystyle \Box ,\square ,\blacksquare ,\diamond ,\Diamond ,\lozenge ,\blacklozenge ,\bigstar }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\bigcirc, \triangle, \bigtriangleup, \bigtriangledown</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>◯</mo> <mo>,</mo> <mi mathvariant="normal">△</mi> <mo>,</mo> <mo>△</mo> <mo>,</mo> <mo>▽</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d87905a9563a582a64820a15ed94e11c58818400" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.623ex; height:2.676ex;" alt="{\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\vartriangle, \triangledown</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vartriangle ,\triangledown }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo class="MJX-variant">△</mo> <mo>,</mo> <mi class="MJX-variant">▽</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vartriangle ,\triangledown }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c96db9c2c06b47766ebbf7dc0f44b2486cea941" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.39ex; height:2.343ex;" alt="{\displaystyle \vartriangle ,\triangledown }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>▴</mi> <mo>,</mo> <mi>▾</mi> <mo>,</mo> <mo>◂</mo> <mo>,</mo> <mo>▸</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f3b2ff16112a800f6e0382bb29dfc5f7518e8fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.074ex; height:2.343ex;" alt="{\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Logic" data-mw-thread-id="h-Logic-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Logic-Functions,_symbols,_special_characters"></span>Logic<span data-mw-comment-end="h-Logic-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=30" title="Edit section: Logic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\forall, \exists, \nexists</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall ,\exists ,\nexists }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mo>,</mo> <mi mathvariant="normal">∃</mi> <mo>,</mo> <mi>∄</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall ,\exists ,\nexists }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28666c5226350ac5bc7de9914f2315f986576bf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.947ex; height:2.676ex;" alt="{\displaystyle \forall ,\exists ,\nexists }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\therefore, \because, \And</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore ,\because ,\And }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> <mo>,</mo> <mo>∵</mo> <mo>,</mo> <mi mathvariant="normal">&</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore ,\because ,\And }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70ebd5209923a92fd416a5cce139f48f0a41cf8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.977ex; height:2.509ex;" alt="{\displaystyle \therefore ,\because ,\And }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\lor, \vee, \curlyvee, \bigvee</code> <p>don't use <code>\or</code> which is now deprecated </p> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lor ,\vee ,\curlyvee ,\bigvee }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> <mo>,</mo> <mo>∨</mo> <mo>,</mo> <mo>⋎</mo> <mo>,</mo> <mo>⋁</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor ,\vee ,\curlyvee ,\bigvee }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dda6c0c13560da1b5ce258f9d78e2bfbdd63011" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:10.55ex; height:3.843ex;" alt="{\displaystyle \lor ,\vee ,\curlyvee ,\bigvee }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\land, \wedge, \curlywedge, \bigwedge</code> <p>don't use <code>\and</code> which is now deprecated </p> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land ,\wedge ,\curlywedge ,\bigwedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> <mo>,</mo> <mo>∧</mo> <mo>,</mo> <mo>⋏</mo> <mo>,</mo> <mo>⋀</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land ,\wedge ,\curlywedge ,\bigwedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ced7ea1cf77e59c853907f7ff45229890609274c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:10.55ex; height:3.843ex;" alt="{\displaystyle \land ,\wedge ,\curlywedge ,\bigwedge }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\lnot, \neg, \not\operatorname{R}, \bot, \top</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lnot ,\neg ,\not \operatorname {R} ,\bot ,\top }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mo>,</mo> <mi mathvariant="normal">¬</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-REL"> <mpadded width="0"> <mtext>⧸</mtext> </mpadded> </mrow> <mi mathvariant="normal">R</mi> <mo>,</mo> <mi mathvariant="normal">⊥</mi> <mo>,</mo> <mi mathvariant="normal">⊤</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lnot ,\neg ,\not \operatorname {R} ,\bot ,\top }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd51fec900e9c1e2a88b645c342d0481afd27ce8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.208ex; height:2.676ex;" alt="{\displaystyle \lnot ,\neg ,\not \operatorname {R} ,\bot ,\top }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\vdash, \dashv, \vDash, \Vdash, \models</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊢</mo> <mo>,</mo> <mo>⊣</mo> <mo>,</mo> <mo>⊨</mo> <mo>,</mo> <mo>⊩</mo> <mo>,</mo> <mo>⊨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f0b5397cc83660b7b469658ae93981158f1967d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.684ex; height:2.843ex;" alt="{\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Vvdash, \nvdash, \nVdash, \nvDash, \nVDash</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Vvdash ,\nvdash ,\nVdash ,\nvDash ,\nVDash }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊪</mo> <mo>,</mo> <mo>⊬</mo> <mo>,</mo> <mo>⊮</mo> <mo>,</mo> <mo>⊭</mo> <mo>,</mo> <mo>⊯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Vvdash ,\nvdash ,\nVdash ,\nvDash ,\nVDash }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/062e8fa620623f35910e65cd3e5c34b670ff1269" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.398ex; height:2.509ex;" alt="{\displaystyle \Vvdash ,\nvdash ,\nVdash ,\nvDash ,\nVDash }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\ulcorner, \urcorner, \llcorner, \lrcorner</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ulcorner ,\urcorner ,\llcorner ,\lrcorner }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⌜</mo> <mo>,</mo> <mo>⌝</mo> <mo>,</mo> <mo>⌞</mo> <mo>,</mo> <mo>⌟</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ulcorner ,\urcorner ,\llcorner ,\lrcorner }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/420267ce1b88f9b30654ddb6cb8bcfa5b2170d6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.752ex; height:2.509ex;" alt="{\displaystyle \ulcorner ,\urcorner ,\llcorner ,\lrcorner }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Arrows" data-mw-thread-id="h-Arrows-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Arrows-Functions,_symbols,_special_characters"></span>Arrows<span data-mw-comment-end="h-Arrows-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=31" title="Edit section: Arrows"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Rrightarrow, \Lleftarrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rrightarrow ,\Lleftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇛</mo> <mo>,</mo> <mo stretchy="false">⇚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rrightarrow ,\Lleftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68d376db1fe5990c9ccf7ee4eb70c80fe3246264" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.681ex; height:2.343ex;" alt="{\displaystyle \Rrightarrow ,\Lleftarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Rightarrow, \nRightarrow, \Longrightarrow, \implies</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow ,\nRightarrow ,\Longrightarrow ,\implies }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> <mo>,</mo> <mo>⇏</mo> <mo>,</mo> <mo stretchy="false">⟹</mo> <mo>,</mo> <mspace width="thickmathspace"></mspace> <mo stretchy="false">⟹</mo> <mspace width="thickmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow ,\nRightarrow ,\Longrightarrow ,\implies }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96edac5c33ea27016e009bdd4e8452e41a930b8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.651ex; height:2.176ex;" alt="{\displaystyle \Rightarrow ,\nRightarrow ,\Longrightarrow ,\implies }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Leftarrow, \nLeftarrow, \Longleftarrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftarrow ,\nLeftarrow ,\Longleftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇐</mo> <mo>,</mo> <mo>⇍</mo> <mo>,</mo> <mo stretchy="false">⟸</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftarrow ,\nLeftarrow ,\Longleftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9717b168b9880fea00c8ab38f7a297373c49e6fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.454ex; height:2.176ex;" alt="{\displaystyle \Leftarrow ,\nLeftarrow ,\Longleftarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow ,\nLeftrightarrow ,\Longleftrightarrow ,\iff }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> <mo>,</mo> <mo>⇎</mo> <mo>,</mo> <mo stretchy="false">⟺</mo> <mo>,</mo> <mspace width="thickmathspace"></mspace> <mo stretchy="false">⟺</mo> <mspace width="thickmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow ,\nLeftrightarrow ,\Longleftrightarrow ,\iff }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95a2e300ba0dd0558ef503ec6d99a4bc96d65881" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.673ex; height:2.176ex;" alt="{\displaystyle \Leftrightarrow ,\nLeftrightarrow ,\Longleftrightarrow ,\iff }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\Uparrow, \Downarrow, \Updownarrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Uparrow ,\Downarrow ,\Updownarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇑</mo> <mo>,</mo> <mo stretchy="false">⇓</mo> <mo>,</mo> <mo stretchy="false">⇕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Uparrow ,\Downarrow ,\Updownarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a29839c7fcdd4d4aa930b36f2f07aeeaa790aec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.329ex; height:2.843ex;" alt="{\displaystyle \Uparrow ,\Downarrow ,\Updownarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\rightarrow, \to, \nrightarrow, \longrightarrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow ,\to ,\nrightarrow ,\longrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mo>,</mo> <mo stretchy="false">→</mo> <mo>,</mo> <mo>↛</mo> <mo>,</mo> <mo stretchy="false">⟶</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow ,\to ,\nrightarrow ,\longrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a1b601586756ab88bdccbc1a09137b6ff9ff4d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.879ex; height:2.176ex;" alt="{\displaystyle \rightarrow ,\to ,\nrightarrow ,\longrightarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\leftarrow, \gets, \nleftarrow, \longleftarrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftarrow ,\gets ,\nleftarrow ,\longleftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> <mo>,</mo> <mo stretchy="false">←</mo> <mo>,</mo> <mo>↚</mo> <mo>,</mo> <mo stretchy="false">⟵</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow ,\gets ,\nleftarrow ,\longleftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3199310b40a24760aa1b40a5f2dbe6d53a0d5178" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.811ex; height:2.176ex;" alt="{\displaystyle \leftarrow ,\gets ,\nleftarrow ,\longleftarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\leftrightarrow, \nleftrightarrow, \longleftrightarrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftrightarrow ,\nleftrightarrow ,\longleftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> <mo>,</mo> <mo>↮</mo> <mo>,</mo> <mo stretchy="false">⟷</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow ,\nleftrightarrow ,\longleftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e1f0d38864f00203c1d97d15447f2eeeb2ef846" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.034ex; height:2.176ex;" alt="{\displaystyle \leftrightarrow ,\nleftrightarrow ,\longleftrightarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\uparrow, \downarrow, \updownarrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \uparrow ,\downarrow ,\updownarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↑</mo> <mo>,</mo> <mo stretchy="false">↓</mo> <mo>,</mo> <mo stretchy="false">↕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \uparrow ,\downarrow ,\updownarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8803aaa446c4ff246daaa0e421cefcd2ce597df3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.555ex; height:2.843ex;" alt="{\displaystyle \uparrow ,\downarrow ,\updownarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\nearrow, \swarrow, \nwarrow, \searrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nearrow ,\swarrow ,\nwarrow ,\searrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↗</mo> <mo>,</mo> <mo stretchy="false">↙</mo> <mo>,</mo> <mo stretchy="false">↖</mo> <mo>,</mo> <mo stretchy="false">↘</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nearrow ,\swarrow ,\nwarrow ,\searrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f089c1415648547a095fba54bb789d3af0246b42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.397ex; height:2.843ex;" alt="{\displaystyle \nearrow ,\swarrow ,\nwarrow ,\searrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\mapsto, \longmapsto</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mapsto ,\longmapsto }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↦</mo> <mo>,</mo> <mo stretchy="false">⟼</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mapsto ,\longmapsto }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9b544547bef1e6e7583995333f6e82cde3a4ef8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.163ex; height:2.176ex;" alt="{\displaystyle \mapsto ,\longmapsto }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft ,\upharpoonright ,\downharpoonleft ,\downharpoonright ,\rightleftharpoons ,\leftrightharpoons }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇀</mo> <mo>,</mo> <mo stretchy="false">⇁</mo> <mo>,</mo> <mo stretchy="false">↼</mo> <mo>,</mo> <mo stretchy="false">↽</mo> <mo>,</mo> <mo stretchy="false">↿</mo> <mo>,</mo> <mo stretchy="false">↾</mo> <mo>,</mo> <mo stretchy="false">⇃</mo> <mo>,</mo> <mo stretchy="false">⇂</mo> <mo>,</mo> <mo class="MJX-variant" stretchy="false">⇌</mo> <mo>,</mo> <mo stretchy="false">⇋</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft ,\upharpoonright ,\downharpoonleft ,\downharpoonright ,\rightleftharpoons ,\leftrightharpoons }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3255a6c277966a489401016f7b5d8a4e0029f02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.127ex; height:2.509ex;" alt="{\displaystyle \rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft ,\upharpoonright ,\downharpoonleft ,\downharpoonright ,\rightleftharpoons ,\leftrightharpoons }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \curvearrowleft ,\circlearrowleft ,\Lsh ,\upuparrows ,\rightrightarrows ,\rightleftarrows ,\rightarrowtail ,\looparrowright }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↶</mo> <mo>,</mo> <mo>↺</mo> <mo>,</mo> <mo stretchy="false">↰</mo> <mo>,</mo> <mo stretchy="false">⇈</mo> <mo>,</mo> <mo stretchy="false">⇉</mo> <mo>,</mo> <mo stretchy="false">⇄</mo> <mo>,</mo> <mo stretchy="false">↣</mo> <mo>,</mo> <mo stretchy="false">↬</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \curvearrowleft ,\circlearrowleft ,\Lsh ,\upuparrows ,\rightrightarrows ,\rightleftarrows ,\rightarrowtail ,\looparrowright }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e39fe91f90bdf106df75d352ed611a4d91c408b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.021ex; height:2.676ex;" alt="{\displaystyle \curvearrowleft ,\circlearrowleft ,\Lsh ,\upuparrows ,\rightrightarrows ,\rightleftarrows ,\rightarrowtail ,\looparrowright }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \curvearrowright ,\circlearrowright ,\Rsh ,\downdownarrows ,\leftleftarrows ,\leftrightarrows ,\leftarrowtail ,\looparrowleft }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↷</mo> <mo>,</mo> <mo>↻</mo> <mo>,</mo> <mo stretchy="false">↱</mo> <mo>,</mo> <mo stretchy="false">⇊</mo> <mo>,</mo> <mo stretchy="false">⇇</mo> <mo>,</mo> <mo stretchy="false">⇆</mo> <mo>,</mo> <mo stretchy="false">↢</mo> <mo>,</mo> <mo stretchy="false">↫</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \curvearrowright ,\circlearrowright ,\Rsh ,\downdownarrows ,\leftleftarrows ,\leftrightarrows ,\leftarrowtail ,\looparrowleft }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29e53723742fe88965687460501feedb9dbe3078" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.021ex; height:2.676ex;" alt="{\displaystyle \curvearrowright ,\circlearrowright ,\Rsh ,\downdownarrows ,\leftleftarrows ,\leftrightarrows ,\leftarrowtail ,\looparrowleft }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hookrightarrow ,\hookleftarrow ,\multimap ,\leftrightsquigarrow ,\rightsquigarrow ,\twoheadrightarrow ,\twoheadleftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↪</mo> <mo>,</mo> <mo stretchy="false">↩</mo> <mo>,</mo> <mo>⊸</mo> <mo>,</mo> <mo stretchy="false">↭</mo> <mo>,</mo> <mo stretchy="false">⇝</mo> <mo>,</mo> <mo stretchy="false">↠</mo> <mo>,</mo> <mo stretchy="false">↞</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hookrightarrow ,\hookleftarrow ,\multimap ,\leftrightsquigarrow ,\rightsquigarrow ,\twoheadrightarrow ,\twoheadleftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56bcb3444cb5056357b1546b21f0d33d2ee73299" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.216ex; height:2.176ex;" alt="{\displaystyle \hookrightarrow ,\hookleftarrow ,\multimap ,\leftrightsquigarrow ,\rightsquigarrow ,\twoheadrightarrow ,\twoheadleftarrow }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Special" data-mw-thread-id="h-Special-Functions,_symbols,_special_characters"><span data-mw-comment-start="" id="h-Special-Functions,_symbols,_special_characters"></span>Special<span data-mw-comment-end="h-Special-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=32" title="Edit section: Special"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\amalg \P \S \% \dagger \ddagger \ldots \cdots \vdots \ddots</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \amalg \P \S \%\dagger \ddagger \ldots \cdots \vdots \ddots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⨿</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>¶</mo> </mrow> <mi mathvariant="normal">§</mi> <mi mathvariant="normal">%</mi> <mo>†</mo> <mo>‡</mo> <mo>…</mo> <mo>⋯</mo> <mo>⋮</mo> <mo>⋱</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \amalg \P \S \%\dagger \ddagger \ldots \cdots \vdots \ddots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/017e5b5a6fe88649864fe4bfba066c2335f07328" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:20.23ex; height:5.009ex;" alt="{\displaystyle \amalg \P \S \%\dagger \ddagger \ldots \cdots \vdots \ddots }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\smile \frown \wr \triangleleft \triangleright</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \smile \frown \wr \triangleleft \triangleright }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⌣⌢</mo> <mo>≀</mo> <mo>◃</mo> <mo>▹</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \smile \frown \wr \triangleleft \triangleright }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46b99896291714ee8e9894ecb6f6539320c46f29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.297ex; height:2.176ex;" alt="{\displaystyle \smile \frown \wr \triangleleft \triangleright }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">♢</mi> <mo>,</mo> <mi mathvariant="normal">♡</mi> <mo>,</mo> <mi mathvariant="normal">♣</mi> <mo>,</mo> <mi mathvariant="normal">♠</mi> <mo>,</mo> <mi>⅁</mi> <mo>,</mo> <mi mathvariant="normal">♭</mi> <mo>,</mo> <mi mathvariant="normal">♮</mi> <mo>,</mo> <mi mathvariant="normal">♯</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba9c9e029d130f04fe16c6703704418b4ed5a154" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.669ex; height:2.843ex;" alt="{\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp }"/></span> </td></tr> <tr> <th colspan="2"> <div class="mw-heading mw-heading4"><h4 id="Unsorted_(new_stuff)" data-mw-thread-id="h-Unsorted_(new_stuff)-Functions,_symbols,_special_characters"><span id="Unsorted_.28new_stuff.29"></span><span data-mw-comment-start="" id="h-Unsorted_(new_stuff)-Functions,_symbols,_special_characters"></span>Unsorted (new stuff)<span data-mw-comment-end="h-Unsorted_(new_stuff)-Functions,_symbols,_special_characters"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=33" title="Edit section: Unsorted (new stuff)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>╱</mi> <mo>,</mo> <mi>╲</mi> <mo>,</mo> <mo class="MJX-variant">⋅</mo> <mo>,</mo> <mo>⋉</mo> <mo>,</mo> <mo>⋊</mo> <mo>,</mo> <mo>⋋</mo> <mo>,</mo> <mo>⋌</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a175bb9c04b3ab5ab3f2e0cda7f2f5fc2565aa89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.215ex; height:2.509ex;" alt="{\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≖</mo> <mo>,</mo> <mo>≗</mo> <mo>,</mo> <mo>≜</mo> <mo>,</mo> <mo>≏</mo> <mo>,</mo> <mo>≎</mo> <mo>,</mo> <mo>≑</mo> <mo>,</mo> <mo>≓</mo> <mo>,</mo> <mo>≒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bd0c7f2e51581abaa666fc6b15fbd070b935528" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.703ex; height:2.843ex;" alt="{\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\intercal \barwedge \veebar \doublebarwedge \between \pitchfork</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊺</mo> <mo>,</mo> <mo>⊼</mo> <mo>,</mo> <mo>⊻</mo> <mo>,</mo> <mo>⩞</mo> <mo>,</mo> <mo>≬</mo> <mo>,</mo> <mo>⋔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2102c674b7c5e9602994d4f3e8ab034c5c01c142" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.436ex; height:3.009ex;" alt="{\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊲</mo> <mo>,</mo> <mo>⋪</mo> <mo>,</mo> <mo>⊳</mo> <mo>,</mo> <mo>⋫</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5bb24042826b7903b411f082f4e14ac073a168c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.334ex; height:2.509ex;" alt="{\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊴</mo> <mo>,</mo> <mo>⋬</mo> <mo>,</mo> <mo>⊵</mo> <mo>,</mo> <mo>⋭</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24d9d4eea3a1ed8697b067adcec4b976902a2665" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.334ex; height:3.176ex;" alt="{\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq }"/></span> </td></tr></tbody></table> <p>For a little more semantics on these symbols, see this brief <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160305074303/https://www.math.upenn.edu/tex-stuff/cookbook.pdf">TeX Cookbook</a> or here <a rel="nofollow" class="external text" href="https://www3.nd.edu/~powers/ame.332/TeXcookbook.pdf">TeX Cookbook</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Larger_expressions" data-mw-thread-id="h-Larger_expressions-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Larger_expressions-Formatting_using_LaTeX"></span>Larger expressions<span data-mw-comment-end="h-Larger_expressions-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=34" title="Edit section: Larger expressions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Subscripts,_superscripts,_integrals" data-mw-thread-id="h-Subscripts,_superscripts,_integrals-Larger_expressions"><span id="Subscripts.2C_superscripts.2C_integrals"></span><span data-mw-comment-start="" id="h-Subscripts,_superscripts,_integrals-Larger_expressions"></span>Subscripts, superscripts, integrals<span data-mw-comment-end="h-Subscripts,_superscripts,_integrals-Larger_expressions"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=35" title="Edit section: Subscripts, superscripts, integrals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="border-collapse:collapse"> <tbody><tr> <th>Feature</th> <th>Syntax</th> <th>How it looks rendered </th></tr> <tr> <td>Superscript </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">a<span class="nb">^</span>2, a<span class="nb">^{</span>x+3<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2},a^{x+3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo>+</mo> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2},a^{x+3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3644eedfcaf40b554ec732c7daf0866ef393188f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.821ex; height:3.009ex;" alt="{\displaystyle a^{2},a^{x+3}}"/></span> </td></tr> <tr> <td>Subscript </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">a<span class="nb">_</span>2</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/270580da7333505d9b73697417d0543c43c98b9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle a_{2}}"/></span> </td></tr> <tr> <td rowspan="2">Grouping </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">10<span class="nb">^{</span>30<span class="nb">}</span> a<span class="nb">^{</span>2+2<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{30}a^{2+2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>30</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>+</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{30}a^{2+2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97f79186665c52930a9c09e17d1676c84b7a64b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.586ex; height:2.676ex;" alt="{\displaystyle 10^{30}a^{2+2}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">a<span class="nb">_{</span>i,j<span class="nb">}</span> b<span class="nb">_{</span>f'<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{i,j}b_{f'}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>f</mi> <mo>′</mo> </msup> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i,j}b_{f'}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/912bedc705983d91f86dfe101a7b442856731451" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.859ex; height:3.009ex;" alt="{\displaystyle a_{i,j}b_{f'}}"/></span> </td></tr> <tr> <td rowspan="2">Combining sub & super without and with horizontal separation </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">x<span class="nb">_</span>2<span class="nb">^</span>3</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{2}^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{2}^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50f3c6f93cf5fad3e7faa14000a61a49cb65d2b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.384ex; height:3.176ex;" alt="{\displaystyle x_{2}^{3}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="nb">{</span>x<span class="nb">_</span>2<span class="nb">}^</span>3</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {x_{2}}^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {x_{2}}^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91e480f94fbabd41a5b8807f5c5412513b73d60b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.438ex; height:3.009ex;" alt="{\displaystyle {x_{2}}^{3}}"/></span> </td></tr> <tr> <td>Super super </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">10<span class="nb">^{</span>10<span class="nb">^{</span>8<span class="nb">}}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{10^{8}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{10^{8}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efe2da741f2b98770ee2fee14ff672daf85cf1ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.033ex; height:3.009ex;" alt="{\displaystyle 10^{10^{8}}}"/></span> </td></tr> <tr> <td rowspan="2">Preceding and/or additional sub & super </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\sideset</span><span class="nb">{_</span>1<span class="nb">^</span>2<span class="nb">}{_</span>3<span class="nb">^</span>4<span class="nb">}</span><span class="k">\prod</span><span class="nb">_</span>a<span class="nb">^</span>b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sideset {_{1}^{2}}{_{3}^{4}}\prod _{a}^{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mrow class="MJX-TeXAtom-OP"> <msubsup> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mpadded width="0"> <mrow class="MJX-TeXAtom-ORD"> <mphantom> <mo>∏</mo> </mphantom> </mrow> </mpadded> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mspace width="negativethinmathspace"></mspace> <msubsup> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo movablelimits="false">∏</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </munderover> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sideset {_{1}^{2}}{_{3}^{4}}\prod _{a}^{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e383d9569631355101b6047c9b6734725fe686f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:5.078ex; height:7.843ex;" alt="{\displaystyle \sideset {_{1}^{2}}{_{3}^{4}}\prod _{a}^{b}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="nb">{}_</span>1<span class="nb">^</span>2<span class="k">\!\Omega</span><span class="nb">_</span>3<span class="nb">^</span>4</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {}_{1}^{2}\!\Omega _{3}^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mspace width="negativethinmathspace"></mspace> <msubsup> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {}_{1}^{2}\!\Omega _{3}^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aabd2ce591d17dad6d3b61b5725424514c840e67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.399ex; height:3.176ex;" alt="{\displaystyle {}_{1}^{2}\!\Omega _{3}^{4}}"/></span> </td></tr> <tr> <td rowspan="4">Stacking </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\overset</span><span class="nb">{</span><span class="k">\alpha</span><span class="nb">}{</span><span class="k">\omega</span><span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overset {\alpha }{\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ω</mi> <mi>α</mi> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overset {\alpha }{\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71009472c4378a2cbf907299bc8c23936aa19291" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:3.009ex;" alt="{\displaystyle {\overset {\alpha }{\omega }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\underset</span><span class="nb">{</span><span class="k">\alpha</span><span class="nb">}{</span><span class="k">\omega</span><span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\underset {\alpha }{\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <munder> <mi>ω</mi> <mi>α</mi> </munder> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\underset {\alpha }{\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3f4488ce56e8bcf504df663f09f8e88f438b14b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:1.446ex; height:3.343ex;" alt="{\displaystyle {\underset {\alpha }{\omega }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\overset</span><span class="nb">{</span><span class="k">\alpha</span><span class="nb">}{</span><span class="k">\underset</span><span class="nb">{</span><span class="k">\gamma</span><span class="nb">}{</span><span class="k">\omega</span><span class="nb">}}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overset {\alpha }{\underset {\gamma }{\omega }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mi>ω</mi> <mi>γ</mi> </munder> <mi>α</mi> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overset {\alpha }{\underset {\gamma }{\omega }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c886687a8ab1db9829a948f569184728eda1ec2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:1.446ex; height:5.009ex;" alt="{\displaystyle {\overset {\alpha }{\underset {\gamma }{\omega }}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\stackrel</span><span class="nb">{</span><span class="k">\alpha</span><span class="nb">}{</span><span class="k">\omega</span><span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\stackrel {\alpha }{\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\stackrel {\alpha }{\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a00e31ce529e009a3ef2d10606ad423342d9cb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:3.009ex;" alt="{\displaystyle {\stackrel {\alpha }{\omega }}}"/></span> </td></tr> <tr> <td rowspan="2">Derivatives </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">x', y'', f', f''</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x',y'',f',f''}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>y</mi> <mo>″</mo> </msup> <mo>,</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>f</mi> <mo>″</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x',y'',f',f''}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ed1721a4e59cd929d65d873fd7d3a879a591ac4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.877ex; height:2.843ex;" alt="{\displaystyle x',y'',f',f''}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">x<span class="nb">^</span><span class="k">\prime</span>, y<span class="nb">^{</span><span class="k">\prime\prime</span><span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{\prime },y^{\prime \prime }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>,</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{\prime },y^{\prime \prime }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f65e90170bc790f3f0e13679cf019327d4192dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.346ex; height:2.843ex;" alt="{\displaystyle x^{\prime },y^{\prime \prime }}"/></span> </td></tr> <tr> <td>Derivative dots </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\dot</span><span class="nb">{</span>x<span class="nb">}</span>, <span class="k">\ddot</span><span class="nb">{</span>x<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {x}},{\ddot {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo>¨</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {x}},{\ddot {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5e71030758285fcd37e8c9fbf1ece5b9b86ea99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.693ex; height:2.509ex;" alt="{\displaystyle {\dot {x}},{\ddot {x}}}"/></span> </td></tr> <tr> <td rowspan="3">Underlines, overlines, vectors </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\hat</span> a <span class="k">\ \bar</span> b <span class="k">\ \vec</span> c</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>b</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>c</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebeb654a69eaacb690eddbf7bc79438011568f76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.777ex; height:2.509ex;" alt="{\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\overrightarrow</span><span class="nb">{</span>a b<span class="nb">}</span> <span class="k">\ \overleftarrow</span><span class="nb">{</span>c d<span class="nb">}</span> <span class="k">\ \widehat</span><span class="nb">{</span>d e f<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {ab}}\ {\overleftarrow {cd}}\ {\widehat {def}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>a</mi> <mi>b</mi> </mrow> <mo>→</mo> </mover> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>c</mi> <mi>d</mi> </mrow> <mo>←</mo> </mover> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>d</mi> <mi>e</mi> <mi>f</mi> </mrow> <mo>^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {ab}}\ {\overleftarrow {cd}}\ {\widehat {def}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469eb4ecf2566aea8ff482d9d040d135da2f86cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.391ex; height:4.009ex;" alt="{\displaystyle {\overrightarrow {ab}}\ {\overleftarrow {cd}}\ {\widehat {def}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\overline</span><span class="nb">{</span>g h i<span class="nb">}</span> <span class="k">\ \underline</span><span class="nb">{</span>j k l<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {ghi}}\ {\underline {jkl}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>g</mi> <mi>h</mi> <mi>i</mi> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <munder> <mrow> <mi>j</mi> <mi>k</mi> <mi>l</mi> </mrow> <mo>_</mo> </munder> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {ghi}}\ {\underline {jkl}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3bde7f4495beed348915bc478aab52eeed5c92f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.985ex; margin-bottom: -0.853ex; width:6.818ex; height:4.509ex;" alt="{\displaystyle {\overline {ghi}}\ {\underline {jkl}}}"/></span> </td></tr> <tr> <td>Arc (workaround) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\overset</span><span class="nb">{</span><span class="k">\frown</span><span class="nb">}</span> <span class="nb">{</span>AB<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overset {\frown }{AB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <mi>B</mi> </mrow> <mo>⌢</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overset {\frown }{AB}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4608fbf7084ad30e15487e824daf74260640f810" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:3.343ex;" alt="{\displaystyle {\overset {\frown }{AB}}}"/></span> </td></tr> <tr> <td>Arrows </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">A <span class="k">\xleftarrow</span><span class="nb">{</span>n+<span class="k">\mu</span>-1<span class="nb">}</span> B <span class="k">\xrightarrow</span><span class="na">[T]</span><span class="nb">{</span>n<span class="k">\pm</span> i-1<span class="nb">}</span> C</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A{\xleftarrow {n+\mu -1}}B{\xrightarrow[{T}]{n\pm i-1}}C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>←</mo> <mpadded width="+0.556em" lspace="0.389em" voffset=".15em"> <mi>n</mi> <mo>+</mo> <mi>μ</mi> <mo>−</mo> <mn>1</mn> </mpadded> </mover> </mrow> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mi>n</mi> <mo>±</mo> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mpadded> </munderover> </mrow> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A{\xleftarrow {n+\mu -1}}B{\xrightarrow[{T}]{n\pm i-1}}C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0645e6df7ace8a40eba2d92f293f5fbd6f929411" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.762ex; margin-top: -0.373ex; margin-bottom: -0.576ex; width:18.166ex; height:5.843ex;" alt="{\displaystyle A{\xleftarrow {n+\mu -1}}B{\xrightarrow[{T}]{n\pm i-1}}C}"/></span> </td></tr> <tr> <td>Overbraces </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\overbrace</span><span class="nb">{</span> 1+2+<span class="k">\cdots</span>+100 <span class="nb">}^{</span>5050<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \overbrace {1+2+\cdots +100} ^{5050}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mover> <mrow> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mn>100</mn> </mrow> <mo>⏞</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5050</mn> </mrow> </mover> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \overbrace {1+2+\cdots +100} ^{5050}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f98367ab3041e58a31d62d829f125a38d9f32426" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.028ex; width:17.085ex; height:5.676ex;" alt="{\displaystyle \overbrace {1+2+\cdots +100} ^{5050}}"/></span> </td></tr> <tr> <td>Underbraces </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\underbrace</span><span class="nb">{</span> a+b+<span class="k">\cdots</span>+z <span class="nb">}_{</span>26<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \underbrace {a+b+\cdots +z} _{26}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mi>z</mi> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>26</mn> </mrow> </munder> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \underbrace {a+b+\cdots +z} _{26}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f932862aa8d0c25aeb0e1abc46894b3fb8dd430" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; margin-right: -0.023ex; width:14.583ex; height:5.676ex;" alt="{\displaystyle \underbrace {a+b+\cdots +z} _{26}}"/></span> </td></tr> <tr> <td>Sum </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\sum</span><span class="nb">_{</span>k=1<span class="nb">}^</span>N k<span class="nb">^</span>2</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=1}^{N}k^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=1}^{N}k^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7956d37c7f782666fd81d18ef8471f96c326113f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:6.008ex; height:7.343ex;" alt="{\displaystyle \sum _{k=1}^{N}k^{2}}"/></span> </td></tr> <tr> <td>Sum (force <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span> <span class="k">\sum</span><span class="nb">_{</span>k=1<span class="nb">}^</span>N k<span class="nb">^</span>2</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle \sum _{k=1}^{N}k^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle \sum _{k=1}^{N}k^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8311da0a77722c17b25e831e13cbeb2517f064a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.296ex; height:3.509ex;" alt="{\displaystyle \textstyle \sum _{k=1}^{N}k^{2}}"/></span> </td></tr> <tr> <td>Sum in a fraction (default <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\frac</span><span class="nb">{</span><span class="k">\sum</span><span class="nb">_{</span>k=1<span class="nb">}^</span>N k<span class="nb">^</span>2<span class="nb">}{</span>a<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sum _{k=1}^{N}k^{2}}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sum _{k=1}^{N}k^{2}}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1b56ce3d54de8524b7ea90a5fe9b7e096dfdcc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.132ex; height:6.176ex;" alt="{\displaystyle {\frac {\sum _{k=1}^{N}k^{2}}{a}}}"/></span> </td></tr> <tr> <td>Sum in a fraction (force <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\displaystyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\frac</span><span class="nb">{</span><span class="k">\displaystyle</span> <span class="k">\sum</span><span class="nb">_{</span>k=1<span class="nb">}^</span>N k<span class="nb">^</span>2<span class="nb">}{</span>a<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\displaystyle \sum _{k=1}^{N}k^{2}}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\displaystyle \sum _{k=1}^{N}k^{2}}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9cf261c3532aba30b0de37d54514b10ff341071" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.844ex; height:10.176ex;" alt="{\displaystyle {\frac {\displaystyle \sum _{k=1}^{N}k^{2}}{a}}}"/></span> </td></tr> <tr> <td>Sum in a fraction (alternative limits style) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\frac</span><span class="nb">{</span><span class="k">\sum\limits</span><span class="nb">^{</span>N<span class="nb">}_{</span>k=1<span class="nb">}</span> k<span class="nb">^</span>2<span class="nb">}{</span>a<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sum \limits _{k=1}^{N}k^{2}}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munderover> <mo movablelimits="false">∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sum \limits _{k=1}^{N}k^{2}}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3684111c38d141f0dc3abd2797d435a21281b949" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.446ex; height:9.176ex;" alt="{\displaystyle {\frac {\sum \limits _{k=1}^{N}k^{2}}{a}}}"/></span> </td></tr> <tr> <td>Product </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\prod</span><span class="nb">_{</span>i=1<span class="nb">}^</span>N x<span class="nb">_</span>i</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \prod _{i=1}^{N}x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \prod _{i=1}^{N}x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa57991fd499c8351007df456760f741fb6e8997" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:5.486ex; height:7.343ex;" alt="{\displaystyle \prod _{i=1}^{N}x_{i}}"/></span> </td></tr> <tr> <td>Product (force <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span> <span class="k">\prod</span><span class="nb">_{</span>i=1<span class="nb">}^</span>N x<span class="nb">_</span>i</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle \prod _{i=1}^{N}x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <munderover> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle \prod _{i=1}^{N}x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4eb7730d2ab12fc4e1c408be3814afdc0a688bd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.61ex; height:3.509ex;" alt="{\displaystyle \textstyle \prod _{i=1}^{N}x_{i}}"/></span> </td></tr> <tr> <td>Coproduct </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\coprod</span><span class="nb">_{</span>i=1<span class="nb">}^</span>N x<span class="nb">_</span>i</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \coprod _{i=1}^{N}x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∐</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \coprod _{i=1}^{N}x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6378fc889e6f561501161c84ca21c2551b3bb688" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:5.486ex; height:7.343ex;" alt="{\displaystyle \coprod _{i=1}^{N}x_{i}}"/></span> </td></tr> <tr> <td>Coproduct (force <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span> <span class="k">\coprod</span><span class="nb">_{</span>i=1<span class="nb">}^</span>N x<span class="nb">_</span>i</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle \coprod _{i=1}^{N}x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <munderover> <mo>∐</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle \coprod _{i=1}^{N}x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e15321707fd76dd010d3e198da9eb8c72277ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.61ex; height:3.509ex;" alt="{\displaystyle \textstyle \coprod _{i=1}^{N}x_{i}}"/></span> </td></tr> <tr> <td>Limit </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\lim</span><span class="nb">_{</span>n <span class="k">\to</span> <span class="k">\infty</span><span class="nb">}</span>x<span class="nb">_</span>n</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{n\to \infty }x_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{n\to \infty }x_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9e68667b4e113488d30c2e1e63bf0ddf238a4ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.208ex; height:3.676ex;" alt="{\displaystyle \lim _{n\to \infty }x_{n}}"/></span> </td></tr> <tr> <td>Limit (force <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span> <span class="k">\lim</span><span class="nb">_{</span>n <span class="k">\to</span> <span class="k">\infty</span><span class="nb">}</span>x<span class="nb">_</span>n</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle \lim _{n\to \infty }x_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle \lim _{n\to \infty }x_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/059cb4851713dea4bf520b9ea4408c40e440ee05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.67ex; height:2.509ex;" alt="{\displaystyle \textstyle \lim _{n\to \infty }x_{n}}"/></span> </td></tr> <tr> <td>Integral </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\int\limits</span><span class="nb">_{</span>1<span class="nb">}^{</span>3<span class="nb">}</span><span class="k">\frac</span><span class="nb">{</span>e<span class="nb">^</span>3/x<span class="nb">}{</span>x<span class="nb">^</span>2<span class="nb">}</span><span class="k">\,</span> dx</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \limits _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>x</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \limits _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a74fbb30a2e06f5e12105d46b2b2f2ce78f183af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:10.979ex; height:9.176ex;" alt="{\displaystyle \int \limits _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx}"/></span> </td></tr> <tr> <td>Integral (alternative limits style) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\int</span><span class="nb">_{</span>1<span class="nb">}^{</span>3<span class="nb">}</span><span class="k">\frac</span><span class="nb">{</span>e<span class="nb">^</span>3/x<span class="nb">}{</span>x<span class="nb">^</span>2<span class="nb">}</span><span class="k">\,</span> dx</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>x</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06bec137ddf2b5a8a0b34863e2bd272baaa297b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.304ex; height:6.343ex;" alt="{\displaystyle \int _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx}"/></span> </td></tr> <tr> <td>Integral (force <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span> <span class="k">\int\limits</span><span class="nb">_{</span>-N<span class="nb">}^{</span>N<span class="nb">}</span> e<span class="nb">^</span>x dx</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle \int \limits _{-N}^{N}e^{x}dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle \int \limits _{-N}^{N}e^{x}dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fb7bf0356c0ffad7efc07c61f50715727591432" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; margin-left: -0.07ex; width:7.788ex; height:6.843ex;" alt="{\displaystyle \textstyle \int \limits _{-N}^{N}e^{x}dx}"/></span> </td></tr> <tr> <td>Integral (force <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>, alternative limits style) </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span> <span class="k">\int</span><span class="nb">_{</span>-N<span class="nb">}^{</span>N<span class="nb">}</span> e<span class="nb">^</span>x dx</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle \int _{-N}^{N}e^{x}dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msubsup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle \int _{-N}^{N}e^{x}dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5aa2936e204a889f60581dd07a5b0e6db75ccf60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:9.256ex; height:3.843ex;" alt="{\displaystyle \textstyle \int _{-N}^{N}e^{x}dx}"/></span> </td></tr> <tr> <td>Double integral </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\iint\limits</span><span class="nb">_</span>D dx<span class="k">\,</span>dy</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \iint \limits _{D}dx\,dy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∬</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </munder> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \iint \limits _{D}dx\,dy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e65ff1d60d4bd9513c3f92024dc675cb43323845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:9.111ex; height:7.343ex;" alt="{\displaystyle \iint \limits _{D}dx\,dy}"/></span> </td></tr> <tr> <td>Triple integral </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\iiint\limits</span><span class="nb">_</span>E dx<span class="k">\,</span>dy<span class="k">\,</span>dz</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \iiint \limits _{E}dx\,dy\,dz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∭</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </munder> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>y</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \iiint \limits _{E}dx\,dy\,dz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60fa07722725aa0f09268679123a22d87841f278" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:12.982ex; height:7.343ex;" alt="{\displaystyle \iiint \limits _{E}dx\,dy\,dz}"/></span> </td></tr> <tr> <td>Quadruple integral </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\iiiint\limits</span><span class="nb">_</span>F dx<span class="k">\,</span>dy<span class="k">\,</span>dz<span class="k">\,</span>dt</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \iiiint \limits _{F}dx\,dy\,dz\,dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>⨌</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </munder> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>y</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>z</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \iiiint \limits _{F}dx\,dy\,dz\,dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a9bffce94b0935a88dff345911385fe8ab42981" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:16.764ex; height:7.343ex;" alt="{\displaystyle \iiiint \limits _{F}dx\,dy\,dz\,dt}"/></span> </td></tr> <tr> <td>Line or path integral </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\int</span><span class="nb">_{</span>(x,y)<span class="k">\in</span> C<span class="nb">}</span> x<span class="nb">^</span>3<span class="k">\,</span> dx + 4y<span class="nb">^</span>2<span class="k">\,</span> dy</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{(x,y)\in C}x^{3}\,dx+4y^{2}\,dy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>C</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mn>4</mn> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{(x,y)\in C}x^{3}\,dx+4y^{2}\,dy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28bd07d27443057e03d4c7e40e40b629172b0368" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:22.044ex; height:6.009ex;" alt="{\displaystyle \int _{(x,y)\in C}x^{3}\,dx+4y^{2}\,dy}"/></span> </td></tr> <tr> <td>Closed line or path integral </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\oint</span><span class="nb">_{</span>(x,y)<span class="k">\in</span> C<span class="nb">}</span> x<span class="nb">^</span>3<span class="k">\,</span> dx + 4y<span class="nb">^</span>2<span class="k">\,</span> dy</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{(x,y)\in C}x^{3}\,dx+4y^{2}\,dy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>C</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mn>4</mn> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{(x,y)\in C}x^{3}\,dx+4y^{2}\,dy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bd8f3ee582e64365cefbfd44860b60a14b4424b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:22.044ex; height:6.009ex;" alt="{\displaystyle \oint _{(x,y)\in C}x^{3}\,dx+4y^{2}\,dy}"/></span> </td></tr> <tr> <td>Intersections </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\bigcap</span><span class="nb">_{</span>i=1<span class="nb">}^</span>n E<span class="nb">_</span>i</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bigcap _{i=1}^{n}E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>⋂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigcap _{i=1}^{n}E_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0afadabd47af16c203b1e68852a4a139e930e697" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:5.57ex; height:6.843ex;" alt="{\displaystyle \bigcap _{i=1}^{n}E_{i}}"/></span> </td></tr> <tr> <td><a href="/wiki/Union_(set_theory)" title="Union (set theory)">Unions</a> </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\bigcup</span><span class="nb">_{</span>i=1<span class="nb">}^</span>n E<span class="nb">_</span>i</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bigcup _{i=1}^{n}E_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>⋃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigcup _{i=1}^{n}E_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/909079836ed3765d4c3093107490aa3880161d16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:5.57ex; height:6.843ex;" alt="{\displaystyle \bigcup _{i=1}^{n}E_{i}}"/></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Fractions,_matrices,_multilines" data-mw-thread-id="h-Fractions,_matrices,_multilines-Formatting_using_LaTeX"><span id="Fractions.2C_matrices.2C_multilines"></span><span data-mw-comment-start="" id="h-Fractions,_matrices,_multilines-Formatting_using_LaTeX"></span>Fractions, matrices, multilines<span data-mw-comment-end="h-Fractions,_matrices,_multilines-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=36" title="Edit section: Fractions, matrices, multilines"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Feature </th> <th>Syntax </th> <th>How it looks rendered </th></tr> <tr> <td>Fractions </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\frac</span><span class="nb">{</span>2<span class="nb">}{</span>4<span class="nb">}</span>=0.5</code> or <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="nb">{</span>2 <span class="k">\over</span> 4<span class="nb">}</span>=0.5</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {2}{4}}=0.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mn>0.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2}{4}}=0.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a6fc96603859414dc324819fa36714978d8f8c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.069ex; height:5.176ex;" alt="{\displaystyle {\frac {2}{4}}=0.5}"/></span> </td></tr> <tr> <td>Small fractions (force <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\tfrac</span><span class="nb">{</span>2<span class="nb">}{</span>4<span class="nb">}</span> = 0.5</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {2}{4}}=0.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>2</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <mo>=</mo> <mn>0.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2}{4}}=0.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2c52511870c711f8cf84a302f32bad585e8a8b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:7.728ex; height:3.509ex;" alt="{\displaystyle {\tfrac {2}{4}}=0.5}"/></span> </td></tr> <tr> <td>Large (normal) fractions (force <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\displaystyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\dfrac</span><span class="nb">{</span>2<span class="nb">}{</span>4<span class="nb">}</span> = 0.5 <span class="k">\qquad</span> <span class="k">\dfrac</span><span class="nb">{</span>2<span class="nb">}{</span>c + <span class="k">\dfrac</span><span class="nb">{</span>2<span class="nb">}{</span>d + <span class="k">\dfrac</span><span class="nb">{</span>2<span class="nb">}{</span>4<span class="nb">}}}</span> = a</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dfrac {2}{4}}=0.5\qquad {\dfrac {2}{c+{\dfrac {2}{d+{\dfrac {2}{4}}}}}}=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>2</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <mo>=</mo> <mn>0.5</mn> <mspace width="2em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>2</mn> <mrow> <mi>c</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>2</mn> <mrow> <mi>d</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>2</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> </mrow> </mfrac> </mstyle> </mrow> </mrow> </mfrac> </mstyle> </mrow> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dfrac {2}{4}}=0.5\qquad {\dfrac {2}{c+{\dfrac {2}{d+{\dfrac {2}{4}}}}}}=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ced99e52615200f58f979a63497dbfb18a98a02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.171ex; width:28.617ex; height:11.509ex;" alt="{\displaystyle {\dfrac {2}{4}}=0.5\qquad {\dfrac {2}{c+{\dfrac {2}{d+{\dfrac {2}{4}}}}}}=a}"/></span> </td></tr> <tr> <td>Large (nested) fractions </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\cfrac</span><span class="nb">{</span>2<span class="nb">}{</span>c + <span class="k">\cfrac</span><span class="nb">{</span>2<span class="nb">}{</span>d + <span class="k">\cfrac</span><span class="nb">{</span>2<span class="nb">}{</span>4<span class="nb">}}}</span> = a</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63bf919f4c77096973446f971625243947999ce2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -10.171ex; width:15.903ex; height:14.343ex;" alt="{\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a}"/></span> </td></tr> <tr> <td>Cancellations in fractions </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\cfrac</span><span class="nb">{</span>x<span class="nb">}{</span>1 + <span class="k">\cfrac</span><span class="nb">{</span><span class="k">\cancel</span><span class="nb">{</span>y<span class="nb">}}{</span><span class="k">\cancel</span><span class="nb">{</span>y<span class="nb">}}}</span> = <span class="k">\cfrac</span><span class="nb">{</span>x<span class="nb">}{</span>2<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\cfrac {x}{1+{\cfrac {\cancel {y}}{\cancel {y}}}}}={\cfrac {x}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <menclose notation="updiagonalstrike"> <mi>y</mi> </menclose> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <menclose notation="updiagonalstrike"> <mi>y</mi> </menclose> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\cfrac {x}{1+{\cfrac {\cancel {y}}{\cancel {y}}}}}={\cfrac {x}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17e2d96b813ea4a7d18fd654938c943a49d0fb0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.505ex; width:13.372ex; height:11.676ex;" alt="{\displaystyle {\cfrac {x}{1+{\cfrac {\cancel {y}}{\cancel {y}}}}}={\cfrac {x}{2}}}"/></span> </td></tr> <tr> <td>Binomial coefficients </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\binom</span><span class="nb">{</span>n<span class="nb">}{</span>k<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\binom {n}{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mi>n</mi> <mi>k</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\binom {n}{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/963a810ba39e3e0725c523d0c98b18f39786ebb2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:4.816ex; height:6.176ex;" alt="{\displaystyle {\binom {n}{k}}}"/></span> </td></tr> <tr> <td>Small binomial coefficients (force <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\textstyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\tbinom</span><span class="nb">{</span>n<span class="nb">}{</span>k<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tbinom {n}{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> <mfrac linethickness="0"> <mi>n</mi> <mi>k</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tbinom {n}{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/206415d3742167e319b2e52c2ca7563b799abad7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.116ex; height:3.176ex;" alt="{\displaystyle {\tbinom {n}{k}}}"/></span> </td></tr> <tr> <td>Large (normal) binomial coefficients (force <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\displaystyle</span></code>) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\dbinom</span><span class="nb">{</span>n<span class="nb">}{</span>k<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dbinom {n}{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mi>n</mi> <mi>k</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dbinom {n}{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/969a3dfca2e52cf8c2ce7c6ff911630e70a2835d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:4.816ex; height:6.176ex;" alt="{\displaystyle {\dbinom {n}{k}}}"/></span> </td></tr> <tr> <td rowspan="7">Matrices </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>matrix<span class="nb">}</span> -x <span class="nb">&</span> y <span class="k">\\</span> z <span class="nb">&</span> -v <span class="k">\end</span><span class="nb">{</span>matrix<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}-x&y\\z&-v\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mo>−</mo> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mo>−</mo> <mi>v</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}-x&y\\z&-v\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e7b684ab8e1b31615ea35fa9353d84bd0a1039e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:9.148ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}-x&y\\z&-v\end{matrix}}}"/></span> </td></tr> <tr> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>vmatrix<span class="nb">}</span> -x <span class="nb">&</span> y <span class="k">\\</span> z <span class="nb">&</span> -v <span class="k">\end</span><span class="nb">{</span>vmatrix<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{vmatrix}-x&y\\z&-v\end{vmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mo>−</mo> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mo>−</mo> <mi>v</mi> </mtd> </mtr> </mtable> <mo>|</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{vmatrix}-x&y\\z&-v\end{vmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68289f59fa48c994001ecb521b98b0580aaa21e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:10.441ex; height:6.176ex;" alt="{\displaystyle {\begin{vmatrix}-x&y\\z&-v\end{vmatrix}}}"/></span> </td></tr> <tr> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>Vmatrix<span class="nb">}</span> -x <span class="nb">&</span> y <span class="k">\\</span> z <span class="nb">&</span> -v <span class="k">\end</span><span class="nb">{</span>Vmatrix<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{Vmatrix}-x&y\\z&-v\end{Vmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo symmetric="true">‖</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mo>−</mo> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mo>−</mo> <mi>v</mi> </mtd> </mtr> </mtable> <mo symmetric="true">‖</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{Vmatrix}-x&y\\z&-v\end{Vmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e238627a6632c8609d581e0af95fe16c26075f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:11.473ex; height:6.176ex;" alt="{\displaystyle {\begin{Vmatrix}-x&y\\z&-v\end{Vmatrix}}}"/></span> </td></tr> <tr> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>bmatrix<span class="nb">}</span> 0 <span class="nb">&</span> <span class="k">\cdots</span> <span class="nb">&</span> 0 <span class="k">\\</span> <span class="k">\vdots</span> <span class="nb">&</span> <span class="k">\ddots</span> <span class="nb">&</span> <span class="k">\vdots</span> <span class="k">\\</span> 0 <span class="nb">&</span> <span class="k">\cdots</span> <span class="nb">&</span> 0 <span class="k">\end</span><span class="nb">{</span>bmatrix<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>⋯</mo> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>⋮</mo> </mtd> <mtd> <mo>⋱</mo> </mtd> <mtd> <mo>⋮</mo> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>⋯</mo> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4f55c58e19b82c51845459aa1ce701775247fa5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.005ex; width:13.801ex; height:11.009ex;" alt="{\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}}"/></span> </td></tr> <tr> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>Bmatrix<span class="nb">}</span> x <span class="nb">&</span> y <span class="k">\\</span> z <span class="nb">&</span> v <span class="k">\end</span><span class="nb">{</span>Bmatrix<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mi>v</mi> </mtd> </mtr> </mtable> <mo>}</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96d51a7c33c262e29df6b3e16c46f5cfd8711ec7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:9.045ex; height:6.176ex;" alt="{\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}}"/></span> </td></tr> <tr> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>pmatrix<span class="nb">}</span> x <span class="nb">&</span> y <span class="k">\\</span> z <span class="nb">&</span> v <span class="k">\end</span><span class="nb">{</span>pmatrix<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mi>v</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c3dec1cace268b4470ef04e59c55f5475764b01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:8.98ex; height:6.176ex;" alt="{\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}}"/></span> </td></tr> <tr> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\bigl</span>( <span class="k">\begin</span><span class="nb">{</span>smallmatrix<span class="nb">}</span> a<span class="nb">&</span>b<span class="k">\\</span> c<span class="nb">&</span>d <span class="k">\end</span><span class="nb">{</span>smallmatrix<span class="nb">}</span> <span class="k">\bigr</span>) </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> </mtd> <mtd> <mi>d</mi> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c11426bdf6c38b6a4e9d1f06f9a6b914614d92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.384ex; height:3.343ex;" alt="{\displaystyle {\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}}"/></span> </td></tr> <tr> <td>Case distinctions </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span>f(n) = <span class="k">\begin</span><span class="nb">{</span>cases<span class="nb">}</span> n/2, <span class="nb">&</span> <span class="k">\text</span><span class="nb">{</span>if <span class="nb">}</span>n<span class="k">\text</span><span class="nb">{</span> is even<span class="nb">}</span> <span class="k">\\</span> 3n+1, <span class="nb">&</span> <span class="k">\text</span><span class="nb">{</span>if <span class="nb">}</span>n<span class="k">\text</span><span class="nb">{</span> is odd<span class="nb">}</span> <span class="k">\end</span><span class="nb">{</span>cases<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(n)={\begin{cases}n/2,&{\text{if }}n{\text{ is even}}\\3n+1,&{\text{if }}n{\text{ is odd}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>,</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>if </mtext> </mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> is even</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>if </mtext> </mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> is odd</mtext> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(n)={\begin{cases}n/2,&{\text{if }}n{\text{ is even}}\\3n+1,&{\text{if }}n{\text{ is odd}}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9886ceef1d61d49304a633be8ef555583a76dc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.248ex; height:6.176ex;" alt="{\displaystyle f(n)={\begin{cases}n/2,&{\text{if }}n{\text{ is even}}\\3n+1,&{\text{if }}n{\text{ is odd}}\end{cases}}}"/></span> </td></tr> <tr> <td>Simultaneous equations </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>cases<span class="nb">}</span> 3x + 5y + z <span class="k">\\</span> 7x - 2y + 4z <span class="k">\\</span> -6x + 3y + 2z <span class="k">\end</span><span class="nb">{</span>cases<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>5</mn> <mi>y</mi> <mo>+</mo> <mi>z</mi> </mtd> </mtr> <mtr> <mtd> <mn>7</mn> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mi>y</mi> <mo>+</mo> <mn>4</mn> <mi>z</mi> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>6</mn> <mi>x</mi> <mo>+</mo> <mn>3</mn> <mi>y</mi> <mo>+</mo> <mn>2</mn> <mi>z</mi> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bcd059275a1fc0bfaf8f67a269115416368c75f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:17.367ex; height:8.509ex;" alt="{\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}}"/></span> </td></tr> <tr> <td rowspan="2">Multiline equations </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>align<span class="nb">}</span> f(x) <span class="nb">&</span> = (a+b)<span class="nb">^</span>2 <span class="k">\\</span> <span class="nb">&</span> = a<span class="nb">^</span>2+2ab+b<span class="nb">^</span>2 <span class="k">\\</span> <span class="k">\end</span><span class="nb">{</span>align<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}f(x)&=(a+b)^{2}\\&=a^{2}+2ab+b^{2}\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>a</mi> <mi>b</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}f(x)&=(a+b)^{2}\\&=a^{2}+2ab+b^{2}\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8225527ac614ac527f50111362774e7c2ea75aad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.674ex; height:6.509ex;" alt="{\displaystyle {\begin{aligned}f(x)&=(a+b)^{2}\\&=a^{2}+2ab+b^{2}\\\end{aligned}}}"/></span> </td></tr> <tr> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>alignat<span class="nb">}{</span>2<span class="nb">}</span> f(x) <span class="nb">&</span> = (a-b)<span class="nb">^</span>2 <span class="k">\\</span> <span class="nb">&</span> = a<span class="nb">^</span>2-2ab+b<span class="nb">^</span>2 <span class="k">\\</span> <span class="k">\end</span><span class="nb">{</span>alignat<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{alignedat}{2}f(x)&=(a-b)^{2}\\&=a^{2}-2ab+b^{2}\\\end{alignedat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left" rowspacing="3pt" columnspacing="0em 0em 0em 0em" displaystyle="true"> <mtr> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mi>a</mi> <mi>b</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{alignedat}{2}f(x)&=(a-b)^{2}\\&=a^{2}-2ab+b^{2}\\\end{alignedat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f39d4e1895c0635326d03139f3433e88411e9847" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.674ex; height:6.509ex;" alt="{\displaystyle {\begin{alignedat}{2}f(x)&=(a-b)^{2}\\&=a^{2}-2ab+b^{2}\\\end{alignedat}}}"/></span> </td></tr> <tr> <td rowspan="2">Multiline equations with multiple alignments per row </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>align<span class="nb">}</span> f(a,b) <span class="nb">&</span> = (a+b)<span class="nb">^</span>2 <span class="nb">&&</span> = (a+b)(a+b) <span class="k">\\</span> <span class="nb">&</span> = a<span class="nb">^</span>2+ab+ba+b<span class="nb">^</span>2 <span class="nb">&&</span> = a<span class="nb">^</span>2+2ab+b<span class="nb">^</span>2 <span class="k">\\</span> <span class="k">\end</span><span class="nb">{</span>align<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}f(a,b)&=(a+b)^{2}&&=(a+b)(a+b)\\&=a^{2}+ab+ba+b^{2}&&=a^{2}+2ab+b^{2}\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>a</mi> <mi>b</mi> <mo>+</mo> <mi>b</mi> <mi>a</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>a</mi> <mi>b</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}f(a,b)&=(a+b)^{2}&&=(a+b)(a+b)\\&=a^{2}+ab+ba+b^{2}&&=a^{2}+2ab+b^{2}\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/906dee75f13021618c7136124ef64e4d9ec35a9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:49.009ex; height:6.509ex;" alt="{\displaystyle {\begin{aligned}f(a,b)&=(a+b)^{2}&&=(a+b)(a+b)\\&=a^{2}+ab+ba+b^{2}&&=a^{2}+2ab+b^{2}\\\end{aligned}}}"/></span> </td></tr> <tr> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>alignat<span class="nb">}{</span>3<span class="nb">}</span> f(a,b) <span class="nb">&</span> = (a+b)<span class="nb">^</span>2 <span class="nb">&&</span> = (a+b)(a+b) <span class="k">\\</span> <span class="nb">&</span> = a<span class="nb">^</span>2+ab+ba+b<span class="nb">^</span>2 <span class="nb">&&</span> = a<span class="nb">^</span>2+2ab+b<span class="nb">^</span>2 <span class="k">\\</span> <span class="k">\end</span><span class="nb">{</span>alignat<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{alignedat}{3}f(a,b)&=(a+b)^{2}&&=(a+b)(a+b)\\&=a^{2}+ab+ba+b^{2}&&=a^{2}+2ab+b^{2}\\\end{alignedat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left" rowspacing="3pt" columnspacing="0em 0em 0em 0em 0em 0em" displaystyle="true"> <mtr> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>a</mi> <mi>b</mi> <mo>+</mo> <mi>b</mi> <mi>a</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>a</mi> <mi>b</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{alignedat}{3}f(a,b)&=(a+b)^{2}&&=(a+b)(a+b)\\&=a^{2}+ab+ba+b^{2}&&=a^{2}+2ab+b^{2}\\\end{alignedat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c9339b8cb2425ae9aba333d8f6cbeb74156c2e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:44.363ex; height:6.509ex;" alt="{\displaystyle {\begin{alignedat}{3}f(a,b)&=(a+b)^{2}&&=(a+b)(a+b)\\&=a^{2}+ab+ba+b^{2}&&=a^{2}+2ab+b^{2}\\\end{alignedat}}}"/></span> </td></tr> <tr> <td>Multiline equations <small>(must define number of columns used ({lcl})) (should not be used unless needed)</small> </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>array<span class="nb">}{</span>lcl<span class="nb">}</span> z <span class="nb">&</span> = <span class="nb">&</span> a <span class="k">\\</span> f(x,y,z) <span class="nb">&</span> = <span class="nb">&</span> x + y + z <span class="k">\end</span><span class="nb">{</span>array<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left center left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo>+</mo> <mi>z</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48b0ec21214150ffb798d991bd7e661bf37f002c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.188ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}"/></span> </td></tr> <tr> <td>Multiline equations (more) </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>array<span class="nb">}{</span>lcr<span class="nb">}</span> z <span class="nb">&</span> = <span class="nb">&</span> a <span class="k">\\</span> f(x,y,z) <span class="nb">&</span> = <span class="nb">&</span> x + y + z <span class="k">\end</span><span class="nb">{</span>array<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left center right" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo>+</mo> <mi>z</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cc898023342d85cdd2b2b80921c3e4140ac0b1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.188ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}"/></span> </td></tr> <tr> <td>Multiline alignment using <code>&</code> to left align (top example) versus <code>&&</code> to right align (bottom example) the last column </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>alignat<span class="nb">}{</span>4<span class="nb">}</span> F:<span class="k">\;</span> <span class="nb">&&</span> C(X) <span class="nb">&&</span> <span class="k">\;\to\;</span> <span class="nb">&</span> C(X) <span class="k">\\</span> <span class="nb">&&</span> g <span class="nb">&&</span> <span class="k">\;\mapsto\;</span> <span class="nb">&</span> g<span class="nb">^</span>2 <span class="k">\end</span><span class="nb">{</span>alignat<span class="nb">}</span> </pre></div> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>alignat<span class="nb">}{</span>4<span class="nb">}</span> F:<span class="k">\;</span> <span class="nb">&&</span> C(X) <span class="nb">&&</span> <span class="k">\;\to\;</span> <span class="nb">&&</span> C(X) <span class="k">\\</span> <span class="nb">&&</span> g <span class="nb">&&</span> <span class="k">\;\mapsto\;</span> <span class="nb">&&</span> g<span class="nb">^</span>2 <span class="k">\end</span><span class="nb">{</span>alignat<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{alignedat}{4}F:\;&&C(X)&&\;\to \;&C(X)\\&&g&&\;\mapsto \;&g^{2}\end{alignedat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left" rowspacing="3pt" columnspacing="0em 0em 0em 0em 0em 0em 0em 0em" displaystyle="true"> <mtr> <mtd> <mi>F</mi> <mo>:</mo> <mspace width="thickmathspace"></mspace> </mtd> <mtd></mtd> <mtd> <mi>C</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mtd> <mtd></mtd> <mtd> <mspace width="thickmathspace"></mspace> <mo stretchy="false">→</mo> <mspace width="thickmathspace"></mspace> </mtd> <mtd> <mi>C</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd></mtd> <mtd></mtd> <mtd> <mi>g</mi> </mtd> <mtd></mtd> <mtd> <mspace width="thickmathspace"></mspace> <mo stretchy="false">↦</mo> <mspace width="thickmathspace"></mspace> </mtd> <mtd> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{alignedat}{4}F:\;&&C(X)&&\;\to \;&C(X)\\&&g&&\;\mapsto \;&g^{2}\end{alignedat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/129cfe75834354298ff2d1d83229868a97b536f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:19.155ex; height:6.176ex;" alt="{\displaystyle {\begin{alignedat}{4}F:\;&&C(X)&&\;\to \;&C(X)\\&&g&&\;\mapsto \;&g^{2}\end{alignedat}}}"/></span><br/><br/> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{alignedat}{4}F:\;&&C(X)&&\;\to \;&&C(X)\\&&g&&\;\mapsto \;&&g^{2}\end{alignedat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left" rowspacing="3pt" columnspacing="0em 0em 0em 0em 0em 0em 0em 0em" displaystyle="true"> <mtr> <mtd> <mi>F</mi> <mo>:</mo> <mspace width="thickmathspace"></mspace> </mtd> <mtd></mtd> <mtd> <mi>C</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mtd> <mtd></mtd> <mtd> <mspace width="thickmathspace"></mspace> <mo stretchy="false">→</mo> <mspace width="thickmathspace"></mspace> </mtd> <mtd></mtd> <mtd> <mi>C</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd></mtd> <mtd></mtd> <mtd> <mi>g</mi> </mtd> <mtd></mtd> <mtd> <mspace width="thickmathspace"></mspace> <mo stretchy="false">↦</mo> <mspace width="thickmathspace"></mspace> </mtd> <mtd></mtd> <mtd> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{alignedat}{4}F:\;&&C(X)&&\;\to \;&&C(X)\\&&g&&\;\mapsto \;&&g^{2}\end{alignedat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdac406c96e6daf6ef29bde7cae08a9c161b1ba0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:19.155ex; height:6.176ex;" alt="{\displaystyle {\begin{alignedat}{4}F:\;&&C(X)&&\;\to \;&&C(X)\\&&g&&\;\mapsto \;&&g^{2}\end{alignedat}}}"/></span> </p> </td></tr> <tr> <td>Breaking up a long expression so that it wraps when necessary (this sometimes requires workarounds for correct spacing) </td> <td> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span>The function <math>f</math> is defined by <math>f(x) = <span class="nb">{}</span></math><math display=inline><span class="k">\sum</span><span class="nb">_{</span>n=0<span class="nb">}^</span><span class="k">\infty</span> a<span class="nb">_</span>n x<span class="nb">^</span>n = <span class="nb">{}</span></math><math>a<span class="nb">_</span>0+a<span class="nb">_</span>1x+a<span class="nb">_</span>2x<span class="nb">^</span>2+<span class="k">\cdots</span>.</math> </pre></div> </td> <td>The function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"/></span> is defined by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)={}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1d6117487dd34f6af11354dbe91eb765a253a8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.516ex; height:2.843ex;" alt="{\displaystyle f(x)={}}"/></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \sum _{n=0}^{\infty }a_{n}x^{n}={}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \sum _{n=0}^{\infty }a_{n}x^{n}={}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ffd53581762c3636af445c91fe985aef0d56c89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.255ex; height:3.176ex;" alt="{\textstyle \sum _{n=0}^{\infty }a_{n}x^{n}={}}"/></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{0}+a_{1}x+a_{2}x^{2}+\cdots .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{0}+a_{1}x+a_{2}x^{2}+\cdots .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65c6347affd1737f4086cc6b3f823acb01f54587" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.844ex; height:3.009ex;" alt="{\displaystyle a_{0}+a_{1}x+a_{2}x^{2}+\cdots .}"/></span> </td></tr> <tr> <td>Arrays </td> <td><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\begin</span><span class="nb">{</span>array<span class="nb">}{</span>|c|c|c|<span class="nb">}</span> a <span class="nb">&</span> b <span class="nb">&</span> S <span class="k">\\</span> <span class="k">\hline</span> 0 <span class="nb">&</span> 0 <span class="nb">&</span> 1 <span class="k">\\</span> 0 <span class="nb">&</span> 1 <span class="nb">&</span> 1 <span class="k">\\</span> 1 <span class="nb">&</span> 0 <span class="nb">&</span> 1 <span class="k">\\</span> 1 <span class="nb">&</span> 1 <span class="nb">&</span> 0 <span class="k">\\</span> <span class="k">\end</span><span class="nb">{</span>array<span class="nb">}</span> </pre></div> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{|c|c|c|}a&b&S\\\hline 0&0&1\\0&1&1\\1&0&1\\1&1&0\\\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <menclose notation="left right"> <mtable columnalign="center center center" rowspacing="4pt" columnspacing="1em" rowlines="solid none" columnlines="solid solid"> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mi>b</mi> </mtd> <mtd> <mi>S</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </menclose> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{|c|c|c|}a&b&S\\\hline 0&0&1\\0&1&1\\1&0&1\\1&1&0\\\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d53f0ae16da2cc7823fe018a22118822fba1d32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.005ex; width:10.719ex; height:17.176ex;" alt="{\displaystyle {\begin{array}{|c|c|c|}a&b&S\\\hline 0&0&1\\0&1&1\\1&0&1\\1&1&0\\\end{array}}}"/></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Parenthesizing_big_expressions,_brackets,_bars" data-mw-thread-id="h-Parenthesizing_big_expressions,_brackets,_bars-Formatting_using_LaTeX"><span id="Parenthesizing_big_expressions.2C_brackets.2C_bars"></span><span data-mw-comment-start="" id="h-Parenthesizing_big_expressions,_brackets,_bars-Formatting_using_LaTeX"></span>Parenthesizing big expressions, brackets, bars<span data-mw-comment-end="h-Parenthesizing_big_expressions,_brackets,_bars-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=37" title="Edit section: Parenthesizing big expressions, brackets, bars"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Feature</th> <th>Syntax</th> <th>How it looks rendered </th></tr> <tr> <td>Bad ✗ </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">( <span class="k">\frac</span><span class="nb">{</span>1<span class="nb">}{</span>2<span class="nb">}</span> )<span class="nb">^</span>n</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\frac {1}{2}})^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\frac {1}{2}})^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7e4b860fdae0b0e1d80291c2fd1250f1b12d975" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.026ex; height:5.176ex;" alt="{\displaystyle ({\frac {1}{2}})^{n}}"/></span> </td></tr> <tr> <td>Good ✓ </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> ( <span class="k">\frac</span><span class="nb">{</span>1<span class="nb">}{</span>2<span class="nb">}</span> <span class="k">\right</span> )<span class="nb">^</span>n</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{2}}\right)^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{2}}\right)^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b02387caab502d21e8711df39c0a90941cb6315" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:6.638ex; height:6.176ex;" alt="{\displaystyle \left({\frac {1}{2}}\right)^{n}}"/></span> </td></tr></tbody></table> <p>You can use various delimiters with \left and \right: </p> <table class="wikitable"> <tbody><tr> <th>Feature </th> <th>Syntax </th> <th>How it looks rendered </th></tr> <tr> <td>Parentheses </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> ( <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> )</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {a}{b}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {a}{b}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00dd2fdf5ae1c8899d36296546fa1dc315a07f15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:4.841ex; height:5.009ex;" alt="{\displaystyle \left({\frac {a}{b}}\right)}"/></span> </td></tr> <tr> <td>Brackets </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> [ <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> ] <span class="k">\quad</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\lbrack</span> <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\rbrack</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{\frac {a}{b}}\right]\quad \left\lbrack {\frac {a}{b}}\right\rbrack }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>]</mo> </mrow> <mspace width="1em"></mspace> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{\frac {a}{b}}\right]\quad \left\lbrack {\frac {a}{b}}\right\rbrack }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8680e564275ad3a1c6179240f28c07f34f7b2858" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.231ex; height:5.009ex;" alt="{\displaystyle \left[{\frac {a}{b}}\right]\quad \left\lbrack {\frac {a}{b}}\right\rbrack }"/></span> </td></tr> <tr> <td>Braces </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\{</span> <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\}</span> <span class="k">\quad</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\lbrace</span> <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\rbrace</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{{\frac {a}{b}}\right\}\quad \left\lbrace {\frac {a}{b}}\right\rbrace }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>{</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>}</mo> </mrow> <mspace width="1em"></mspace> <mrow> <mo>{</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>}</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{{\frac {a}{b}}\right\}\quad \left\lbrace {\frac {a}{b}}\right\rbrace }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e32a8d0bb05d7e24e69a3927bb1cf940f9526a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.043ex; height:5.009ex;" alt="{\displaystyle \left\{{\frac {a}{b}}\right\}\quad \left\lbrace {\frac {a}{b}}\right\rbrace }"/></span> </td></tr> <tr> <td>Angle brackets </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\langle</span> <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\rangle</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\langle {\frac {a}{b}}\right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\langle {\frac {a}{b}}\right\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67ddc72b657af90a71036ff196873f443862da59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:4.906ex; height:5.009ex;" alt="{\displaystyle \left\langle {\frac {a}{b}}\right\rangle }"/></span> </td></tr> <tr> <td>Bars and double bars </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> | <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\vert</span> <span class="k">\quad</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\Vert</span> <span class="k">\frac</span><span class="nb">{</span>c<span class="nb">}{</span>d<span class="nb">}</span> <span class="k">\right</span> <span class="k">\|</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left|{\frac {a}{b}}\right\vert \quad \left\Vert {\frac {c}{d}}\right\|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>|</mo> </mrow> <mspace width="1em"></mspace> <mrow> <mo symmetric="true">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>d</mi> </mfrac> </mrow> <mo symmetric="true">‖</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|{\frac {a}{b}}\right\vert \quad \left\Vert {\frac {c}{d}}\right\|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92051abfe823f78ede4fdf12fb4d631dfc93250e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.446ex; height:5.176ex;" alt="{\displaystyle \left|{\frac {a}{b}}\right\vert \quad \left\Vert {\frac {c}{d}}\right\|}"/></span> </td></tr> <tr> <td>Floor and ceiling functions: </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\lfloor</span> <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\rfloor</span> <span class="k">\quad</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\lceil</span> <span class="k">\frac</span><span class="nb">{</span>c<span class="nb">}{</span>d<span class="nb">}</span> <span class="k">\right</span> <span class="k">\rceil</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\lfloor {\frac {a}{b}}\right\rfloor \quad \left\lceil {\frac {c}{d}}\right\rceil }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⌊</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>⌋</mo> </mrow> <mspace width="1em"></mspace> <mrow> <mo>⌈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>d</mi> </mfrac> </mrow> <mo>⌉</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\lfloor {\frac {a}{b}}\right\rfloor \quad \left\lceil {\frac {c}{d}}\right\rceil }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea880dba8c354264620a2f9d798ccc5518053227" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.738ex; height:5.009ex;" alt="{\displaystyle \left\lfloor {\frac {a}{b}}\right\rfloor \quad \left\lceil {\frac {c}{d}}\right\rceil }"/></span> </td></tr> <tr> <td>Slashes and backslashes </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> / <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\backslash</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left/{\frac {a}{b}}\right\backslash }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo fence="true" stretchy="true" symmetric="true">/</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo fence="true" stretchy="true" symmetric="true">\</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left/{\frac {a}{b}}\right\backslash }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1218880f4d48a8a48b87ce6dbdb34e76eaa002a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:5.836ex; height:5.009ex;" alt="{\displaystyle \left/{\frac {a}{b}}\right\backslash }"/></span> </td></tr> <tr> <td>Up, down, and up-down arrows </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\uparrow</span> <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\downarrow</span> <span class="k">\quad</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\Uparrow</span> <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\Downarrow</span> <span class="k">\quad</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\updownarrow</span> <span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span> <span class="k">\right</span> <span class="k">\Updownarrow</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\uparrow {\frac {a}{b}}\right\downarrow \quad \left\Uparrow {\frac {a}{b}}\right\Downarrow \quad \left\updownarrow {\frac {a}{b}}\right\Updownarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo fence="true" symmetric="true">↑</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo fence="true" symmetric="true">↓</mo> </mrow> <mspace width="1em"></mspace> <mrow> <mo fence="true" symmetric="true">⇑</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo fence="true" symmetric="true">⇓</mo> </mrow> <mspace width="1em"></mspace> <mrow> <mo fence="true" symmetric="true">↕</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo fence="true" symmetric="true">⇕</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\uparrow {\frac {a}{b}}\right\downarrow \quad \left\Uparrow {\frac {a}{b}}\right\Downarrow \quad \left\updownarrow {\frac {a}{b}}\right\Updownarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20d6b8c7566e51876eb03a65b87e0515feb80cd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.693ex; height:5.176ex;" alt="{\displaystyle \left\uparrow {\frac {a}{b}}\right\downarrow \quad \left\Uparrow {\frac {a}{b}}\right\Downarrow \quad \left\updownarrow {\frac {a}{b}}\right\Updownarrow }"/></span> </td></tr> <tr> <td>Delimiters can be mixed,<br/>as long as \left and \right match </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> [ 0,1 <span class="k">\right</span> )</code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> <span class="k">\langle</span> <span class="k">\psi</span> <span class="k">\right</span> |</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[0,1\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[0,1\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/232328a85dbb3301146f3a1fd302bfe1408fb902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.91ex; height:2.843ex;" alt="{\displaystyle \left[0,1\right)}"/></span><br/> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\langle \psi \right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⟨</mo> <mi>ψ</mi> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\langle \psi \right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e49a8b4981aed51cf30885a8e0bad5e40ae499b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.065ex; height:2.843ex;" alt="{\displaystyle \left\langle \psi \right|}"/></span> </td></tr> <tr> <td>Use \left. and \right. if you<br/> do not want a delimiter to appear </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span> . <span class="k">\frac</span><span class="nb">{</span>A<span class="nb">}{</span>B<span class="nb">}</span> <span class="k">\right</span> <span class="k">\}</span> <span class="k">\to</span> X</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left.{\frac {A}{B}}\right\}\to X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mi>B</mi> </mfrac> </mrow> <mo>}</mo> </mrow> <mo stretchy="false">→</mo> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left.{\frac {A}{B}}\right\}\to X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/345c73c3f474f869f413863ba652a3607b27b68d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:9.937ex; height:6.176ex;" alt="{\displaystyle \left.{\frac {A}{B}}\right\}\to X}"/></span> </td></tr> <tr> <td rowspan="7">Size of the delimiters (add "l" or "r" to indicate the side for proper spacing) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">( <span class="k">\bigl</span>( <span class="k">\Bigl</span>( <span class="k">\biggl</span>( <span class="k">\Biggl</span>( <span class="k">\dots</span> <span class="k">\Biggr</span>] <span class="k">\biggr</span>] <span class="k">\Bigr</span>] <span class="k">\bigr</span>] ]</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\bigl (}{\Bigl (}{\biggl (}{\Biggl (}\dots {\Biggr ]}{\biggr ]}{\Bigr ]}{\bigr ]}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mo>…</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.470em" minsize="2.470em">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">]</mo> </mrow> </mrow> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\bigl (}{\Bigl (}{\biggl (}{\Biggl (}\dots {\Biggr ]}{\biggr ]}{\Bigr ]}{\bigr ]}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d166c08a30ad598edc84d0bbe0223be8bcc5a6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:15.703ex; height:7.509ex;" alt="{\displaystyle ({\bigl (}{\Bigl (}{\biggl (}{\Biggl (}\dots {\Biggr ]}{\biggr ]}{\Bigr ]}{\bigr ]}]}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\{</span> <span class="k">\bigl\{</span> <span class="k">\Bigl\{</span> <span class="k">\biggl\{</span> <span class="k">\Biggl\{</span> <span class="k">\dots</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\Biggr\rangle</span> <span class="k">\biggr\rangle</span> <span class="k">\Bigr\rangle</span> <span class="k">\bigr\rangle</span> <span class="k">\rangle</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{{\bigl \{}{\Bigl \{}{\biggl \{}{\Biggl \{}\dots {\Biggr \rangle }{\biggr \rangle }{\Bigr \rangle }{\bigr \rangle }\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">{</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">{</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">{</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.470em" minsize="2.470em">{</mo> </mrow> </mrow> <mo>…</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.470em" minsize="2.470em">⟩</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">⟩</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">⟩</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">⟩</mo> </mrow> </mrow> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{{\bigl \{}{\Bigl \{}{\biggl \{}{\Biggl \{}\dots {\Biggr \rangle }{\biggr \rangle }{\Bigr \rangle }{\bigr \rangle }\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62f0df0a815b5be3f7be2a67e5b22c8d78c0fff1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.22ex; height:7.509ex;" alt="{\displaystyle \{{\bigl \{}{\Bigl \{}{\biggl \{}{\Biggl \{}\dots {\Biggr \rangle }{\biggr \rangle }{\Bigr \rangle }{\bigr \rangle }\rangle }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\|</span> <span class="k">\big\|</span> <span class="k">\Big\|</span> <span class="k">\bigg\|</span> <span class="k">\Bigg\|</span> <span class="k">\dots</span> <span class="k">\Bigg</span>| <span class="k">\bigg</span>| <span class="k">\Big</span>| <span class="k">\big</span>| |</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \|{\big \|}{\Big \|}{\bigg \|}{\Bigg \|}\dots {\Bigg |}{\bigg |}{\Big |}{\big |}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo symmetric="true" maxsize="1.2em" minsize="1.2em">‖</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo symmetric="true" maxsize="1.623em" minsize="1.623em">‖</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo symmetric="true" maxsize="2.047em" minsize="2.047em">‖</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo symmetric="true" maxsize="2.470em" minsize="2.470em">‖</mo> </mrow> </mrow> <mo>…</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">|</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.047em" minsize="2.047em">|</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">|</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">|</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \|{\big \|}{\Big \|}{\bigg \|}{\Bigg \|}\dots {\Bigg |}{\bigg |}{\Big |}{\big |}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf02dbcab015524b52d8914505316ccde3e033f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:12.544ex; height:6.176ex;" alt="{\displaystyle \|{\big \|}{\Big \|}{\bigg \|}{\Bigg \|}\dots {\Bigg |}{\bigg |}{\Big |}{\big |}|}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\lfloor</span> <span class="k">\bigl\lfloor</span> <span class="k">\Bigl\lfloor</span> <span class="k">\biggl\lfloor</span> <span class="k">\Biggl\lfloor</span> <span class="k">\dots</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\Biggr\rceil</span> <span class="k">\biggr\rceil</span> <span class="k">\Bigr\rceil</span> <span class="k">\bigr\rceil</span> <span class="k">\ceil</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lfloor {\bigl \lfloor }{\Bigl \lfloor }{\biggl \lfloor }{\Biggl \lfloor }\dots {\Biggr \rceil }{\biggr \rceil }{\Bigr \rceil }{\bigr \rceil }\rceil }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⌊</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">⌊</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.623em" minsize="1.623em">⌊</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">⌊</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.470em" minsize="2.470em">⌊</mo> </mrow> </mrow> <mo>…</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.470em" minsize="2.470em">⌉</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">⌉</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.623em" minsize="1.623em">⌉</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">⌉</mo> </mrow> </mrow> <mo fence="false" stretchy="false">⌉</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lfloor {\bigl \lfloor }{\Bigl \lfloor }{\biggl \lfloor }{\Biggl \lfloor }\dots {\Biggr \rceil }{\biggr \rceil }{\Bigr \rceil }{\bigr \rceil }\rceil }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f7c3699bbfc396cdcb79dbbc220feb5dddd8e11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:15.893ex; height:7.509ex;" alt="{\displaystyle \lfloor {\bigl \lfloor }{\Bigl \lfloor }{\biggl \lfloor }{\Biggl \lfloor }\dots {\Biggr \rceil }{\biggr \rceil }{\Bigr \rceil }{\bigr \rceil }\rceil }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\uparrow</span> <span class="k">\big\uparrow</span> <span class="k">\Big\uparrow</span> <span class="k">\bigg\uparrow</span> <span class="k">\Bigg\uparrow</span> <span class="k">\dots</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\Bigg\Downarrow</span> <span class="k">\bigg\Downarrow</span> <span class="k">\Big\Downarrow</span> <span class="k">\big\Downarrow</span> <span class="k">\Downarrow</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \uparrow {\big \uparrow }{\Big \uparrow }{\bigg \uparrow }{\Bigg \uparrow }\dots {\Bigg \Downarrow }{\bigg \Downarrow }{\Big \Downarrow }{\big \Downarrow }\Downarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↑</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="1.2em" minsize="1.2em">↑</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="1.623em" minsize="1.623em">↑</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="2.047em" minsize="2.047em">↑</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="2.470em" minsize="2.470em">↑</mo> </mrow> </mrow> <mo>⋯</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="2.470em" minsize="2.470em">⇓</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="2.047em" minsize="2.047em">⇓</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="1.623em" minsize="1.623em">⇓</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="1.2em" minsize="1.2em">⇓</mo> </mrow> </mrow> <mo stretchy="false">⇓</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \uparrow {\big \uparrow }{\Big \uparrow }{\bigg \uparrow }{\Bigg \uparrow }\dots {\Bigg \Downarrow }{\bigg \Downarrow }{\Big \Downarrow }{\big \Downarrow }\Downarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/367f10c221e53b5e732b953c3c2f041efc89ea22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.804ex; height:6.176ex;" alt="{\displaystyle \uparrow {\big \uparrow }{\Big \uparrow }{\bigg \uparrow }{\Bigg \uparrow }\dots {\Bigg \Downarrow }{\bigg \Downarrow }{\Big \Downarrow }{\big \Downarrow }\Downarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\updownarrow</span> <span class="k">\big\updownarrow</span> <span class="k">\Big\updownarrow</span> <span class="k">\bigg\updownarrow</span> <span class="k">\Bigg\updownarrow</span> <span class="k">\dots</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\Bigg\Updownarrow</span> <span class="k">\bigg\Updownarrow</span> <span class="k">\Big\Updownarrow</span> <span class="k">\big\Updownarrow</span> <span class="k">\Updownarrow</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \updownarrow {\big \updownarrow }{\Big \updownarrow }{\bigg \updownarrow }{\Bigg \updownarrow }\dots {\Bigg \Updownarrow }{\bigg \Updownarrow }{\Big \Updownarrow }{\big \Updownarrow }\Updownarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↕</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="1.2em" minsize="1.2em">↕</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="1.623em" minsize="1.623em">↕</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="2.047em" minsize="2.047em">↕</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="2.470em" minsize="2.470em">↕</mo> </mrow> </mrow> <mo>⋯</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="2.470em" minsize="2.470em">⇕</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="2.047em" minsize="2.047em">⇕</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="1.623em" minsize="1.623em">⇕</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" symmetric="true" maxsize="1.2em" minsize="1.2em">⇕</mo> </mrow> </mrow> <mo stretchy="false">⇕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \updownarrow {\big \updownarrow }{\Big \updownarrow }{\bigg \updownarrow }{\Bigg \updownarrow }\dots {\Bigg \Updownarrow }{\bigg \Updownarrow }{\Big \Updownarrow }{\big \Updownarrow }\Updownarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c80dfd51f2b16ca1d56fa2e977d933e0f19cd4c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.804ex; height:6.176ex;" alt="{\displaystyle \updownarrow {\big \updownarrow }{\Big \updownarrow }{\bigg \updownarrow }{\Bigg \updownarrow }\dots {\Bigg \Updownarrow }{\bigg \Updownarrow }{\Big \Updownarrow }{\big \Updownarrow }\Updownarrow }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">/ <span class="k">\big</span>/ <span class="k">\Big</span>/ <span class="k">\bigg</span>/ <span class="k">\Bigg</span>/ <span class="k">\dots</span></code><br/> <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\Bigg\backslash</span> <span class="k">\bigg\backslash</span> <span class="k">\Big\backslash</span> <span class="k">\big\backslash</span> <span class="k">\backslash</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle /{\big /}{\Big /}{\bigg /}{\Bigg /}\dots {\Bigg \backslash }{\bigg \backslash }{\Big \backslash }{\big \backslash }\backslash }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em">/</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.623em" minsize="1.623em">/</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="2.047em" minsize="2.047em">/</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="2.470em" minsize="2.470em">/</mo> </mrow> </mrow> <mo>…</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="2.470em" minsize="2.470em">\</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="2.047em" minsize="2.047em">\</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.623em" minsize="1.623em">\</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo fence="true" stretchy="true" symmetric="true" maxsize="1.2em" minsize="1.2em">\</mo> </mrow> </mrow> <mi class="MJX-variant" mathvariant="normal">∖</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle /{\big /}{\Big /}{\bigg /}{\Bigg /}\dots {\Bigg \backslash }{\bigg \backslash }{\Big \backslash }{\big \backslash }\backslash }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49179250dc76609a33af4492ab118d22ea35fefb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:23.07ex; height:7.509ex;" alt="{\displaystyle /{\big /}{\Big /}{\bigg /}{\Bigg /}\dots {\Bigg \backslash }{\bigg \backslash }{\Big \backslash }{\big \backslash }\backslash }"/></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Display_attribute" data-mw-thread-id="h-Display_attribute-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Display_attribute-Formatting_using_LaTeX"></span>Display attribute<span data-mw-comment-end="h-Display_attribute-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=38" title="Edit section: Display attribute"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <code class="nowrap" style=""><math></code> tag can take a <code>display</code> attribute with possible values of <code>inline</code> and <code>block</code>. </p> <div class="mw-heading mw-heading4"><h4 id="Inline" data-mw-thread-id="h-Inline-Display_attribute"><span data-mw-comment-start="" id="h-Inline-Display_attribute"></span>Inline<span data-mw-comment-end="h-Inline-Display_attribute"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=39" title="Edit section: Inline"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If the value of the <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">display</code> attribute is <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">inline</code>, the contents will be rendered in inline mode: there will be no new paragraph for the equation and the operators will be rendered to consume only a small amount of vertical space. </p><p>The sum <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \sum _{i=0}^{\infty }2^{-i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>i</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \sum _{i=0}^{\infty }2^{-i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/632818299003b79547489c56439a7374f6c33810" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.982ex; height:3.343ex;" alt="{\textstyle \sum _{i=0}^{\infty }2^{-i}}"/></span> converges to 2. </p><p>The next line-width is not disturbed by large operators. </p><p>The code for the math example reads: </p> <dl><dd><code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math</span><span class="w"> </span><span class="na">display=</span><span class="s">"inline"</span><span class="nt">></span>\sum_{i=0}^\infty<span class="w"> </span>2^{-i}<span class="nt"></math></span></code></dd></dl> <p>The quotation marks around <code>inline</code> are optional and <code>display=inline</code> is also valid.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Technically, the command <i>\textstyle</i> will be added to the user input before the TeX command is passed to the renderer. The result will be displayed without further formatting by outputting the image or MathML element to the page. </p> <div class="mw-heading mw-heading4"><h4 id="Block" data-mw-thread-id="h-Block-Display_attribute"><span data-mw-comment-start="" id="h-Block-Display_attribute"></span>Block<span data-mw-comment-end="h-Block-Display_attribute"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=40" title="Edit section: Block"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In block-style the equation is rendered in its own paragraph and the operators are rendered consuming less horizontal space. The equation is indented. </p><p>The sum <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \sum _{i=0}^{\infty }2^{-i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>i</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{\infty }2^{-i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/694e519e2794c3610fbeefdc78be97abc0e69872" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:6.983ex; height:6.843ex;" alt="{\displaystyle \sum _{i=0}^{\infty }2^{-i}}"/></span> converges to 2. </p><p>It was entered as </p> <dl><dd><code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math</span><span class="w"> </span><span class="na">display=</span><span class="s">"block"</span><span class="nt">></span>\sum_{i=0}^\infty<span class="w"> </span>2^{-i}<span class="nt"></math></span></code></dd></dl> <p>Technically, the command <i>\displaystyle</i> will be added to the user input (if the user input does not already contain the string <i>\displaystyle</i> or <i>\align</i>) before the TeX command is passed to the renderer. The result will be displayed in a new paragraph. Therefore, the style of the MathImage is altered, i.e. the style attribute "display:block;margin:auto" is added. For MathML it is ensured that display=inline is replaced by display block which produces a new paragraph </p> <div class="mw-heading mw-heading4"><h4 id="Not_specified" data-mw-thread-id="h-Not_specified-Display_attribute"><span data-mw-comment-start="" id="h-Not_specified-Display_attribute"></span>Not specified<span data-mw-comment-end="h-Not_specified-Display_attribute"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=41" title="Edit section: Not specified"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If nothing is specified, the equation is rendered in the same display style as "block", but without using a new paragraph. If the equation does appear on a line by itself, it is not automatically indented. </p><p>The sum <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=0}^{\infty }2^{-i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>i</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{\infty }2^{-i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/694e519e2794c3610fbeefdc78be97abc0e69872" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:6.983ex; height:6.843ex;" alt="{\displaystyle \sum _{i=0}^{\infty }2^{-i}}"/></span> converges to 2. </p><p>The next line-width is disturbed by large operators. </p><p>Or: </p><p>The sum </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=0}^{\infty }2^{-i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>i</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{\infty }2^{-i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/694e519e2794c3610fbeefdc78be97abc0e69872" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:6.983ex; height:6.843ex;" alt="{\displaystyle \sum _{i=0}^{\infty }2^{-i}}"/></span> </p><p>converges to 2. </p><p>In both cases, the math is coded as: </p> <dl><dd><code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math></span>\sum_{i=0}^\infty<span class="w"> </span>2^{-i}<span class="nt"></math></span></code></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Equation_numbering" data-mw-thread-id="h-Equation_numbering-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Equation_numbering-Formatting_using_LaTeX"></span>Equation numbering<span data-mw-comment-end="h-Equation_numbering-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=42" title="Edit section: Equation numbering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:DISPLAYTAG"></span></div><div class="module-shortcutboxplain noprint" role="note"><div class="module-shortcutlist"><a href="/wiki/Wikipedia:Shortcut" title="Wikipedia:Shortcut">Shortcut</a></div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:DISPLAYTAG&redirect=no">WP:DISPLAYTAG</a></span></li></ul></div></div> <p>The templates <span class="nowrap">{{</span><a href="/wiki/Template:NumBlk" class="mw-redirect" title="Template:NumBlk">NumBlk</a><span class="nowrap">}}</span> and <span class="nowrap">{{</span><a href="/wiki/Template:EquationRef" title="Template:EquationRef">EquationRef</a><span class="nowrap">}}</span> can be used to number equations. The template <span class="nowrap">{{</span><a href="/wiki/Template:EquationNote" title="Template:EquationNote">EquationNote</a><span class="nowrap">}}</span> can be used to refer to a numbered equation from surrounding text. For example, the following syntax: </p> <dl><dd><code class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><span class="p">{{</span><span class="nt">NumBlk</span><span class="p">|</span>:<span class="p">|<</span><span class="nt">math</span><span class="p">></span>x<span class="nb">^</span>2 + y<span class="nb">^</span>2 + z<span class="nb">^</span>2 = 1<span class="p"></</span><span class="nt">math</span><span class="p">>|{{</span><span class="nt">EquationRef</span><span class="p">|</span>1<span class="p">}}}}</span></code></dd></dl> <p>produces the following result (note the equation number in the right margin): </p> <style data-mw-deduplicate="TemplateStyles:r1266403038">.mw-parser-output table.numblk{border-collapse:collapse;border:none;margin-top:0;margin-right:0;margin-bottom:0}.mw-parser-output table.numblk>tbody>tr>td{vertical-align:middle;padding:0}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2){width:99%}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table{border-collapse:collapse;margin:0;border:none;width:100%}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td:first-child,.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td:last-child{padding:0 0.4ex}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td:nth-child(2){width:100%;padding:0}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:last-child>td{padding:0}.mw-parser-output table.numblk>tbody>tr>td:last-child{font-weight:bold}.mw-parser-output table.numblk.numblk-raw-n>tbody>tr>td:last-child{font-weight:unset}.mw-parser-output table.numblk>tbody>tr>td:last-child::before{content:"("}.mw-parser-output table.numblk>tbody>tr>td:last-child::after{content:")"}.mw-parser-output table.numblk.numblk-raw-n>tbody>tr>td:last-child::before,.mw-parser-output table.numblk.numblk-raw-n>tbody>tr>td:last-child::after{content:none}.mw-parser-output table.numblk>tbody>tr>td{border:none}.mw-parser-output table.numblk.numblk-border>tbody>tr>td{border:thin solid}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td{border:none}.mw-parser-output table.numblk.numblk-border>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td{border:thin solid}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:last-child>td{border-left:none;border-right:none;border-bottom:none}.mw-parser-output table.numblk.numblk-border>tbody>tr>td:nth-child(2)>table>tbody>tr:last-child>td{border-left:thin solid;border-right:thin solid;border-bottom:thin solid}.mw-parser-output table.numblk:target{color:var(--color-base,#202122);background-color:#cfe8fd}@media screen{html.skin-theme-clientpref-night .mw-parser-output table.numblk:target{color:var(--color-base,#eaecf0);background-color:#301702}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output table.numblk:target{color:var(--color-base,#eaecf0);background-color:#301702}}</style><table role="presentation" class="numblk" style="margin-left: 1.6em;"><tbody><tr><td class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}+z^{2}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}+z^{2}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b5c3e3525a1604f9425edb80835d236fe7af82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.685ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}+z^{2}=1}"/></span></td> <td></td> <td class="nowrap"><span id="math_1" class="reference nourlexpansion" style="font-weight:bold;">1</span></td></tr></tbody></table> <p>Later on, the text can refer to this equation by its number using syntax like this: </p> <dl><dd><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr">As seen in equation ({{EquationNote|1}}), example text...</code></dd></dl> <p>The result looks like this: </p> <dl><dd>As seen in equation (<b><a href="#math_1">1</a></b>), example text...</dd></dl> <p>The equation number produced by <span class="nowrap">{{</span><a href="/wiki/Template:EquationNote" title="Template:EquationNote">EquationNote</a><span class="nowrap">}}</span> is a link that the user can click to go immediately to the cited equation. </p> <div class="mw-heading mw-heading3"><h3 id="Alphabets_and_typefaces" data-mw-thread-id="h-Alphabets_and_typefaces-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Alphabets_and_typefaces-Formatting_using_LaTeX"></span>Alphabets and typefaces<span data-mw-comment-end="h-Alphabets_and_typefaces-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=43" title="Edit section: Alphabets and typefaces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Wikipedia:LaTeX_symbols#Fonts" class="mw-redirect" title="Wikipedia:LaTeX symbols">Wikipedia:LaTeX symbols § Fonts</a></div> <p><a href="/w/index.php?title=Texvc&action=edit&redlink=1" class="new" title="Texvc (page does not exist)">Texvc</a> cannot render arbitrary <a href="/wiki/Unicode" title="Unicode">Unicode</a> characters. Those it can handle can be entered by the expressions below. For others, such as <a href="/wiki/Cyrillic" class="mw-redirect" title="Cyrillic">Cyrillic</a>, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas. </p> <table class="wikitable"> <tbody><tr> <th colspan="2">Greek alphabet </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\Alpha</span> <span class="k">\Beta</span> <span class="k">\Gamma</span> <span class="k">\Delta</span> <span class="k">\Epsilon</span> <span class="k">\Zeta</span> <span class="k">\Eta</span> <span class="k">\Theta</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mi mathvariant="normal">Γ</mi> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> <mi mathvariant="normal">Θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb6a8ea8d28766c95fae95272dc1bc7dd24ee83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.332ex; height:2.176ex;" alt="{\displaystyle \mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\Iota</span> <span class="k">\Kappa</span> <span class="k">\Lambda</span> <span class="k">\Mu</span> <span class="k">\Nu</span> <span class="k">\Xi</span> <span class="k">\Omicron</span> <span class="k">\Pi</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">K</mi> </mrow> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> </mrow> <mi mathvariant="normal">Ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> <mi mathvariant="normal">Π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc2e6e694c933709595ff0efa0f9c2d15b7f5b8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.236ex; height:2.176ex;" alt="{\displaystyle \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\Rho</span> <span class="k">\Sigma</span> <span class="k">\Tau</span> <span class="k">\Upsilon</span> <span class="k">\Phi</span> <span class="k">\Chi</span> <span class="k">\Psi</span> <span class="k">\Omega</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> <mi mathvariant="normal">Σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mi mathvariant="normal">Υ</mi> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">X</mi> </mrow> <mi mathvariant="normal">Ψ</mi> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b1bb41322d6ed54092bbe526971bfc40d92e033" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.655ex; height:2.176ex;" alt="{\displaystyle \mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\alpha</span> <span class="k">\beta</span> <span class="k">\gamma</span> <span class="k">\delta</span> <span class="k">\epsilon</span> <span class="k">\zeta</span> <span class="k">\eta</span> <span class="k">\theta</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mi>β</mi> <mi>γ</mi> <mi>δ</mi> <mi>ϵ</mi> <mi>ζ</mi> <mi>η</mi> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92775e1b04282ff8160a3162f5e67109a59672a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.43ex; height:2.843ex;" alt="{\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\iota</span> <span class="k">\kappa</span> <span class="k">\lambda</span> <span class="k">\mu</span> <span class="k">\nu</span> <span class="k">\xi</span> <span class="k">\omicron</span> <span class="k">\pi</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \iota \kappa \lambda \mu \nu \xi \mathrm {o} \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ι</mi> <mi>κ</mi> <mi>λ</mi> <mi>μ</mi> <mi>ν</mi> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \iota \kappa \lambda \mu \nu \xi \mathrm {o} \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3c252c504683d23a77714b238a126ea1fe5420c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.676ex; height:2.676ex;" alt="{\displaystyle \iota \kappa \lambda \mu \nu \xi \mathrm {o} \pi }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\rho</span> <span class="k">\sigma</span> <span class="k">\tau</span> <span class="k">\upsilon</span> <span class="k">\phi</span> <span class="k">\chi</span> <span class="k">\psi</span> <span class="k">\omega</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho \sigma \tau \upsilon \phi \chi \psi \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mi>σ</mi> <mi>τ</mi> <mi>υ</mi> <mi>ϕ</mi> <mi>χ</mi> <mi>ψ</mi> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho \sigma \tau \upsilon \phi \chi \psi \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b717bda9e549206523611254c7bcb813072579a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.788ex; height:2.676ex;" alt="{\displaystyle \rho \sigma \tau \upsilon \phi \chi \psi \omega }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\varGamma</span> <span class="k">\varDelta</span> <span class="k">\varTheta</span> <span class="k">\varLambda</span> <span class="k">\varXi</span> <span class="k">\varPi</span> <span class="k">\varSigma</span> <span class="k">\varPhi</span> <span class="k">\varUpsilon</span> <span class="k">\varOmega</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Γ</mi> <mi>Δ</mi> <mi>Θ</mi> <mi>Λ</mi> <mi>Ξ</mi> <mi>Π</mi> <mi>Σ</mi> <mi>Φ</mi> <mi>Υ</mi> <mi>Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c3cfd1152be864297bc426c6da2689993cd01dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:17.707ex; height:2.176ex;" alt="{\displaystyle \varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\varepsilon</span> <span class="k">\digamma</span> <span class="k">\varkappa</span> <span class="k">\varpi</span> <span class="k">\varrho</span> <span class="k">\varsigma</span> <span class="k">\vartheta</span> <span class="k">\varphi</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mi>ϝ</mi> <mi>ϰ</mi> <mi>ϖ</mi> <mi>ϱ</mi> <mi>ς</mi> <mi>ϑ</mi> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9576d6d8b0f1ddd9754d43287fed62edc6e3ea19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.56ex; height:2.676ex;" alt="{\displaystyle \varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi }"/></span> </td></tr> <tr> <th colspan="2">Hebrew symbols </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\aleph</span> <span class="k">\beth</span> <span class="k">\gimel</span> <span class="k">\daleth</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \aleph \beth \gimel \daleth }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">ℵ</mi> <mi>ℶ</mi> <mi>ℷ</mi> <mi>ℸ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph \beth \gimel \daleth }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa99b102c61463b8e9bb831e0cb40dca9acd47d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.6ex; height:2.343ex;" alt="{\displaystyle \aleph \beth \gimel \daleth }"/></span> </td></tr> <tr> <th colspan="2">Blackboard bold/scripts </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbb</span><span class="nb">{</span>ABCDEFGHI<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {ABCDEFGHI} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> <mi mathvariant="double-struck">B</mi> <mi mathvariant="double-struck">C</mi> <mi mathvariant="double-struck">D</mi> <mi mathvariant="double-struck">E</mi> <mi mathvariant="double-struck">F</mi> <mi mathvariant="double-struck">G</mi> <mi mathvariant="double-struck">H</mi> <mi mathvariant="double-struck">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {ABCDEFGHI} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a949ec73bc992bf6d3a6dfdf6b85e594c21db62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.076ex; height:2.176ex;" alt="{\displaystyle \mathbb {ABCDEFGHI} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbb</span><span class="nb">{</span>JKLMNOPQR<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {JKLMNOPQR} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">J</mi> <mi mathvariant="double-struck">K</mi> <mi mathvariant="double-struck">L</mi> <mi mathvariant="double-struck">M</mi> <mi mathvariant="double-struck">N</mi> <mi mathvariant="double-struck">O</mi> <mi mathvariant="double-struck">P</mi> <mi mathvariant="double-struck">Q</mi> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {JKLMNOPQR} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/645a73dd67c9922dfbc922b8ed1aa081072e631d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.107ex; height:2.509ex;" alt="{\displaystyle \mathbb {JKLMNOPQR} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbb</span><span class="nb">{</span>STUVWXYZ<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {STUVWXYZ} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">S</mi> <mi mathvariant="double-struck">T</mi> <mi mathvariant="double-struck">U</mi> <mi mathvariant="double-struck">V</mi> <mi mathvariant="double-struck">W</mi> <mi mathvariant="double-struck">X</mi> <mi mathvariant="double-struck">Y</mi> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {STUVWXYZ} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d10635e329b5a212679b03ef0d7e093218c26b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.429ex; height:2.176ex;" alt="{\displaystyle \mathbb {STUVWXYZ} }"/></span> </td></tr> <tr> <th colspan="2">Boldface </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbf</span><span class="nb">{</span>ABCDEFGHI<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {ABCDEFGHI} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> <mi mathvariant="bold">B</mi> <mi mathvariant="bold">C</mi> <mi mathvariant="bold">D</mi> <mi mathvariant="bold">E</mi> <mi mathvariant="bold">F</mi> <mi mathvariant="bold">G</mi> <mi mathvariant="bold">H</mi> <mi mathvariant="bold">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {ABCDEFGHI} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a0a6fd98a056c57605520bc2b8a3cc893b5b53c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.547ex; height:2.176ex;" alt="{\displaystyle \mathbf {ABCDEFGHI} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbf</span><span class="nb">{</span>JKLMNOPQR<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {JKLMNOPQR} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> <mi mathvariant="bold">K</mi> <mi mathvariant="bold">L</mi> <mi mathvariant="bold">M</mi> <mi mathvariant="bold">N</mi> <mi mathvariant="bold">O</mi> <mi mathvariant="bold">P</mi> <mi mathvariant="bold">Q</mi> <mi mathvariant="bold">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {JKLMNOPQR} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d54d2e66d9d2f40fc18bd05b394a08ebfa67032" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.558ex; height:2.509ex;" alt="{\displaystyle \mathbf {JKLMNOPQR} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbf</span><span class="nb">{</span>STUVWXYZ<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {STUVWXYZ} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> <mi mathvariant="bold">T</mi> <mi mathvariant="bold">U</mi> <mi mathvariant="bold">V</mi> <mi mathvariant="bold">W</mi> <mi mathvariant="bold">X</mi> <mi mathvariant="bold">Y</mi> <mi mathvariant="bold">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {STUVWXYZ} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132f98b34d92ec46e833ed23dece1713e66da521" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.856ex; height:2.176ex;" alt="{\displaystyle \mathbf {STUVWXYZ} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbf</span><span class="nb">{</span>abcdefghijklm<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {abcdefghijklm} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> <mi mathvariant="bold">b</mi> <mi mathvariant="bold">c</mi> <mi mathvariant="bold">d</mi> <mi mathvariant="bold">e</mi> <mi mathvariant="bold">f</mi> <mi mathvariant="bold">g</mi> <mi mathvariant="bold">h</mi> <mi mathvariant="bold">i</mi> <mi mathvariant="bold">j</mi> <mi mathvariant="bold">k</mi> <mi mathvariant="bold">l</mi> <mi mathvariant="bold">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {abcdefghijklm} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5e48fa05a16c954d1f7a7ecfd4fa2dba367f3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.496ex; height:2.509ex;" alt="{\displaystyle \mathbf {abcdefghijklm} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbf</span><span class="nb">{</span>nopqrstuvwxyz<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {nopqrstuvwxyz} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">n</mi> <mi mathvariant="bold">o</mi> <mi mathvariant="bold">p</mi> <mi mathvariant="bold">q</mi> <mi mathvariant="bold">r</mi> <mi mathvariant="bold">s</mi> <mi mathvariant="bold">t</mi> <mi mathvariant="bold">u</mi> <mi mathvariant="bold">v</mi> <mi mathvariant="bold">w</mi> <mi mathvariant="bold">x</mi> <mi mathvariant="bold">y</mi> <mi mathvariant="bold">z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {nopqrstuvwxyz} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/637ec33f73c20486b47964b823a8f82e55c190d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.757ex; height:2.343ex;" alt="{\displaystyle \mathbf {nopqrstuvwxyz} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathbf</span><span class="nb">{</span>0123456789<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {0123456789} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0123456789</mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {0123456789} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23e7eba18b613f33f3879205b263105d2745f756" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.366ex; height:2.176ex;" alt="{\displaystyle \mathbf {0123456789} }"/></span> </td></tr> <tr> <th colspan="2">Boldface (Greek) </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\Alpha</span> <span class="k">\Beta</span> <span class="k">\Gamma</span> <span class="k">\Delta</span> <span class="k">\Epsilon</span> <span class="k">\Zeta</span> <span class="k">\Eta</span> <span class="k">\Theta</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mi mathvariant="bold">Γ</mi> <mi mathvariant="bold">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">H</mi> </mrow> <mi mathvariant="bold">Θ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7664b5a4f548db9d95f10642d9ee581f75b89e21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.315ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\Iota</span> <span class="k">\Kappa</span> <span class="k">\Lambda</span> <span class="k">\Mu</span> <span class="k">\Nu</span> <span class="k">\Xi</span> <span class="k">\Omicron</span> <span class="k">\Pi</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">K</mi> </mrow> <mi mathvariant="bold">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mi mathvariant="bold">Ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">O</mi> </mrow> <mi mathvariant="bold">Π</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/855e815a5ea4e31d4414e7e57a9eac2b6eb86fd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.492ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\Rho</span> <span class="k">\Sigma</span> <span class="k">\Tau</span> <span class="k">\Upsilon</span> <span class="k">\Phi</span> <span class="k">\Chi</span> <span class="k">\Psi</span> <span class="k">\Omega</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mi mathvariant="bold">Σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mi mathvariant="bold">Υ</mi> <mi mathvariant="bold">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">X</mi> </mrow> <mi mathvariant="bold">Ψ</mi> <mi mathvariant="bold">Ω</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/634135ff4188dbe45bb0b57a72f2cc3bbd90e9d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.654ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {\mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\alpha</span> <span class="k">\beta</span> <span class="k">\gamma</span> <span class="k">\delta</span> <span class="k">\epsilon</span> <span class="k">\zeta</span> <span class="k">\eta</span> <span class="k">\theta</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\alpha \beta \gamma \delta \epsilon \zeta \eta \theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">α</mi> <mi mathvariant="bold-italic">β</mi> <mi mathvariant="bold-italic">γ</mi> <mi mathvariant="bold-italic">δ</mi> <mi mathvariant="bold-italic">ϵ</mi> <mi mathvariant="bold-italic">ζ</mi> <mi mathvariant="bold-italic">η</mi> <mi mathvariant="bold-italic">θ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\alpha \beta \gamma \delta \epsilon \zeta \eta \theta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c234db2d130db2b49864a0a8a9306ab189fd3d5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.986ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {\alpha \beta \gamma \delta \epsilon \zeta \eta \theta }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\iota</span> <span class="k">\kappa</span> <span class="k">\lambda</span> <span class="k">\mu</span> <span class="k">\nu</span> <span class="k">\xi</span> <span class="k">\omicron</span> <span class="k">\pi</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\iota \kappa \lambda \mu \nu \xi \mathrm {o} \pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ι</mi> <mi mathvariant="bold-italic">κ</mi> <mi mathvariant="bold-italic">λ</mi> <mi mathvariant="bold-italic">μ</mi> <mi mathvariant="bold-italic">ν</mi> <mi mathvariant="bold-italic">ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">o</mi> </mrow> <mi mathvariant="bold-italic">π</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\iota \kappa \lambda \mu \nu \xi \mathrm {o} \pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c6c6c2b4e389db6d18217bc701bd7d3423eff5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.232ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {\iota \kappa \lambda \mu \nu \xi \mathrm {o} \pi }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\rho</span> <span class="k">\sigma</span> <span class="k">\tau</span> <span class="k">\upsilon</span> <span class="k">\phi</span> <span class="k">\chi</span> <span class="k">\psi</span> <span class="k">\omega</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\rho \sigma \tau \upsilon \phi \chi \psi \omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ρ</mi> <mi mathvariant="bold-italic">σ</mi> <mi mathvariant="bold-italic">τ</mi> <mi mathvariant="bold-italic">υ</mi> <mi mathvariant="bold-italic">ϕ</mi> <mi mathvariant="bold-italic">χ</mi> <mi mathvariant="bold-italic">ψ</mi> <mi mathvariant="bold-italic">ω</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\rho \sigma \tau \upsilon \phi \chi \psi \omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b23add2190bc1497de6dd54d5d22760cb32c70be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.656ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {\rho \sigma \tau \upsilon \phi \chi \psi \omega }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\varepsilon\digamma\varkappa\varpi</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\varepsilon \digamma \varkappa \varpi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ε</mi> <mi mathvariant="bold-italic">ϝ</mi> <mi mathvariant="bold-italic">ϰ</mi> <mi mathvariant="bold-italic">ϖ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\varepsilon \digamma \varkappa \varpi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0223dad8308723165a03ad6cf1d974c9a595fba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.01ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {\varepsilon \digamma \varkappa \varpi }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\varrho\varsigma\vartheta\varphi</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\varrho \varsigma \vartheta \varphi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ϱ</mi> <mi mathvariant="bold-italic">ς</mi> <mi mathvariant="bold-italic">ϑ</mi> <mi mathvariant="bold-italic">φ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\varrho \varsigma \vartheta \varphi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c6b1250bbdf29aa32a0130a2d0397272761fc9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.83ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {\varrho \varsigma \vartheta \varphi }}}"/></span> </td></tr> <tr> <th colspan="2">Italics (default for Latin alphabet) </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathit</span><span class="nb">{</span>0123456789<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {0123456789}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">0123456789</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {0123456789}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba8bbe26c3209befcdc74d2ff33bdc7f59f73621" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.1ex; width:11.98ex; height:2.509ex;" alt="{\displaystyle {\mathit {0123456789}}}"/></span> </td></tr> <tr> <th colspan="2">Greek italics (default for lowercase Greek) </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathit</span><span class="nb">{</span><span class="k">\Alpha</span> <span class="k">\Beta</span> <span class="k">\Gamma</span> <span class="k">\Delta</span> <span class="k">\Epsilon</span> <span class="k">\Zeta</span> <span class="k">\Eta</span> <span class="k">\Theta</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mi class="MJX-tex-mathit" mathvariant="italic">Γ</mi> <mi class="MJX-tex-mathit" mathvariant="italic">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> <mi class="MJX-tex-mathit" mathvariant="italic">Θ</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45789ec3d3b87f81a59eaaa102dbb860cf0f17a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.049ex; width:13.325ex; height:2.176ex;" alt="{\displaystyle {\mathit {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathit</span><span class="nb">{</span><span class="k">\Iota</span> <span class="k">\Kappa</span> <span class="k">\Lambda</span> <span class="k">\Mu</span> <span class="k">\Nu</span> <span class="k">\Xi</span> <span class="k">\Omicron</span> <span class="k">\Pi</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">K</mi> </mrow> <mi class="MJX-tex-mathit" mathvariant="italic">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> </mrow> <mi class="MJX-tex-mathit" mathvariant="italic">Ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> <mi class="MJX-tex-mathit" mathvariant="italic">Π</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2887230b9f4ccc7e824ebecebc6f39b0a745fbf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.269ex; width:13.478ex; height:2.176ex;" alt="{\displaystyle {\mathit {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathit</span><span class="nb">{</span><span class="k">\Rho</span> <span class="k">\Sigma</span> <span class="k">\Tau</span> <span class="k">\Upsilon</span> <span class="k">\Phi</span> <span class="k">\Chi</span> <span class="k">\Psi</span> <span class="k">\Omega</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">Σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mi class="MJX-tex-mathit" mathvariant="italic">Υ</mi> <mi class="MJX-tex-mathit" mathvariant="italic">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">X</mi> </mrow> <mi class="MJX-tex-mathit" mathvariant="italic">Ψ</mi> <mi class="MJX-tex-mathit" mathvariant="italic">Ω</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b4468f979f03e16e883a8f496cefc14865bce37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.1ex; width:12.079ex; height:2.176ex;" alt="{\displaystyle {\mathit {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}"/></span> </td></tr> <tr> <th colspan="2">Greek uppercase boldface italics </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\varGamma</span> <span class="k">\varDelta</span> <span class="k">\varTheta</span> <span class="k">\varLambda</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\varGamma \varDelta \varTheta \varLambda }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">Γ</mi> <mi mathvariant="bold-italic">Δ</mi> <mi mathvariant="bold-italic">Θ</mi> <mi mathvariant="bold-italic">Λ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\varGamma \varDelta \varTheta \varLambda }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbf0388694941c2587a8c13a5f284370c7781b4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.92ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {\varGamma \varDelta \varTheta \varLambda }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\varXi</span> <span class="k">\varPi</span> <span class="k">\varSigma</span> <span class="k">\varUpsilon</span> <span class="k">\varOmega</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\varXi \varPi \varSigma \varUpsilon \varOmega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">Ξ</mi> <mi mathvariant="bold-italic">Π</mi> <mi mathvariant="bold-italic">Σ</mi> <mi mathvariant="bold-italic">Υ</mi> <mi mathvariant="bold-italic">Ω</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\varXi \varPi \varSigma \varUpsilon \varOmega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e170f2e4ccecb53919c696e8089ff58111390be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.42ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {\varXi \varPi \varSigma \varUpsilon \varOmega }}}"/></span> </td></tr> <tr> <th colspan="2">Roman typeface </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathrm</span><span class="nb">{</span>ABCDEFGHI<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {ABCDEFGHI} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">D</mi> <mi mathvariant="normal">E</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">G</mi> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {ABCDEFGHI} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f80f41a157c41732f4977e46da0e0c547ee7e06f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.35ex; height:2.176ex;" alt="{\displaystyle \mathrm {ABCDEFGHI} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathrm</span><span class="nb">{</span>JKLMNOPQR<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {JKLMNOPQR} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">J</mi> <mi mathvariant="normal">K</mi> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">O</mi> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">Q</mi> <mi mathvariant="normal">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {JKLMNOPQR} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e10b845ea40bd9874a5d829bac05be513a60d18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.24ex; height:2.509ex;" alt="{\displaystyle \mathrm {JKLMNOPQR} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathrm</span><span class="nb">{</span>STUVWXYZ<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {STUVWXYZ} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">U</mi> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">W</mi> <mi mathvariant="normal">X</mi> <mi mathvariant="normal">Y</mi> <mi mathvariant="normal">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {STUVWXYZ} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da08f1a6bf60c4be2322a9c68030ebe0b6a98a09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.752ex; height:2.176ex;" alt="{\displaystyle \mathrm {STUVWXYZ} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathrm</span><span class="nb">{</span>abcdefghijklm<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {abcdefghijklm} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">j</mi> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {abcdefghijklm} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/daf5b9ca4c007dccf836047cdf8f4ea79c8e9a99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.301ex; height:2.509ex;" alt="{\displaystyle \mathrm {abcdefghijklm} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathrm</span><span class="nb">{</span>nopqrstuvwxyz<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {nopqrstuvwxyz} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">q</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">w</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">y</mi> <mi mathvariant="normal">z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {nopqrstuvwxyz} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/870a7b8115c96d03538aac2cfec95ab185e6003f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.409ex; height:2.343ex;" alt="{\displaystyle \mathrm {nopqrstuvwxyz} }"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathrm</span><span class="nb">{</span>0123456789<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {0123456789} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>0123456789</mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {0123456789} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdb865fa61891efe896235e84ae5ec324cb96581" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.625ex; height:2.176ex;" alt="{\displaystyle \mathrm {0123456789} }"/></span> </td></tr> <tr> <th colspan="2">Sans serif </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span>ABCDEFGHI<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {ABCDEFGHI}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">A</mi> <mi mathvariant="sans-serif">B</mi> <mi mathvariant="sans-serif">C</mi> <mi mathvariant="sans-serif">D</mi> <mi mathvariant="sans-serif">E</mi> <mi mathvariant="sans-serif">F</mi> <mi mathvariant="sans-serif">G</mi> <mi mathvariant="sans-serif">H</mi> <mi mathvariant="sans-serif">I</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {ABCDEFGHI}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df74426801b63a4e6b5fee912ba71f22ff371d30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.817ex; height:2.176ex;" alt="{\displaystyle {\mathsf {ABCDEFGHI}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span>JKLMNOPQR<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {JKLMNOPQR}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">J</mi> <mi mathvariant="sans-serif">K</mi> <mi mathvariant="sans-serif">L</mi> <mi mathvariant="sans-serif">M</mi> <mi mathvariant="sans-serif">N</mi> <mi mathvariant="sans-serif">O</mi> <mi mathvariant="sans-serif">P</mi> <mi mathvariant="sans-serif">Q</mi> <mi mathvariant="sans-serif">R</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {JKLMNOPQR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e0cd59e315277c7e2f5018693def8a37f8d385b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:14.057ex; height:2.343ex;" alt="{\displaystyle {\mathsf {JKLMNOPQR}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span>STUVWXYZ<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {STUVWXYZ}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">S</mi> <mi mathvariant="sans-serif">T</mi> <mi mathvariant="sans-serif">U</mi> <mi mathvariant="sans-serif">V</mi> <mi mathvariant="sans-serif">W</mi> <mi mathvariant="sans-serif">X</mi> <mi mathvariant="sans-serif">Y</mi> <mi mathvariant="sans-serif">Z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {STUVWXYZ}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8564cc964261defc80363fa791b0f5240c1460f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.739ex; height:2.176ex;" alt="{\displaystyle {\mathsf {STUVWXYZ}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span>abcdefghijklm<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {abcdefghijklm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">a</mi> <mi mathvariant="sans-serif">b</mi> <mi mathvariant="sans-serif">c</mi> <mi mathvariant="sans-serif">d</mi> <mi mathvariant="sans-serif">e</mi> <mi mathvariant="sans-serif">f</mi> <mi mathvariant="sans-serif">g</mi> <mi mathvariant="sans-serif">h</mi> <mi mathvariant="sans-serif">i</mi> <mi mathvariant="sans-serif">j</mi> <mi mathvariant="sans-serif">k</mi> <mi mathvariant="sans-serif">l</mi> <mi mathvariant="sans-serif">m</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {abcdefghijklm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be559adf2403e464c4e234df364b04f4e57284e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.475ex; height:2.509ex;" alt="{\displaystyle {\mathsf {abcdefghijklm}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span>nopqrstuvwxyz<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {nopqrstuvwxyz}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">n</mi> <mi mathvariant="sans-serif">o</mi> <mi mathvariant="sans-serif">p</mi> <mi mathvariant="sans-serif">q</mi> <mi mathvariant="sans-serif">r</mi> <mi mathvariant="sans-serif">s</mi> <mi mathvariant="sans-serif">t</mi> <mi mathvariant="sans-serif">u</mi> <mi mathvariant="sans-serif">v</mi> <mi mathvariant="sans-serif">w</mi> <mi mathvariant="sans-serif">x</mi> <mi mathvariant="sans-serif">y</mi> <mi mathvariant="sans-serif">z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {nopqrstuvwxyz}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc4c101caa7feb32033d904a93f685537a19f323" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.311ex; height:2.176ex;" alt="{\displaystyle {\mathsf {nopqrstuvwxyz}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span>0123456789<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {0123456789}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="sans-serif">0123456789</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {0123456789}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/251b0ea5e3d6945989fc20b3116c21f2204db2a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.625ex; height:2.176ex;" alt="{\displaystyle {\mathsf {0123456789}}}"/></span> </td></tr> <tr> <th colspan="2">Sans serif Greek (capital only) </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span><span class="k">\Alpha</span> <span class="k">\Beta</span> <span class="k">\Gamma</span> <span class="k">\Delta</span> <span class="k">\Epsilon</span> <span class="k">\Zeta</span> <span class="k">\Eta</span> <span class="k">\Theta</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mi mathvariant="sans-serif">Γ</mi> <mi mathvariant="sans-serif">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> <mi mathvariant="sans-serif">Θ</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43e47f4d41d5dd1c35ee878b6e7465505e3ee817" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.139ex; height:2.176ex;" alt="{\displaystyle {\mathsf {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span><span class="k">\Iota</span> <span class="k">\Kappa</span> <span class="k">\Lambda</span> <span class="k">\Mu</span> <span class="k">\Nu</span> <span class="k">\Xi</span> <span class="k">\Omicron</span> <span class="k">\Pi</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">K</mi> </mrow> <mi mathvariant="sans-serif">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> </mrow> <mi mathvariant="sans-serif">Ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> <mi mathvariant="sans-serif">Π</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0f8ce201dd33061131e6636a801534033d1863d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.946ex; height:2.176ex;" alt="{\displaystyle {\mathsf {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \mathrm {O} \Pi }}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathsf</span><span class="nb">{</span><span class="k">\Rho</span> <span class="k">\Sigma</span> <span class="k">\Tau</span> <span class="k">\Upsilon</span> <span class="k">\Phi</span> <span class="k">\Chi</span> <span class="k">\Psi</span> <span class="k">\Omega</span><span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">Σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> </mrow> <mi mathvariant="sans-serif">Υ</mi> <mi mathvariant="sans-serif">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">X</mi> </mrow> <mi mathvariant="sans-serif">Ψ</mi> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd8ad7fa308693b30ca04e7d0c3e644bac245f4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.072ex; height:2.176ex;" alt="{\displaystyle {\mathsf {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}"/></span> </td></tr> <tr> <th colspan="2">Calligraphy/script </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathcal</span><span class="nb">{</span>ABCDEFGHI<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {ABCDEFGHI}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">B</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">C</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">D</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">F</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">G</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">I</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {ABCDEFGHI}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1e947d382d132ad94416f3099869d4e422b69a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:14.564ex; height:2.509ex;" alt="{\displaystyle {\mathcal {ABCDEFGHI}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathcal</span><span class="nb">{</span>JKLMNOPQR<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {JKLMNOPQR}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">J</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">K</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">N</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">Q</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {JKLMNOPQR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20b4e55a68ce9d31b2f20c9892fc3226dc944dcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:17.813ex; height:2.676ex;" alt="{\displaystyle {\mathcal {JKLMNOPQR}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathcal</span><span class="nb">{</span>STUVWXYZ<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {STUVWXYZ}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">S</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">T</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">U</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">V</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">W</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">X</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">Y</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">Z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {STUVWXYZ}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38e55e3cc2233f5e18d21b065503b3c1993bcd14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.277ex; height:2.676ex;" alt="{\displaystyle {\mathcal {STUVWXYZ}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathcal</span><span class="nb">{</span>abcdefghi<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {abcdefghi}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">a</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">b</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">c</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">d</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">e</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">f</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">g</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">h</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">i</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {abcdefghi}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6178dacd8b0e2f164a590ca3428d04186f6e4c6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.07ex; height:2.509ex;" alt="{\displaystyle {\mathcal {abcdefghi}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathcal</span><span class="nb">{</span>jklmnopqr<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {jklmnopqr}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">j</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">k</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">l</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">m</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">n</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">o</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">p</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">q</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">r</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {jklmnopqr}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23e6d384f960b330c59c6f8503b42b279ea371de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:10.74ex; height:2.509ex;" alt="{\displaystyle {\mathcal {jklmnopqr}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathcal</span><span class="nb">{</span>stuvwxyz<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {stuvwxyz}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">s</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">t</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">u</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">v</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">w</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">x</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">y</mi> <mi class="MJX-tex-caligraphic" mathvariant="script">z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {stuvwxyz}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/707498f1bfb01b53ed6ff1492dee0303d031efff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.625ex; height:2.343ex;" alt="{\displaystyle {\mathcal {stuvwxyz}}}"/></span> </td></tr> <tr> <th colspan="2">Fraktur typeface </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathfrak</span><span class="nb">{</span>ABCDEFGHI<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {ABCDEFGHI}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">A</mi> <mi mathvariant="fraktur">B</mi> <mi mathvariant="fraktur">C</mi> <mi mathvariant="fraktur">D</mi> <mi mathvariant="fraktur">E</mi> <mi mathvariant="fraktur">F</mi> <mi mathvariant="fraktur">G</mi> <mi mathvariant="fraktur">H</mi> <mi mathvariant="fraktur">I</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {ABCDEFGHI}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d79ad67a088fb3287b6096a7b474904583a2997" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.831ex; height:2.509ex;" alt="{\displaystyle {\mathfrak {ABCDEFGHI}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathfrak</span><span class="nb">{</span>JKLMNOPQR<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {JKLMNOPQR}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">J</mi> <mi mathvariant="fraktur">K</mi> <mi mathvariant="fraktur">L</mi> <mi mathvariant="fraktur">M</mi> <mi mathvariant="fraktur">N</mi> <mi mathvariant="fraktur">O</mi> <mi mathvariant="fraktur">P</mi> <mi mathvariant="fraktur">Q</mi> <mi mathvariant="fraktur">R</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {JKLMNOPQR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b19f30c047a4ee5168fb5b23fefc8b5af5f6154" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.022ex; width:16.504ex; height:2.843ex;" alt="{\displaystyle {\mathfrak {JKLMNOPQR}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathfrak</span><span class="nb">{</span>STUVWXYZ<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {STUVWXYZ}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">S</mi> <mi mathvariant="fraktur">T</mi> <mi mathvariant="fraktur">U</mi> <mi mathvariant="fraktur">V</mi> <mi mathvariant="fraktur">W</mi> <mi mathvariant="fraktur">X</mi> <mi mathvariant="fraktur">Y</mi> <mi mathvariant="fraktur">Z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {STUVWXYZ}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/768dd908073a5883f13b14b460c1029eef4add46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.43ex; height:2.843ex;" alt="{\displaystyle {\mathfrak {STUVWXYZ}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathfrak</span><span class="nb">{</span>abcdefghijklm<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {abcdefghijklm}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">a</mi> <mi mathvariant="fraktur">b</mi> <mi mathvariant="fraktur">c</mi> <mi mathvariant="fraktur">d</mi> <mi mathvariant="fraktur">e</mi> <mi mathvariant="fraktur">f</mi> <mi mathvariant="fraktur">g</mi> <mi mathvariant="fraktur">h</mi> <mi mathvariant="fraktur">i</mi> <mi mathvariant="fraktur">j</mi> <mi mathvariant="fraktur">k</mi> <mi mathvariant="fraktur">l</mi> <mi mathvariant="fraktur">m</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {abcdefghijklm}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87179ac9295d5333181015066b5d6bc04f569cf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.135ex; height:2.676ex;" alt="{\displaystyle {\mathfrak {abcdefghijklm}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathfrak</span><span class="nb">{</span>nopqrstuvwxyz<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {nopqrstuvwxyz}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">n</mi> <mi mathvariant="fraktur">o</mi> <mi mathvariant="fraktur">p</mi> <mi mathvariant="fraktur">q</mi> <mi mathvariant="fraktur">r</mi> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">t</mi> <mi mathvariant="fraktur">u</mi> <mi mathvariant="fraktur">v</mi> <mi mathvariant="fraktur">w</mi> <mi mathvariant="fraktur">x</mi> <mi mathvariant="fraktur">y</mi> <mi mathvariant="fraktur">z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {nopqrstuvwxyz}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac1221ba6a395e318e9e945a64237783a2316139" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.571ex; height:2.509ex;" alt="{\displaystyle {\mathfrak {nopqrstuvwxyz}}}"/></span> </td></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathfrak</span><span class="nb">{</span>0123456789<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {0123456789}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="fraktur">0123456789</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {0123456789}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c11851434af3dbdada5177cbbba2063a30c6a28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.671ex; height:2.509ex;" alt="{\displaystyle {\mathfrak {0123456789}}}"/></span> </td></tr> <tr> <th colspan="2">Small scriptstyle text </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="nb">{</span><span class="k">\scriptstyle\text</span><span class="nb">{</span>abcdefghijklm<span class="nb">}}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\scriptstyle {\text{abcdefghijklm}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>abcdefghijklm</mtext> </mrow> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\scriptstyle {\text{abcdefghijklm}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d994c04e973d43a9e8e239cec9802ca47fda21f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.004ex; height:2.009ex;" alt="{\displaystyle {\scriptstyle {\text{abcdefghijklm}}}}"/></span> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Mixed_text_faces" data-mw-thread-id="h-Mixed_text_faces-Alphabets_and_typefaces"><span data-mw-comment-start="" id="h-Mixed_text_faces-Alphabets_and_typefaces"></span>Mixed text faces<span data-mw-comment-end="h-Mixed_text_faces-Alphabets_and_typefaces"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=44" title="Edit section: Mixed text faces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Feature </th> <th>Syntax </th> <th>How it looks rendered </th></tr> <tr> <td>Italicised characters (spaces are ignored) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">x y z</code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle xyz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mi>y</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle xyz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d3957b3fbfe29dfdb2f7cdad4e3d7fc2ea7be84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.573ex; height:2.009ex;" alt="{\displaystyle xyz}"/></span> </td></tr> <tr> <td>Non-italicised characters </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>x y z<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{x y z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>x y z</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{x y z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97107836419627c15d881f23d125b73c126cf751" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.649ex; height:2.009ex;" alt="{\displaystyle {\text{x y z}}}"/></span> </td></tr> <tr> <td>Mixed italics (bad) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>if<span class="nb">}</span> n <span class="k">\text</span><span class="nb">{</span>is even<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{if}}n{\text{is even}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>if</mtext> </mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>is even</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{if}}n{\text{is even}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3efb49838b82dbc6a63f4a86d1fa09d53693c13e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.482ex; height:2.176ex;" alt="{\displaystyle {\text{if}}n{\text{is even}}}"/></span> </td></tr> <tr> <td>Mixed italics (good) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>if <span class="nb">}</span>n<span class="k">\text</span><span class="nb">{</span> is even<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{if }}n{\text{ is even}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>if </mtext> </mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> is even</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{if }}n{\text{ is even}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40cee08717362e9643aaabba9cf13c003dc4f700" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.643ex; height:2.176ex;" alt="{\displaystyle {\text{if }}n{\text{ is even}}}"/></span> </td></tr> <tr> <td>Mixed italics (alternative: ~ or "\ " forces a space) </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\text</span><span class="nb">{</span>if<span class="nb">}</span>~n<span class="k">\ \text</span><span class="nb">{</span>is even<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{if}}~n\ {\text{is even}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>if</mtext> </mrow> <mtext> </mtext> <mi>n</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>is even</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{if}}~n\ {\text{is even}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85b47cc0c6f607bc897e23a6bbcfdbff91f58b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.643ex; height:2.176ex;" alt="{\displaystyle {\text{if}}~n\ {\text{is even}}}"/></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Color" data-mw-thread-id="h-Color-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Color-Formatting_using_LaTeX"></span>Color<span data-mw-comment-end="h-Color-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=45" title="Edit section: Color"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Equations can use color with the <code>\color</code> command. For example, </p> <table class="wikitable"> <tbody><tr> <th>How it looks rendered </th> <th>Syntax </th> <th>Feature </th></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\color {Blue}x^{2}}+{\color {Orange}2x}-{\color {LimeGreen}1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#2D2F92"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#F58137"> <mn>2</mn> <mi>x</mi> </mstyle> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#8DC73E"> <mn>1</mn> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\color {Blue}x^{2}}+{\color {Orange}2x}-{\color {LimeGreen}1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bbe9cc843c08cf5158d4fd78c0efbf2720bfbf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.719ex; height:2.843ex;" alt="{\displaystyle {\color {Blue}x^{2}}+{\color {Orange}2x}-{\color {LimeGreen}1}}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>Blue<span class="nb">}</span>x<span class="nb">^</span>2<span class="nb">}</span>+<span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>Orange<span class="nb">}</span>2x<span class="nb">}</span>-<span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>LimeGreen<span class="nb">}</span>1<span class="nb">}</span></code> </td> <td> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x={\frac {{\color {Blue}-b}\pm {\sqrt {\color {Red}b^{2}-4ac}}}{\color {Green}2a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#2D2F92"> <mo>−</mo> <mi>b</mi> </mstyle> </mrow> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mstyle mathcolor="#ED1B23"> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mi>a</mi> <mi>c</mi> </mstyle> </msqrt> </mrow> </mrow> <mstyle mathcolor="#00A64F"> <mn>2</mn> <mi>a</mi> </mstyle> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x={\frac {{\color {Blue}-b}\pm {\sqrt {\color {Red}b^{2}-4ac}}}{\color {Green}2a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/052eaa15f67bd73ae5c4a21900d39c8d906c7e93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.525ex; height:6.176ex;" alt="{\displaystyle x={\frac {{\color {Blue}-b}\pm {\sqrt {\color {Red}b^{2}-4ac}}}{\color {Green}2a}}}"/></span> </td> <td><span class="nowrap"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">x=<span class="k">\frac</span><span class="nb">{{</span><span class="k">\color</span><span class="nb">{</span>Blue<span class="nb">}</span>-b<span class="nb">}</span><span class="k">\pm\sqrt</span><span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>Red<span class="nb">}</span>b<span class="nb">^</span>2-4ac<span class="nb">}}{</span><span class="k">\color</span><span class="nb">{</span>Green<span class="nb">}</span>2a<span class="nb">}</span></code></span> </td> <td> </td></tr></tbody></table> <p>The <code>\color</code> command colors all symbols to its right. However, if the <code>\color</code> command is enclosed in a pair of braces (e.g. <code>{\color{Red}...}</code>) then no symbols outside of those braces are affected. </p> <table class="wikitable"> <tbody><tr> <th>How it looks rendered </th> <th>Syntax </th> <th>Feature </th></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\color {red}\neq y=z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mstyle mathcolor="red"> <mo>≠</mo> <mi>y</mi> <mo>=</mo> <mi>z</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\color {red}\neq y=z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c316db27605dcb9cb7c0819539779df0d3628311" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.77ex; height:2.676ex;" alt="{\displaystyle x\color {red}\neq y=z}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">x<span class="k">\color</span><span class="nb">{</span>red<span class="nb">}</span><span class="k">\neq</span> y=z</code> </td> <td> <p>Colors <span style="color:red;">red</span> everything to the right of <code>\color{red}</code>. To only color the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }"/></span> symbol red, place braces around <code>\color{red}\neq</code> or insert <code>\color{black}</code> to the right of <code>\neq</code>. </p> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x{\color {red}\neq }y=z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="red"> <mo>≠</mo> </mstyle> </mrow> <mi>y</mi> <mo>=</mo> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x{\color {red}\neq }y=z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc9c26e5862767815493a4decc4a27cf043d67b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.48ex; height:2.676ex;" alt="{\displaystyle x{\color {red}\neq }y=z}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">x<span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>red<span class="nb">}</span><span class="k">\neq</span><span class="nb">}</span> y=z</code> </td> <td> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\color {red}\neq \color {black}y=z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mstyle mathcolor="red"> <mo>≠</mo> <mstyle mathcolor="black"> <mi>y</mi> <mo>=</mo> <mi>z</mi> </mstyle> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\color {red}\neq \color {black}y=z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a91f7aba435b565a7f0edc439025d268e36beae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.77ex; height:2.676ex;" alt="{\displaystyle x\color {red}\neq \color {black}y=z}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">x<span class="k">\color</span><span class="nb">{</span>red<span class="nb">}</span><span class="k">\neq\color</span><span class="nb">{</span>black<span class="nb">}</span> y=z</code> </td> <td> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {-b\color {Green}\pm {\sqrt {b^{2}\color {Blue}-4{\color {Red}a}c}}}{2a}}=x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>b</mi> <mstyle mathcolor="#00A64F"> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mstyle mathcolor="#2D2F92"> <mo>−</mo> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#ED1B23"> <mi>a</mi> </mstyle> </mrow> <mi>c</mi> </mstyle> </msqrt> </mrow> </mstyle> </mrow> <mrow> <mn>2</mn> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {-b\color {Green}\pm {\sqrt {b^{2}\color {Blue}-4{\color {Red}a}c}}}{2a}}=x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2590290e93cf4d59eb97607467e30fd0ff3c48e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.525ex; height:6.176ex;" alt="{\displaystyle {\frac {-b\color {Green}\pm {\sqrt {b^{2}\color {Blue}-4{\color {Red}a}c}}}{2a}}=x}"/></span> </td> <td><span class="nowrap"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\frac</span><span class="nb">{</span>-b<span class="k">\color</span><span class="nb">{</span>Green<span class="nb">}</span><span class="k">\pm\sqrt</span><span class="nb">{</span>b<span class="nb">^</span>2<span class="k">\color</span><span class="nb">{</span>Blue<span class="nb">}</span>-4<span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>Red<span class="nb">}</span>a<span class="nb">}</span>c<span class="nb">}}{</span>2a<span class="nb">}</span>=x</code></span> </td> <td>The outermost braces in <code>{\color{Red}a}c</code> limit the effect of <code>\color{Red}</code> to the symbol <code>a</code>. Similarly, <code>\color{Blue}</code> does not affect any symbols outside of the <code>\sqrt{}</code> that encloses it, and <code>\color{Green}</code> does not affect any symbols outside of the numerator. </td></tr></tbody></table> <p>There are several alternate notations styles </p> <table class="wikitable"> <tbody><tr> <th>How it looks rendered </th> <th>Syntax </th> <th>Feature </th></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\color {Blue}x^{2}}+{\color {Orange}2x}-{\color {LimeGreen}1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#2D2F92"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#F58137"> <mn>2</mn> <mi>x</mi> </mstyle> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#8DC73E"> <mn>1</mn> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\color {Blue}x^{2}}+{\color {Orange}2x}-{\color {LimeGreen}1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bbe9cc843c08cf5158d4fd78c0efbf2720bfbf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.719ex; height:2.843ex;" alt="{\displaystyle {\color {Blue}x^{2}}+{\color {Orange}2x}-{\color {LimeGreen}1}}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>Blue<span class="nb">}</span>x<span class="nb">^</span>2<span class="nb">}</span>+<span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>Orange<span class="nb">}</span>2x<span class="nb">}</span>-<span class="nb">{</span><span class="k">\color</span><span class="nb">{</span>LimeGreen<span class="nb">}</span>1<span class="nb">}</span></code> </td> <td>works with both texvc and MathJax </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Blue}x^{2}\color {Black}+\color {Orange}2x\color {Black}-\color {LimeGreen}1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#2D2F92"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mstyle mathcolor="#221E1F"> <mo>+</mo> <mstyle mathcolor="#F58137"> <mn>2</mn> <mi>x</mi> <mstyle mathcolor="#221E1F"> <mo>−</mo> <mstyle mathcolor="#8DC73E"> <mn>1</mn> </mstyle> </mstyle> </mstyle> </mstyle> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Blue}x^{2}\color {Black}+\color {Orange}2x\color {Black}-\color {LimeGreen}1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11ea92ebdff85ab44114bc9de7378ffa410201a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.719ex; height:2.843ex;" alt="{\displaystyle \color {Blue}x^{2}\color {Black}+\color {Orange}2x\color {Black}-\color {LimeGreen}1}"/></span> </td> <td><span class="nowrap"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\color</span><span class="nb">{</span>Blue<span class="nb">}</span>x<span class="nb">^</span>2<span class="k">\color</span><span class="nb">{</span>Black<span class="nb">}</span>+<span class="k">\color</span><span class="nb">{</span>Orange<span class="nb">}</span>2x<span class="k">\color</span><span class="nb">{</span>Black<span class="nb">}</span>-<span class="k">\color</span><span class="nb">{</span>LimeGreen<span class="nb">}</span>1</code></span> </td> <td>works with both texvc and MathJax </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Blue}{x^{2}}+\color {Orange}{2x}-\color {LimeGreen}{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#2D2F92"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>+</mo> <mstyle mathcolor="#F58137"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>x</mi> </mrow> <mo>−</mo> <mstyle mathcolor="#8DC73E"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </mstyle> </mstyle> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Blue}{x^{2}}+\color {Orange}{2x}-\color {LimeGreen}{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4468245906c792339ead1afb237770719ab93c40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.719ex; height:2.843ex;" alt="{\displaystyle \color {Blue}{x^{2}}+\color {Orange}{2x}-\color {LimeGreen}{1}}"/></span> </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\color</span><span class="nb">{</span>Blue<span class="nb">}{</span>x<span class="nb">^</span>2<span class="nb">}</span>+<span class="k">\color</span><span class="nb">{</span>Orange<span class="nb">}{</span>2x<span class="nb">}</span>-<span class="k">\color</span><span class="nb">{</span>LimeGreen<span class="nb">}{</span>1<span class="nb">}</span></code> </td> <td>only works with MathJax </td></tr></tbody></table> <p>Some color names are predeclared according to the following table, you can use them directly for the rendering of formulas (or for declaring the intended color of the page background). </p> <table class="wikitable"> <caption><a class="mw-selflink-fragment" href="#Color">Colors supported</a><span class="anchor" id="Colors_supported"></span> </caption> <tbody><tr> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Apricot}{\text{Apricot}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#FBB982"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Apricot</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Apricot}{\text{Apricot}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1af7b0a0587815720879c32352ba1d79025b0f76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.694ex; height:2.509ex;" alt="{\displaystyle \color {Apricot}{\text{Apricot}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Aquamarine}{\text{Aquamarine}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00B5BE"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Aquamarine</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Aquamarine}{\text{Aquamarine}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94cd7f57b17f6692bfe6773161b8db35cb0d15ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.407ex; height:2.509ex;" alt="{\displaystyle \color {Aquamarine}{\text{Aquamarine}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Bittersweet}{\text{Bittersweet}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#C04F17"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Bittersweet</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Bittersweet}{\text{Bittersweet}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e39467f93b5012b3d2818e39a490e543ea4c7ee1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.609ex; height:2.176ex;" alt="{\displaystyle \color {Bittersweet}{\text{Bittersweet}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Black}{\text{Black}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#221E1F"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Black</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Black}{\text{Black}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/028d34eea3bcf8eae2461d4a2f4b0d4ed6ce52cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.715ex; height:2.176ex;" alt="{\displaystyle \color {Black}{\text{Black}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Blue}{\text{Blue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#2D2F92"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Blue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Blue}{\text{Blue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27d62dadaaf4024997c55f8783cb9104072b3582" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.617ex; height:2.176ex;" alt="{\displaystyle \color {Blue}{\text{Blue}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {BlueGreen}{\text{BlueGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00B3B8"> <mrow class="MJX-TeXAtom-ORD"> <mtext>BlueGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {BlueGreen}{\text{BlueGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad026317d58810592e1dffb436cf588dfcdfa4da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.711ex; height:2.176ex;" alt="{\displaystyle \color {BlueGreen}{\text{BlueGreen}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {BlueViolet}{\text{BlueViolet}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#473992"> <mrow class="MJX-TeXAtom-ORD"> <mtext>BlueViolet</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {BlueViolet}{\text{BlueViolet}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17030d46bab59bba86e89eb7fc9f31ce9ec012be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.754ex; height:2.176ex;" alt="{\displaystyle \color {BlueViolet}{\text{BlueViolet}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {BrickRed}{\text{BrickRed}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#B6321C"> <mrow class="MJX-TeXAtom-ORD"> <mtext>BrickRed</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {BrickRed}{\text{BrickRed}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d54112f2691124ec6cab99e2ee25108511de92d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.499ex; height:2.176ex;" alt="{\displaystyle \color {BrickRed}{\text{BrickRed}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Brown}{\text{Brown}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#792500"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Brown</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Brown}{\text{Brown}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74395b772d0aee45384f928f8dd5e298896538d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.69ex; height:2.176ex;" alt="{\displaystyle \color {Brown}{\text{Brown}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {BurntOrange}{\text{BurntOrange}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#F7921D"> <mrow class="MJX-TeXAtom-ORD"> <mtext>BurntOrange</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {BurntOrange}{\text{BurntOrange}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/399d21d2f1a46daa9d2b211218e1c082d85a9b29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.416ex; height:2.509ex;" alt="{\displaystyle \color {BurntOrange}{\text{BurntOrange}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {CadetBlue}{\text{CadetBlue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#74729A"> <mrow class="MJX-TeXAtom-ORD"> <mtext>CadetBlue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {CadetBlue}{\text{CadetBlue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6b6b110c0990c23015a2df54f2ff33685bcc07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.687ex; height:2.176ex;" alt="{\displaystyle \color {CadetBlue}{\text{CadetBlue}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {CarnationPink}{\text{CarnationPink}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#F282B4"> <mrow class="MJX-TeXAtom-ORD"> <mtext>CarnationPink</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {CarnationPink}{\text{CarnationPink}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6972d3553b5588a9faaf1a41df402abb414f9dd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.963ex; height:2.176ex;" alt="{\displaystyle \color {CarnationPink}{\text{CarnationPink}}}"/></span> </td></tr> <tr> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Cerulean}{\text{Cerulean}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00A2E3"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Cerulean</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Cerulean}{\text{Cerulean}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30b8fbf0e1b5388991c92e30db3d0efe7c70608a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.049ex; height:2.176ex;" alt="{\displaystyle \color {Cerulean}{\text{Cerulean}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {CornflowerBlue}{\text{CornflowerBlue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#41B0E4"> <mrow class="MJX-TeXAtom-ORD"> <mtext>CornflowerBlue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {CornflowerBlue}{\text{CornflowerBlue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f5cca6db097d487d56aa0c0fa3a255c383a03a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.805ex; height:2.176ex;" alt="{\displaystyle \color {CornflowerBlue}{\text{CornflowerBlue}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Cyan}{\text{Cyan}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00AEEF"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Cyan</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Cyan}{\text{Cyan}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93335b8295443ac59d0a5dd3d3efb32f9727089b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.361ex; height:2.509ex;" alt="{\displaystyle \color {Cyan}{\text{Cyan}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Dandelion}{\text{Dandelion}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#FDBC42"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Dandelion</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Dandelion}{\text{Dandelion}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fbe3bcf5e08ec234d886a6091c65259663166a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.304ex; height:2.176ex;" alt="{\displaystyle \color {Dandelion}{\text{Dandelion}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {DarkOrchid}{\text{DarkOrchid}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#A4538A"> <mrow class="MJX-TeXAtom-ORD"> <mtext>DarkOrchid</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {DarkOrchid}{\text{DarkOrchid}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/066266243b8b236e56d90175ebb3f9ad766c412e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.061ex; height:2.176ex;" alt="{\displaystyle \color {DarkOrchid}{\text{DarkOrchid}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Emerald}{\text{Emerald}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00A99D"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Emerald</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Emerald}{\text{Emerald}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f359e904d77c52e19a9845dffd7b63cde08a079" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.565ex; height:2.176ex;" alt="{\displaystyle \color {Emerald}{\text{Emerald}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {ForestGreen}{\text{ForestGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#009B55"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ForestGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {ForestGreen}{\text{ForestGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6aea4368de0cccd210fb7533595871ee2433c9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.538ex; height:2.176ex;" alt="{\displaystyle \color {ForestGreen}{\text{ForestGreen}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Fuchsia}{\text{Fuchsia}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#8C368C"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Fuchsia</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Fuchsia}{\text{Fuchsia}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64dacdb2abb2551459b0fef061101925625470cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.861ex; height:2.176ex;" alt="{\displaystyle \color {Fuchsia}{\text{Fuchsia}}}"/></span> </td></tr> <tr> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Goldenrod}{\text{Goldenrod}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#FFDF42"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Goldenrod</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Goldenrod}{\text{Goldenrod}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/783cfa0b1509eeae1386260fa7f1b03c2f1f4c88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.618ex; height:2.176ex;" alt="{\displaystyle \color {Goldenrod}{\text{Goldenrod}}}"/></span></td> <td style="background-color: Gray;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {white}{\text{Gray}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="white"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Gray</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {white}{\text{Gray}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51f0e7c6ba34689c564f258ed4fee3aa8c919e16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.126ex; height:2.509ex;" alt="{\displaystyle \color {white}{\text{Gray}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Green}{\text{Green}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00A64F"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Green</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Green}{\text{Green}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31fa58df27edf3b9ee5da67fe3dc860ab5e2f800" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.093ex; height:2.176ex;" alt="{\displaystyle \color {Green}{\text{Green}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {GreenYellow}{\text{GreenYellow}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#DFE674"> <mrow class="MJX-TeXAtom-ORD"> <mtext>GreenYellow</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {GreenYellow}{\text{GreenYellow}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b70292ded8a12b4eb357592a7fa2f24af7785c19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.003ex; height:2.176ex;" alt="{\displaystyle \color {GreenYellow}{\text{GreenYellow}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {JungleGreen}{\text{JungleGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00A99A"> <mrow class="MJX-TeXAtom-ORD"> <mtext>JungleGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {JungleGreen}{\text{JungleGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87c7011e935788081747479bfcdd587960429fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.715ex; height:2.509ex;" alt="{\displaystyle \color {JungleGreen}{\text{JungleGreen}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Lavender}{\text{Lavender}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#F49EC4"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Lavender</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Lavender}{\text{Lavender}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9aa0a82450646a8de1897099f9c6f8c612506bf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.404ex; height:2.176ex;" alt="{\displaystyle \color {Lavender}{\text{Lavender}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {LimeGreen}{\text{LimeGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#8DC73E"> <mrow class="MJX-TeXAtom-ORD"> <mtext>LimeGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {LimeGreen}{\text{LimeGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c795d60e88070f8cc1b58bb44f892ad0526ca2fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.161ex; height:2.176ex;" alt="{\displaystyle \color {LimeGreen}{\text{LimeGreen}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Magenta}{\text{Magenta}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#EC008C"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Magenta</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Magenta}{\text{Magenta}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f37c86c1247d31b337934296c4ec8ff1a97d977a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.848ex; height:2.509ex;" alt="{\displaystyle \color {Magenta}{\text{Magenta}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Mahogany}{\text{Mahogany}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#A9341F"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Mahogany</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Mahogany}{\text{Mahogany}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/608ecfbf467f6e64f26de823561bef63d2abcec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.593ex; height:2.509ex;" alt="{\displaystyle \color {Mahogany}{\text{Mahogany}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Maroon}{\text{Maroon}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#AF3235"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Maroon</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Maroon}{\text{Maroon}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/044067e35c6d7300bb3eae363ded1474ba41cc66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.822ex; height:2.176ex;" alt="{\displaystyle \color {Maroon}{\text{Maroon}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Melon}{\text{Melon}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#F89E7B"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Melon</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Melon}{\text{Melon}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b294c896e672f30be984a6ed6231133a5c21759" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.265ex; height:2.176ex;" alt="{\displaystyle \color {Melon}{\text{Melon}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {MidnightBlue}{\text{MidnightBlue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#006795"> <mrow class="MJX-TeXAtom-ORD"> <mtext>MidnightBlue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {MidnightBlue}{\text{MidnightBlue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc907eed134a852f879bcefcc6d13b6f3be1bd9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.987ex; height:2.509ex;" alt="{\displaystyle \color {MidnightBlue}{\text{MidnightBlue}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Mulberry}{\text{Mulberry}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#A93C93"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Mulberry</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Mulberry}{\text{Mulberry}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f2f17a6590904b66c988f413f2d7c4b87b5b9b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.446ex; height:2.509ex;" alt="{\displaystyle \color {Mulberry}{\text{Mulberry}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {NavyBlue}{\text{NavyBlue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#006EB8"> <mrow class="MJX-TeXAtom-ORD"> <mtext>NavyBlue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {NavyBlue}{\text{NavyBlue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48fd2fded6ba3f887be3d2804cba25aa16df71b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.978ex; height:2.509ex;" alt="{\displaystyle \color {NavyBlue}{\text{NavyBlue}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {OliveGreen}{\text{OliveGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#3C8031"> <mrow class="MJX-TeXAtom-ORD"> <mtext>OliveGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {OliveGreen}{\text{OliveGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9d7067aca83dcc1e06c13aabc5eb9b6797d7aad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.455ex; height:2.176ex;" alt="{\displaystyle \color {OliveGreen}{\text{OliveGreen}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Orange}{\text{Orange}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#F58137"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Orange</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Orange}{\text{Orange}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3353fcf1a14db06c2231c94f31d3d81a795cbdc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.37ex; height:2.509ex;" alt="{\displaystyle \color {Orange}{\text{Orange}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {OrangeRed}{\text{OrangeRed}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#ED135A"> <mrow class="MJX-TeXAtom-ORD"> <mtext>OrangeRed</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {OrangeRed}{\text{OrangeRed}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f017a4f98a7e517114678c038dbcb578154d7e90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.405ex; height:2.509ex;" alt="{\displaystyle \color {OrangeRed}{\text{OrangeRed}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Orchid}{\text{Orchid}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#AF72B0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Orchid</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Orchid}{\text{Orchid}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08e38d66a6682711544fae2a1b11871b597b7d31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.984ex; height:2.176ex;" alt="{\displaystyle \color {Orchid}{\text{Orchid}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Peach}{\text{Peach}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#F7965A"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Peach</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Peach}{\text{Peach}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf121e2665402a0f97e2ef8a06aaf0ce094d7c8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.103ex; height:2.176ex;" alt="{\displaystyle \color {Peach}{\text{Peach}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Periwinkle}{\text{Periwinkle}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#7977B8"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Periwinkle</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Periwinkle}{\text{Periwinkle}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63cfcff2b07c668ea68466dc3fae0d75b68f06ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.698ex; height:2.176ex;" alt="{\displaystyle \color {Periwinkle}{\text{Periwinkle}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {PineGreen}{\text{PineGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#008B72"> <mrow class="MJX-TeXAtom-ORD"> <mtext>PineGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {PineGreen}{\text{PineGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2482178ba361a0252af0346b3470b3e9cbd9ea7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.648ex; height:2.176ex;" alt="{\displaystyle \color {PineGreen}{\text{PineGreen}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Plum}{\text{Plum}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#92268F"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Plum</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Plum}{\text{Plum}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bea41a372002b96c773cf9b68432b0a864086713" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.458ex; height:2.176ex;" alt="{\displaystyle \color {Plum}{\text{Plum}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {ProcessBlue}{\text{ProcessBlue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00B0F0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ProcessBlue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {ProcessBlue}{\text{ProcessBlue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddeb0bedc89f555096fe5db91a880010e1b5e0c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.172ex; height:2.176ex;" alt="{\displaystyle \color {ProcessBlue}{\text{ProcessBlue}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Purple}{\text{Purple}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#99479B"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Purple</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Purple}{\text{Purple}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3adecc8e0bc61c122a2abf10dfb5fa882cb5faa3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.759ex; height:2.509ex;" alt="{\displaystyle \color {Purple}{\text{Purple}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {RawSienna}{\text{RawSienna}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#974006"> <mrow class="MJX-TeXAtom-ORD"> <mtext>RawSienna</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {RawSienna}{\text{RawSienna}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a3a4fa198c3318ab96d9a260043e26c33be11a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.27ex; height:2.176ex;" alt="{\displaystyle \color {RawSienna}{\text{RawSienna}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Red}{\text{Red}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#ED1B23"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Red</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Red}{\text{Red}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f16d4c73d264f217f63060eaefe6a9268570b8ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.035ex; height:2.176ex;" alt="{\displaystyle \color {Red}{\text{Red}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {RedOrange}{\text{RedOrange}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#F26035"> <mrow class="MJX-TeXAtom-ORD"> <mtext>RedOrange</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {RedOrange}{\text{RedOrange}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7587f81039d518a1cd36a21f1009d7b7e4091231" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.405ex; height:2.509ex;" alt="{\displaystyle \color {RedOrange}{\text{RedOrange}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {RedViolet}{\text{RedViolet}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#A1246B"> <mrow class="MJX-TeXAtom-ORD"> <mtext>RedViolet</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {RedViolet}{\text{RedViolet}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab645c47cc32ef8f3c83fcdfa67accaf8df305d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.172ex; height:2.176ex;" alt="{\displaystyle \color {RedViolet}{\text{RedViolet}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Rhodamine}{\text{Rhodamine}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#EF559F"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Rhodamine</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Rhodamine}{\text{Rhodamine}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11ae4bc9207163b2552133758f1003c75a3a0192" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.528ex; height:2.176ex;" alt="{\displaystyle \color {Rhodamine}{\text{Rhodamine}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {RoyalBlue}{\text{RoyalBlue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#0071BC"> <mrow class="MJX-TeXAtom-ORD"> <mtext>RoyalBlue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {RoyalBlue}{\text{RoyalBlue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74bd6d025f1f910f7ef801eabe070cffade2240b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.527ex; height:2.509ex;" alt="{\displaystyle \color {RoyalBlue}{\text{RoyalBlue}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {RoyalPurple}{\text{RoyalPurple}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#613F99"> <mrow class="MJX-TeXAtom-ORD"> <mtext>RoyalPurple</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {RoyalPurple}{\text{RoyalPurple}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dc439e89c993b21e67af30eda8facdd4a4cc87f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.669ex; height:2.509ex;" alt="{\displaystyle \color {RoyalPurple}{\text{RoyalPurple}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {RubineRed}{\text{RubineRed}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#ED017D"> <mrow class="MJX-TeXAtom-ORD"> <mtext>RubineRed</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {RubineRed}{\text{RubineRed}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4b90e97f502bfff15df435d6542aea7e887863" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.303ex; height:2.176ex;" alt="{\displaystyle \color {RubineRed}{\text{RubineRed}}}"/></span> </td></tr> <tr> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Salmon}{\text{Salmon}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#F69289"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Salmon</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Salmon}{\text{Salmon}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b69033e30c09b9b85083b9a3962caf290eee96e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.493ex; height:2.176ex;" alt="{\displaystyle \color {Salmon}{\text{Salmon}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {SeaGreen}{\text{SeaGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#3FBC9D"> <mrow class="MJX-TeXAtom-ORD"> <mtext>SeaGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {SeaGreen}{\text{SeaGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cda6f69a8439d27939aed44567e3071cc519e7d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.581ex; height:2.176ex;" alt="{\displaystyle \color {SeaGreen}{\text{SeaGreen}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Sepia}{\text{Sepia}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#671800"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Sepia</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Sepia}{\text{Sepia}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72287ba5bf689ad8d016caec1fa0df9f60c8f891" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.427ex; height:2.509ex;" alt="{\displaystyle \color {Sepia}{\text{Sepia}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {SkyBlue}{\text{SkyBlue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#46C5DD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>SkyBlue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {SkyBlue}{\text{SkyBlue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14730537d98c7afb4881d2fccbd155e2c1ca6d51" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.365ex; height:2.509ex;" alt="{\displaystyle \color {SkyBlue}{\text{SkyBlue}}}"/></span> </td></tr> <tr> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {SpringGreen}{\text{SpringGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#C6DC67"> <mrow class="MJX-TeXAtom-ORD"> <mtext>SpringGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {SpringGreen}{\text{SpringGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d359e9881409618c2bbaa48117f5ec24efec772c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.692ex; height:2.509ex;" alt="{\displaystyle \color {SpringGreen}{\text{SpringGreen}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Tan}{\text{Tan}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#DA9D76"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Tan</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Tan}{\text{Tan}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b31994a9d3d361aaeceeb6bea08e8d5b6e6fd35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.133ex; height:2.176ex;" alt="{\displaystyle \color {Tan}{\text{Tan}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {TealBlue}{\text{TealBlue}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00AEB3"> <mrow class="MJX-TeXAtom-ORD"> <mtext>TealBlue</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {TealBlue}{\text{TealBlue}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5df7e8bea9382b102717d3df248486063a204a32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.137ex; height:2.176ex;" alt="{\displaystyle \color {TealBlue}{\text{TealBlue}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Thistle}{\text{Thistle}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#D883B7"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Thistle</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Thistle}{\text{Thistle}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/630bc23d464b9714bc61f09f5bb533565902da3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.118ex; height:2.176ex;" alt="{\displaystyle \color {Thistle}{\text{Thistle}}}"/></span> </td></tr> <tr> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Turquoise}{\text{Turquoise}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#00B4CE"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Turquoise</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Turquoise}{\text{Turquoise}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fce53ff2bc491c0e7334d4c4400b328d4caaf8ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.16ex; height:2.509ex;" alt="{\displaystyle \color {Turquoise}{\text{Turquoise}}}"/></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Violet}{\text{Violet}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#58429B"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Violet</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Violet}{\text{Violet}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e9be4147e73c6111bbb268b8c36ae2c80c69ed8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.136ex; height:2.176ex;" alt="{\displaystyle \color {Violet}{\text{Violet}}}"/></span></td> <td style="background-color: white;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {VioletRed}{\text{VioletRed}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#EF58A0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>VioletRed</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {VioletRed}{\text{VioletRed}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e52b3e67846dab931b4b039db3b745ad55747af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.172ex; height:2.176ex;" alt="{\displaystyle \color {VioletRed}{\text{VioletRed}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\color {White}{\text{White}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#FFFFFF"> <mrow class="MJX-TeXAtom-ORD"> <mtext>White</mtext> </mrow> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\color {White}{\text{White}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25722ae3723561faddd9504839cd2bd6f11f9070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.265ex; height:2.176ex;" alt="{\displaystyle {\color {White}{\text{White}}}}"/></span> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {WildStrawberry}{\text{WildStrawberry}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#EE2967"> <mrow class="MJX-TeXAtom-ORD"> <mtext>WildStrawberry</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {WildStrawberry}{\text{WildStrawberry}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac1e37d4f01306e3c2ffd31a305ad12a85565f72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.3ex; height:2.509ex;" alt="{\displaystyle \color {WildStrawberry}{\text{WildStrawberry}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {Yellow}{\text{Yellow}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#FFF200"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Yellow</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {Yellow}{\text{Yellow}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb139eff2ef1145099c09f02bfb996673841bee0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.91ex; height:2.176ex;" alt="{\displaystyle \color {Yellow}{\text{Yellow}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {YellowGreen}{\text{YellowGreen}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#98CC70"> <mrow class="MJX-TeXAtom-ORD"> <mtext>YellowGreen</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {YellowGreen}{\text{YellowGreen}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23abea6447eebff86c8fd61ea0cc8f3be26046f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.003ex; height:2.176ex;" alt="{\displaystyle \color {YellowGreen}{\text{YellowGreen}}}"/></span></td> <td style="background-color: black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \color {YellowOrange}{\text{YellowOrange}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#FAA21A"> <mrow class="MJX-TeXAtom-ORD"> <mtext>YellowOrange</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \color {YellowOrange}{\text{YellowOrange}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a10bf6828901303381659d98052767d68e57c342" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.279ex; height:2.509ex;" alt="{\displaystyle \color {YellowOrange}{\text{YellowOrange}}}"/></span> </td></tr></tbody></table> <p>Color should not be used as the <i>only</i> way to identify something, because it will become meaningless on black-and-white media or for color-blind people. See <a href="/wiki/Wikipedia:Manual_of_Style_(accessibility)#Color" class="mw-redirect" title="Wikipedia:Manual of Style (accessibility)">WP:Manual of Style (accessibility)#Color</a>. </p><p>Latex does not have a command for setting the background color. The most effective way of setting a background color is by setting a CSS styling rule for a table cell: </p> <div style="display: inline-block;" class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><pre><span></span><span class="p">{|</span><span class="w"> </span><span class="na">class</span><span class="o">=</span><span class="s2">"wikitable"</span><span class="w"> </span><span class="na">align</span><span class="o">=</span><span class="s2">"center"</span> <span class="p">|</span><span class="w"> </span><span class="na">style</span><span class="o">=</span><span class="s2">"background-color: gray;"</span><span class="w"> </span><span class="p">|</span> <span class="p"><</span><span class="nt">math</span><span class="p">></span>x<span class="nb">^</span>2<span class="p"></</span><span class="nt">math</span><span class="p">></span> <span class="p">|</span><span class="w"> </span><span class="na">style</span><span class="o">=</span><span class="s2">"background-color: Goldenrod;"</span><span class="w"> </span><span class="p">|</span> <span class="p"><</span><span class="nt">math</span><span class="p">></span>y<span class="nb">^</span>3<span class="p"></</span><span class="nt">math</span><span class="p">></span> <span class="p">|}</span> </pre></div> <p>Rendered as: </p> <table class="wikitable" align="center"> <tbody><tr> <td style="background-color: gray;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf0bf28fd28f45d07e1ceb909ce333c18c558c93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.384ex; height:2.676ex;" alt="{\displaystyle x^{2}}"/></span> </td> <td style="background-color: Goldenrod;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82fc450dcc989516e27075a2a87b926cd0d8dfb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.215ex; height:3.009ex;" alt="{\displaystyle y^{3}}"/></span> </td></tr></tbody></table> <p>Custom colors can be defined using: </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\definecolor</span><span class="nb">{</span>myorange<span class="nb">}{</span>rgb<span class="nb">}{</span>1,0.65,0.4<span class="nb">}</span><span class="k">\color</span><span class="nb">{</span>myorange<span class="nb">}</span>e<span class="nb">^{</span>i <span class="k">\pi</span><span class="nb">}</span><span class="k">\color</span><span class="nb">{</span>Black<span class="nb">}</span> + 1 = 0 </pre></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \definecolor {myorange}{rgb}{1,0.65,0.4}\color {myorange}e^{i\pi }\color {Black}+1=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle mathcolor="#ffa566"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>π</mi> </mrow> </msup> <mstyle mathcolor="#221E1F"> <mo>+</mo> <mn>1</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \definecolor {myorange}{rgb}{1,0.65,0.4}\color {myorange}e^{i\pi }\color {Black}+1=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed4c1c7a7c85fdb9f00abd7de2eecd272e863a6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.089ex; height:2.843ex;" alt="{\displaystyle \definecolor {myorange}{rgb}{1,0.65,0.4}\color {myorange}e^{i\pi }\color {Black}+1=0}"/></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Formatting_issues" data-mw-thread-id="h-Formatting_issues-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Formatting_issues-Formatting_using_LaTeX"></span>Formatting issues<span data-mw-comment-end="h-Formatting_issues-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=46" title="Edit section: Formatting issues"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Spacing_2" data-mw-thread-id="h-Spacing_2-Formatting_issues"><span data-mw-comment-start="" id="h-Spacing_2-Formatting_issues"></span>Spacing<span data-mw-comment-end="h-Spacing_2-Formatting_issues"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=47" title="Edit section: Spacing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Quad_(typography)" title="Quad (typography)">Quad (typography)</a></div> <p>TeX handles most spacing automatically, but you may sometimes want manual control. </p> <table class="wikitable"> <tbody><tr> <th>Feature</th> <th>Syntax</th> <th>How it looks rendered </th></tr> <tr> <td>double quad space</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a <span class="k">\qquad</span> b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\qquad b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="2em"></mspace> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\qquad b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4a8df0bfb40654ae8d589e4387f2461d1844732" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.873ex; height:2.176ex;" alt="{\displaystyle a\qquad b}"/></span> </td></tr> <tr> <td>quad space</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a <span class="k">\quad</span> b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\quad b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="1em"></mspace> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\quad b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5ca965cb32ecf465636a8a130828745cc95de57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.55ex; height:2.176ex;" alt="{\displaystyle a\quad b}"/></span> </td></tr> <tr> <td>text space</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a<span class="k">\ </span>b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\ b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mtext> </mtext> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\ b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41b2e86093e63e6ba70d588bae01e959dccc6ee3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.808ex; height:2.176ex;" alt="{\displaystyle a\ b}"/></span> </td></tr> <tr> <td>text space in text mode</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a <span class="k">\text</span><span class="nb">{</span> <span class="nb">}</span> b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a{\text{ }}b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> </mrow> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a{\text{ }}b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e156e468c9077ba71593f893770cb36b606bb53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.808ex; height:2.176ex;" alt="{\displaystyle a{\text{ }}b}"/></span> </td></tr> <tr> <td>large space</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a<span class="k">\;</span>b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\;b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thickmathspace"></mspace> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\;b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8941182a6282415d9a472358243171ced1543936" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.873ex; height:2.176ex;" alt="{\displaystyle a\;b}"/></span> </td></tr> <tr> <td>medium space</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a<span class="k">\<</span>b</code></td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">Not supported </td></tr> <tr> <td>small space</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a<span class="k">\,</span>b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\,b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace"></mspace> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c05a31dfe5e0968f155a73d46d6fbb44d412960e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.614ex; height:2.176ex;" alt="{\displaystyle a\,b}"/></span> </td></tr> <tr> <td>tiny space (use for multiplication of factors)</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">ab</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ab}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49337c5cf256196e2292f7047cb5da68c24ca95d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.227ex; height:2.176ex;" alt="{\displaystyle ab}"/></span> </td></tr> <tr> <td>tiny space (syntax space ignored)</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ab}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49337c5cf256196e2292f7047cb5da68c24ca95d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.227ex; height:2.176ex;" alt="{\displaystyle ab}"/></span> </td></tr> <tr> <td>no space (use for multi-letter variables)</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\mathit</span><span class="nb">{</span>ab<span class="nb">}</span></code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {ab}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">a</mi> <mi class="MJX-tex-mathit" mathvariant="italic">b</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {ab}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dba9758a72f5538857c424abb0b377967d0ef71b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.016ex; width:2.274ex; height:2.176ex;" alt="{\displaystyle {\mathit {ab}}}"/></span> </td></tr> <tr> <td>small negative space</td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a<span class="k">\!</span>b</code></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\!b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="negativethinmathspace"></mspace> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\!b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/528e2a50a16b3e049f6c282703312c93d27f3ae1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.84ex; height:2.176ex;" alt="{\displaystyle a\!b}"/></span> </td></tr> <tr> <td><a href="/wiki/Zero-width_space" title="Zero-width space">zero-width space</a></td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">a<span class="k">\hspace</span><span class="nb">{</span>0pt<span class="nb">}</span>b</code></td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">Not supported </td></tr></tbody></table> <p>Automatic spacing may be broken in very long expressions (because they produce an overfull hbox in TeX): </p> <dl><dd><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+<span class="k">\cdots</span></code></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mn>4</mn> <mo>+</mo> <mn>5</mn> <mo>+</mo> <mn>6</mn> <mo>+</mo> <mn>7</mn> <mo>+</mo> <mn>8</mn> <mo>+</mo> <mn>9</mn> <mo>+</mo> <mn>10</mn> <mo>+</mo> <mn>11</mn> <mo>+</mo> <mn>12</mn> <mo>+</mo> <mn>13</mn> <mo>+</mo> <mn>14</mn> <mo>+</mo> <mn>15</mn> <mo>+</mo> <mn>16</mn> <mo>+</mo> <mn>17</mn> <mo>+</mo> <mn>18</mn> <mo>+</mo> <mn>19</mn> <mo>+</mo> <mn>20</mn> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eff380965a1da31dcca881d7170fa55ee991980b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:99.57ex; height:2.343ex;" alt="{\displaystyle 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots }"/></span></dd></dl> <p>This can be remedied by putting a pair of braces { } around the whole expression: </p> <dl><dd><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="nb">{</span>0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+<span class="k">\cdots</span><span class="nb">}</span></code></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mo>+</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mn>4</mn> <mo>+</mo> <mn>5</mn> <mo>+</mo> <mn>6</mn> <mo>+</mo> <mn>7</mn> <mo>+</mo> <mn>8</mn> <mo>+</mo> <mn>9</mn> <mo>+</mo> <mn>10</mn> <mo>+</mo> <mn>11</mn> <mo>+</mo> <mn>12</mn> <mo>+</mo> <mn>13</mn> <mo>+</mo> <mn>14</mn> <mo>+</mo> <mn>15</mn> <mo>+</mo> <mn>16</mn> <mo>+</mo> <mn>17</mn> <mo>+</mo> <mn>18</mn> <mo>+</mo> <mn>19</mn> <mo>+</mo> <mn>20</mn> <mo>+</mo> <mo>⋯</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ec77750eb3623dca0dc573b6c2403056b860740" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:99.57ex; height:2.343ex;" alt="{\displaystyle {0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots }}"/></span></dd></dl> <p>When relational symbols such as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \uparrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↑</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \uparrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddb20b28c74cdaa09e1f101d426441da1996072f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \uparrow }"/></span> are employed as ordinary symbols, for example in <a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">bra–ket notation</a>, additional spacing may have to be avoided: </p> <table class="wikitable"> <tbody><tr> <th>Feature </th> <th>Syntax </th> <th>How it looks rendered </th></tr> <tr> <td>without special formatting </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">| <span class="k">\uparrow</span> <span class="k">\rangle</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\uparrow \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo stretchy="false">↑</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\uparrow \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b194dca66d255bc2bac6210dc32be258cabcda3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.359ex; height:2.843ex;" alt="{\displaystyle |\uparrow \rangle }"/></span> </td></tr> <tr> <td>explicit opening and closing delimiter </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\left</span>| <span class="k">\uparrow</span> <span class="k">\right\rangle</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left|\uparrow \right\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mo stretchy="false">↑</mo> <mo>⟩</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|\uparrow \right\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b63af311377b1ea64952f5b9389a8a8f9d994a32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle \left|\uparrow \right\rangle }"/></span> </td></tr> <tr> <td>with additional braces </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">| <span class="nb">{</span><span class="k">\uparrow</span><span class="nb">}</span> <span class="k">\rangle</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\uparrow }\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↑</mo> </mrow> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\uparrow }\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e81fba5ac4e54a40f5b9d63e66548328b7ffb6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle |{\uparrow }\rangle }"/></span> </td></tr> <tr> <td>arrow as ordinary symbol </td> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">| <span class="k">\mathord\uparrow</span> <span class="k">\rangle</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\mathord {\uparrow }}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↑</mo> </mrow> </mrow> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\mathord {\uparrow }}\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80c2fb78517946b1381235725514c361e60e197c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.714ex; height:2.843ex;" alt="{\displaystyle |{\mathord {\uparrow }}\rangle }"/></span> </td></tr></tbody></table> <div class="mw-heading mw-heading5"><h5 id="Empty_horizontal_or_vertical_spacing" data-mw-thread-id="h-Empty_horizontal_or_vertical_spacing-Spacing_2"><span data-mw-comment-start="" id="h-Empty_horizontal_or_vertical_spacing-Spacing_2"></span>Empty horizontal or vertical spacing<span data-mw-comment-end="h-Empty_horizontal_or_vertical_spacing-Spacing_2"></span></h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=48" title="Edit section: Empty horizontal or vertical spacing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <code>phantom</code> commands create empty horizontal and/or vertical space the same height and/or width of the argument. </p> <table class="wikitable"> <tbody><tr> <th>Feature </th> <th>Syntax </th> <th>How it looks rendered </th></tr> <tr> <td>Empty horizontal and vertical spacing </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\Gamma</span><span class="nb">^{</span><span class="k">\phantom</span><span class="nb">{</span>i<span class="nb">}</span>j<span class="nb">}_{</span>i<span class="k">\phantom</span><span class="nb">{</span>j<span class="nb">}</span>k<span class="nb">}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma _{i{\phantom {j}}k}^{{\phantom {i}}j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi mathvariant="normal">Γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mphantom> <mi>j</mi> </mphantom> </mrow> </mrow> <mi>k</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mphantom> <mi>i</mi> </mphantom> </mrow> </mrow> <mi>j</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma _{i{\phantom {j}}k}^{{\phantom {i}}j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b47f35beb1b1c4e137be2d65aa9b06c1b3b034f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:3.786ex; height:3.843ex;" alt="{\displaystyle \Gamma _{i{\phantom {j}}k}^{{\phantom {i}}j}}"/></span> </td></tr> <tr> <td>Empty vertical spacing </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr">-e<span class="k">\sqrt</span><span class="nb">{</span><span class="k">\vphantom</span><span class="nb">{</span>p'<span class="nb">}</span>p<span class="nb">}</span>,<span class="k">\;</span> -e'<span class="k">\sqrt</span><span class="nb">{</span>p'<span class="nb">}</span>,<span class="k">\;</span> <span class="k">\ldots</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -e{\sqrt {{\vphantom {p'}}p}},\;-e'{\sqrt {p'}},\;\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mpadded width="0"> <mphantom> <msup> <mi>p</mi> <mo>′</mo> </msup> </mphantom> </mpadded> </mrow> </mrow> <mi>p</mi> </msqrt> </mrow> <mo>,</mo> <mspace width="thickmathspace"></mspace> <mo>−</mo> <msup> <mi>e</mi> <mo>′</mo> </msup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>p</mi> <mo>′</mo> </msup> </msqrt> </mrow> <mo>,</mo> <mspace width="thickmathspace"></mspace> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -e{\sqrt {{\vphantom {p'}}p}},\;-e'{\sqrt {p'}},\;\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f164eef493a76f886009a6f48db3778ef4b733c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:20.22ex; height:4.843ex;" alt="{\displaystyle -e{\sqrt {{\vphantom {p'}}p}},\;-e'{\sqrt {p'}},\;\ldots }"/></span> </td></tr> <tr> <td>Empty horizontal spacing </td> <td><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="k">\int</span> u<span class="nb">^</span>2<span class="k">\,</span>du=<span class="k">\underline</span><span class="nb">{</span><span class="k">\hphantom</span><span class="nb">{</span>(2/3)u<span class="nb">^</span>3+C<span class="nb">}}</span></code> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int u^{2}\,du={\underline {\hphantom {(2/3)u^{3}+C}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>u</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <munder> <mrow class="MJX-TeXAtom-ORD"> <mpadded height="0" depth="0"> <mphantom> <mo stretchy="false">(</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> <mo stretchy="false">)</mo> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mi>C</mi> </mphantom> </mpadded> </mrow> <mo>_</mo> </munder> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int u^{2}\,du={\underline {\hphantom {(2/3)u^{3}+C}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0fe7ac7c68b8b2b67e9ad99d9dc26aecc061a28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.285ex; height:5.676ex;" alt="{\displaystyle \int u^{2}\,du={\underline {\hphantom {(2/3)u^{3}+C}}}}"/></span> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Alignment_with_normal_text_flow" data-mw-thread-id="h-Alignment_with_normal_text_flow-Formatting_issues"><span data-mw-comment-start="" id="h-Alignment_with_normal_text_flow-Formatting_issues"></span>Alignment with normal text flow<span data-mw-comment-end="h-Alignment_with_normal_text_flow-Formatting_issues"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=49" title="Edit section: Alignment with normal text flow"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Because of the default CSS </p> <div class="mw-highlight mw-highlight-lang-css mw-content-ltr" dir="ltr"><pre><span></span><span class="nt">img</span><span class="p">.</span><span class="nc">tex</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">vertical-align</span><span class="p">:</span><span class="w"> </span><span class="kc">middle</span><span class="p">;</span><span class="w"> </span><span class="p">}</span> </pre></div> <p>an inline expression like <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{-N}^{N}e^{x}\,dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msubsup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{-N}^{N}e^{x}\,dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e46aa8f0e931b68cb38803d3881553c51d87b16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:9.838ex; height:6.343ex;" alt="{\displaystyle \int _{-N}^{N}e^{x}\,dx}"/></span> should look good. </p><p>If you need to align it otherwise, use <code><math style="vertical-align:-100%;">...</math></code> and play with the <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">vertical-align</code> argument until you get it right; however, how it looks may depend on the browser and the browser settings. </p><p>If you rely on this workaround, if and when the rendering on the server gets fixed in a future release, this extra manual offset will suddenly make every affected formula align <i>incorrectly</i>. So use it sparingly, if at all. </p> <div class="mw-heading mw-heading3"><h3 id="Unimplemented_elements_and_workarounds" data-mw-thread-id="h-Unimplemented_elements_and_workarounds-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Unimplemented_elements_and_workarounds-Formatting_using_LaTeX"></span>Unimplemented elements and workarounds<span data-mw-comment-end="h-Unimplemented_elements_and_workarounds-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=50" title="Edit section: Unimplemented elements and workarounds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The current Mathoid–MathJax backend has the following elements unimplemented (see also <a rel="nofollow" class="external text" href="https://docs.mathjax.org/en/v2.7-latest/tex.html?highlight=differences#differences">MathJax's own description of differences</a>): </p> <div class="mw-heading mw-heading4"><h4 id="Special_integral_operators" data-mw-thread-id="h-Special_integral_operators-Unimplemented_elements_and_workarounds"><span data-mw-comment-start="" id="h-Special_integral_operators-Unimplemented_elements_and_workarounds"></span>Special integral operators<span data-mw-comment-end="h-Special_integral_operators-Unimplemented_elements_and_workarounds"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=51" title="Edit section: Special integral operators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following integral operators that are not supported by the default font of MathJax 2.7 are available </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span> <span class="k">\oiint</span>, <span class="k">\oiiint</span>, <span class="k">\ointctrclockwise</span>, <span class="k">\varointclockwise</span>, <span class="k">\intbar</span>, <span class="k">\intBar</span> </pre></div> <p>they have poor horizontal spacing, generate cropped SVG images unless used with other tall characters, and appear different from the usual integral symbol <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\int</span></code>: </p><p><br/> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oiint ,\oiiint ,\ointctrclockwise ,\varointclockwise ,\intbar ,\intBar ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-VCENTER"> <mstyle mathsize="2.07em"> <mtext>∯</mtext> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-VCENTER"> <mstyle mathsize="2.07em"> <mtext>∰</mtext> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-VCENTER"> <mstyle mathsize="2.07em"> <mtext>∳</mtext> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-VCENTER"> <mstyle mathsize="2.07em"> <mtext>∲</mtext> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-VCENTER"> <mstyle mathsize="2.07em"> <mtext>⨍</mtext> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-VCENTER"> <mstyle mathsize="2.07em"> <mtext>⨎</mtext> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oiint ,\oiiint ,\ointctrclockwise ,\varointclockwise ,\intbar ,\intBar ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa6cd4bbf935f764c0d5fdcef21ee8eeecfb09b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.581ex; margin-top: -2.596ex; margin-bottom: -1.924ex; width:28.057ex; height:6.843ex;" alt="{\displaystyle \oiint ,\oiiint ,\ointctrclockwise ,\varointclockwise ,\intbar ,\intBar ,}"/></span></dd></dl> <p>cf. <a href="https://phabricator.wikimedia.org/T348587" class="extiw" title="phab:T348587">phab:T348587</a>. However, they render fine <a href="https://www.mediawiki.org/wiki/Extension:Math#Viewing_math" class="extiw" title="mw:Extension:Math"> when MathML is used</a>. </p> <div class="mw-heading mw-heading4"><h4 id="\oiint_and_\oiiint" data-mw-thread-id="h-\oiint_and_\oiiint-Unimplemented_elements_and_workarounds"><span id=".5Coiint_and_.5Coiiint"></span><span data-mw-comment-start="" id="h-\oiint_and_\oiiint-Unimplemented_elements_and_workarounds"></span><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiint</span></code> and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiiint</span></code><span data-mw-comment-end="h-\oiint_and_\oiiint-Unimplemented_elements_and_workarounds"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=52" title="Edit section: \oiint and \oiiint"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Elements which are not yet implemented are <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiint</span></code>, namely a two-fold integral <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\iint</span></code> <span class="nowrap">(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \iint }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∬</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \iint }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1534cac573e0e2b359c385293720bfca1193dde3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:3.42ex; height:5.676ex;" alt="{\displaystyle \iint }"/></span>)</span> with a circular curve through the centre of the two integrals, and similarly <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiiint</span></code>, a circular curve through three integrals. In contrast, <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oint</span></code> <span class="nowrap">(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbbea2707a4ee041ddc4da8dd11924d25aa59c89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:2.194ex; height:5.676ex;" alt="{\displaystyle \oint }"/></span>)</span> exists for the single dimension (integration over a curved line within a plane or any space with higher dimension). </p><p>These elements appear in many contexts: <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiint</span></code> denotes a <a href="/wiki/Surface_integral" title="Surface integral">surface integral</a> over the closed 2d boundary of a 3d region (which occurs in much of 3d <a href="/wiki/Vector_calculus" title="Vector calculus">vector calculus</a> and physical applications – like <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a>), likewise <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiiint</span></code> denotes integration over the closed 3d boundary (surface volume) of a 4d region, and they would be strong candidates for the next TeX version. As such there are a lot of workarounds in the present version. </p> <dl><dd><table class="toccolours collapsible collapsed" width="80%" style="text-align:left"> <tbody><tr> <th><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiint</span></code> and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiiint</span></code> using currently implemented symbols </th></tr> <tr> <td><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiint</span></code> looks like: <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \iint \limits _{S}\!\!\!\!\!\!\!\!\!\!\!\subset \!\supset \mathbf {D} \cdot \mathrm {d} \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∬</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </munder> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mo>⊂</mo> <mspace width="negativethinmathspace"></mspace> <mo>⊃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \iint \limits _{S}\!\!\!\!\!\!\!\!\!\!\!\subset \!\supset \mathbf {D} \cdot \mathrm {d} \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/778dadd253487d8defeb7048d936c40c9a460bf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; margin-left: -0.838ex; width:11.56ex; height:7.343ex;" alt="{\displaystyle \iint \limits _{S}\!\!\!\!\!\!\!\!\!\!\!\subset \!\supset \mathbf {D} \cdot \mathrm {d} \mathbf {A} }"/></span>, which uses <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\iint</span></code> along with <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\subset</span></code> and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\supset</span></code> (overdrawn after backspacing):</li></ul> <dl><dd><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\iint\limits</span><span class="nb">_{</span>S<span class="nb">}</span><span class="k">\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset</span> <span class="k">\mathbf</span> D <span class="k">\cdot</span> <span class="k">\mathrm</span><span class="nb">{</span>d<span class="nb">}</span><span class="k">\mathbf</span> A</code></dd></dl> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc \,\,\mathbf {D} \cdot \mathrm {d} \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mo>◯</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc \,\,\mathbf {D} \cdot \mathrm {d} \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37026edfd5c48c45f849dc1d2fc7602a9d88313e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-left: -1.828ex; width:12.461ex; height:5.676ex;" alt="{\displaystyle \int \!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc \,\,\mathbf {D} \cdot \mathrm {d} \mathbf {A} }"/></span>, which uses <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\int</span></code> twice (with some backward <a href="/wiki/Kern_(typography)" class="mw-redirect" title="Kern (typography)">kerning</a>) along with <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\bigcirc</span></code> (also overdrawn after backpacing) to produce a more consistent circle:</li></ul> <dl><dd><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\int\!\!\!\!\int</span><span class="nb">_{</span><span class="k">\partial</span> V<span class="nb">}</span><span class="k">\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf</span> D<span class="k">\cdot\mathrm</span><span class="nb">{</span>d<span class="nb">}</span><span class="k">\mathbf</span> A</code></dd></dl> <p><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiiint</span></code> (should also be preferably more tightly kerned) looks more or less like: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \!\!\!\!\!\int \!\!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset \!\supset \mathbf {D} \cdot \mathrm {d} \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mo>∫</mo> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mo>⊂</mo> <mspace width="negativethinmathspace"></mspace> <mo>⊃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \!\!\!\!\!\int \!\!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset \!\supset \mathbf {D} \cdot \mathrm {d} \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/502118c4895e2dc8d9559583154540362df09216" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-left: -2.344ex; width:13.496ex; height:5.676ex;" alt="{\displaystyle \int \!\!\!\!\!\int \!\!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset \!\supset \mathbf {D} \cdot \mathrm {d} \mathbf {A} }"/></span> which uses three \int symbols (with more backward kerning) with \subset and \supset (overdrawn after backspacing):</li></ul> <dl><dd><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\int\!\!\!\!\!\int\!\!\!\!\!\int</span><span class="nb">_{</span><span class="k">\partial</span> V<span class="nb">}</span><span class="k">\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset</span> <span class="k">\mathbf</span> D<span class="k">\;\cdot\mathrm</span><span class="nb">{</span>d<span class="nb">}</span><span class="k">\mathbf</span> A</code></dd></dl> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \!\!\!\!\!\int \!\!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc \,\,\mathbf {D} \;\cdot \mathrm {d} \mathbf {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mo>∫</mo> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mo>◯</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">D</mi> </mrow> <mspace width="thickmathspace"></mspace> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \!\!\!\!\!\int \!\!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc \,\,\mathbf {D} \;\cdot \mathrm {d} \mathbf {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03b767bb613fd6096c6b807f75739720611a0642" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-left: -1.57ex; width:13.106ex; height:5.676ex;" alt="{\displaystyle \int \!\!\!\!\!\int \!\!\!\!\!\int _{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc \,\,\mathbf {D} \;\cdot \mathrm {d} \mathbf {A} }"/></span>, which uses three <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\int</span></code> symbols (with more backward kerning) along with <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\bigcirc</span></code> (also overdrawn after backspacing):</li></ul> <dl><dd><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\int\!\!\!\!\!\int\!\!\!\!\!\int</span><span class="nb">_{</span><span class="k">\partial</span> V<span class="nb">}</span><span class="k">\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf</span> D<span class="k">\;\cdot\mathrm</span><span class="nb">{</span>d<span class="nb">}</span><span class="k">\mathbf</span> A</code></dd></dl> </td></tr></tbody></table></dd></dl> <p>However, since no standardisation exists as yet, any workaround like this (which uses many <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\!</span></code> symbols for backspacing) should be avoided, if possible. See below for a possibility using PNG image enforcement. </p><p>Note that <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\iint</span></code> (the double integral) and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\iiint</span></code> (the triple integral) are still not kerned as they should preferably be, and are currently rendered as if they were successive <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\int</span></code> symbols; this is not a major problem for reading the formulas, even if the integral symbols before the last one do not have bounds, so it's best to avoid backspacing "hacks" as they may be inconsistent with a possible future better implementation of integrals symbols (with more precisely computed kerning positions). </p><p><br/> </p> <div class="mw-heading mw-heading5"><h5 id="\oiint_and_\oiiint_as_PNG_images" data-mw-thread-id="h-\oiint_and_\oiiint_as_PNG_images-\oiint_and_\oiiint"><span id=".5Coiint_and_.5Coiiint_as_PNG_images"></span><span data-mw-comment-start="" id="h-\oiint_and_\oiiint_as_PNG_images-\oiint_and_\oiiint"></span><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiint</span></code> and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiiint</span></code> as PNG images<span data-mw-comment-end="h-\oiint_and_\oiiint_as_PNG_images-\oiint_and_\oiiint"></span></h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=53" title="Edit section: \oiint and \oiiint as PNG images"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>These symbols are available as PNG images which are also integrated into two templates, <span class="nowrap">{{</span><a href="/wiki/Template:Oiint" title="Template:Oiint">oiint</a><span class="nowrap">}}</span> and <span class="nowrap">{{</span><a href="/wiki/Template:Oiiint" title="Template:Oiiint">oiiint</a><span class="nowrap">}}</span>, which take care of the formatting around the symbols. </p><p>The templates have three parameters: </p> <dl><dt>preintegral</dt> <dd>the text or formula immediately before the integral</dd> <dt>intsubscpt</dt> <dd>the subscript below the integral</dd> <dt>integrand</dt> <dd>the text or formula immediately after the integral</dd></dl> <div class="mw-heading mw-heading6"><h6 id="Examples" data-mw-thread-id="h-Examples-\oiint_and_\oiiint_as_PNG_images"><span data-mw-comment-start="" id="h-Examples-\oiint_and_\oiiint_as_PNG_images"></span>Examples<span data-mw-comment-end="h-Examples-\oiint_and_\oiiint_as_PNG_images"></span></h6><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=54" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Stokes%27_theorem" title="Stokes' theorem">Stokes' theorem</a>: <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="nb">{{</span>oiint | intsubscpt=<math><span class="k">\scriptstyle</span> S</math> | integrand=<math>( <span class="k">\nabla</span> <span class="k">\times</span> <span class="k">\mathbf</span><span class="nb">{</span>F<span class="nb">}</span> ) <span class="k">\cdot</span> <span class="nb">{</span><span class="k">\mathrm</span> d<span class="nb">}</span><span class="k">\mathbf</span><span class="nb">{</span>S<span class="nb">}</span> = <span class="k">\oint</span><span class="nb">_{</span><span class="k">\partial</span> S<span class="nb">}</span> <span class="k">\mathbf</span><span class="nb">{</span>F<span class="nb">}</span> <span class="k">\cdot</span> <span class="nb">{</span><span class="k">\mathrm</span> d<span class="nb">}</span><span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\ell</span><span class="nb">}</span></math><span class="nb">}}</span></code></li></ul> <dl><dd><span class="nowrap mw-no-invert"> <span class="mw-default-size" typeof="mw:File"><span><img alt="\oiint" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/OiintLaTeX.svg/25px-OiintLaTeX.svg.png" decoding="async" width="25" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/OiintLaTeX.svg/38px-OiintLaTeX.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/OiintLaTeX.svg/50px-OiintLaTeX.svg.png 2x" data-file-width="204" data-file-height="354"/></span></span><span style="position:relative; right:8px; top:18px; margin-right:-8px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>S</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62e91bf22a258bad807b5a9ae8068ef38202ca30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.06ex; height:1.676ex;" alt="{\displaystyle \scriptstyle S}"/></span></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\nabla \times \mathbf {F} )\cdot {\mathrm {d} }\mathbf {S} =\oint _{\partial S}\mathbf {F} \cdot {\mathrm {d} }{\boldsymbol {\ell }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo stretchy="false">)</mo> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> <mo>=</mo> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\nabla \times \mathbf {F} )\cdot {\mathrm {d} }\mathbf {S} =\oint _{\partial S}\mathbf {F} \cdot {\mathrm {d} }{\boldsymbol {\ell }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c169a3fc142097392977fe963d91019fcf80b421" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.484ex; height:5.676ex;" alt="{\displaystyle (\nabla \times \mathbf {F} )\cdot {\mathrm {d} }\mathbf {S} =\oint _{\partial S}\mathbf {F} \cdot {\mathrm {d} }{\boldsymbol {\ell }}}"/></span></span></dd></dl> <ul><li><a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère's law</a> + correction: <code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="nb">{{</span>oiint | preintegral=<math><span class="k">\oint</span><span class="nb">_</span>C <span class="k">\mathbf</span><span class="nb">{</span>B<span class="nb">}</span> <span class="k">\cdot</span> <span class="nb">{</span><span class="k">\mathrm</span> d<span class="nb">}</span> <span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\ell</span><span class="nb">}</span> = <span class="k">\mu</span><span class="nb">_</span>0 </math> | intsubscpt = <math><span class="nb">{</span><span class="k">\scriptstyle</span> S<span class="nb">}</span></math> | integrand = <math><span class="k">\left</span> ( <span class="k">\mathbf</span><span class="nb">{</span>J<span class="nb">}</span> + <span class="k">\epsilon</span><span class="nb">_</span>0<span class="k">\frac</span><span class="nb">{</span><span class="k">\partial</span> <span class="k">\mathbf</span><span class="nb">{</span>E<span class="nb">}}{</span><span class="k">\partial</span> t<span class="nb">}</span> <span class="k">\right</span> ) <span class="k">\cdot</span> <span class="nb">{</span><span class="k">\mathrm</span> d<span class="nb">}</span><span class="k">\mathbf</span><span class="nb">{</span>S<span class="nb">}</span></math> <span class="nb">}}</span></code></li></ul> <dl><dd><span class="nowrap mw-no-invert"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oint _{\partial S}\mathbf {B} \cdot {\mathrm {d} }{\boldsymbol {\ell }}=\mu _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oint _{\partial S}\mathbf {B} \cdot {\mathrm {d} }{\boldsymbol {\ell }}=\mu _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df078d02dd15b3f2f634ab7a3846930e1b7b3d90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.433ex; height:5.676ex;" alt="{\displaystyle \oint _{\partial S}\mathbf {B} \cdot {\mathrm {d} }{\boldsymbol {\ell }}=\mu _{0}}"/></span> <span class="mw-default-size" typeof="mw:File"><span><img alt="\oiint" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/OiintLaTeX.svg/25px-OiintLaTeX.svg.png" decoding="async" width="25" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/OiintLaTeX.svg/38px-OiintLaTeX.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/OiintLaTeX.svg/50px-OiintLaTeX.svg.png 2x" data-file-width="204" data-file-height="354"/></span></span><span style="position:relative; right:8px; top:18px; margin-right:-8px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\scriptstyle S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="1"> <mi>S</mi> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\scriptstyle S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1dca5757c655f5ab53abd4b0d246dcfb478810e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.06ex; height:1.676ex;" alt="{\displaystyle {\scriptstyle S}}"/></span></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(\mathbf {J} +\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)\cdot {\mathrm {d} }\mathbf {S} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mo>+</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(\mathbf {J} +\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)\cdot {\mathrm {d} }\mathbf {S} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1570a32f2960011a3300314cbb11ce9fdcc229f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.009ex; height:6.176ex;" alt="{\displaystyle \left(\mathbf {J} +\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)\cdot {\mathrm {d} }\mathbf {S} }"/></span></span></dd></dl> <ul><li>Continuity of <a href="/wiki/4-momentum" class="mw-redirect" title="4-momentum">4-momentum</a> flux (in <a href="/wiki/General_relativity" title="General relativity">general relativity</a>):<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><span class="nb">{{</span>oiiint | preintegral=<math><span class="k">\mathbf</span><span class="nb">{</span>P<span class="nb">}</span> = </math> | intsubscpt=<math><span class="k">\scriptstyle</span> <span class="k">\partial</span> <span class="k">\Omega</span></math> | integrand=<math><span class="k">\mathbf</span><span class="nb">{</span>T<span class="nb">}</span> <span class="k">\cdot</span> <span class="nb">{</span><span class="k">\mathrm</span> d<span class="nb">}^</span>3<span class="k">\boldsymbol</span><span class="nb">{</span><span class="k">\Sigma</span><span class="nb">}</span></math> <math>=0</math><span class="nb">}}</span></code></li></ul> <p><span class="nowrap mw-no-invert"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f240a6b8168dffac4e8cc44066616445a7f7c7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.28ex; height:2.176ex;" alt="{\displaystyle \mathbf {P} =}"/></span> <span class="mw-default-size" typeof="mw:File"><span><img alt="\oiiint" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/OiiintLaTeX.svg/33px-OiiintLaTeX.svg.png" decoding="async" width="33" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/OiiintLaTeX.svg/49px-OiiintLaTeX.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/OiiintLaTeX.svg/65px-OiiintLaTeX.svg.png 2x" data-file-width="263" data-file-height="353"/></span></span><span style="position:relative; right:8px; top:18px; margin-right:-8px;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \partial \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Ω</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \partial \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcd456781c94b0c25b62a55863a43e976a5b3389" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.119ex; height:1.843ex;" alt="{\displaystyle \scriptstyle \partial \Omega }"/></span></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {T} \cdot {\mathrm {d} }^{3}{\boldsymbol {\Sigma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Σ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {T} \cdot {\mathrm {d} }^{3}{\boldsymbol {\Sigma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2156e91b737207fd7ff6ba69c34cf3267062fb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.816ex; height:2.676ex;" alt="{\displaystyle \mathbf {T} \cdot {\mathrm {d} }^{3}{\boldsymbol {\Sigma }}}"/></span><br/><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dc9e66de468806365c20e32e83456cc526ce29e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.616ex; height:2.176ex;" alt="{\displaystyle =0}"/></span></span> </p> <div class="mw-heading mw-heading5"><h5 id="Oriented_\oiint_and_\oiiint_as_PNG_images" data-mw-thread-id="h-Oriented_\oiint_and_\oiiint_as_PNG_images-\oiint_and_\oiiint"><span id="Oriented_.5Coiint_and_.5Coiiint_as_PNG_images"></span><span data-mw-comment-start="" id="h-Oriented_\oiint_and_\oiiint_as_PNG_images-\oiint_and_\oiiint"></span>Oriented <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiint</span></code> and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiiint</span></code> as PNG images<span data-mw-comment-end="h-Oriented_\oiint_and_\oiiint_as_PNG_images-\oiint_and_\oiiint"></span></h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=55" title="Edit section: Oriented \oiint and \oiiint as PNG images"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some variants of <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiint</span></code> and <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\oiiint</span></code> have arrows on them to indicate the sense of integration, such as a line integral around a closed curve in the clockwise sense, and higher dimensional analogues. These are not implemented in <a href="/wiki/TeX" title="TeX">TeX</a> on Wikipedia either, although the template <span class="nowrap">{{</span><a href="/wiki/Template:Intorient" title="Template:Intorient">intorient</a><span class="nowrap">}}</span> is available - see link for details. </p> <div class="mw-heading mw-heading4"><h4 id="Arc_notation_\overarc" data-mw-thread-id="h-Arc_notation_\overarc-Unimplemented_elements_and_workarounds"><span id="Arc_notation_.5Coverarc"></span><span data-mw-comment-start="" id="h-Arc_notation_\overarc-Unimplemented_elements_and_workarounds"></span>Arc notation <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\overarc</span></code><span data-mw-comment-end="h-Arc_notation_\overarc-Unimplemented_elements_and_workarounds"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=56" title="Edit section: Arc notation \overarc"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\overarc</span></code> is not yet implemented to display the arc notation. However, there exists a workaround: use <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\overset</span><span class="nb">{</span><span class="k">\frown</span><span class="nb">}{</span>AB<span class="nb">}</span></code>, which gives </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overset {\frown }{AB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <mi>B</mi> </mrow> <mo>⌢</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overset {\frown }{AB}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4608fbf7084ad30e15487e824daf74260640f810" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:3.343ex;" alt="{\displaystyle {\overset {\frown }{AB}}}"/></span> </p><p>For longer arcs, use <span class="nowrap">{{</span><a href="/wiki/Template:Overarc" title="Template:Overarc">Overarc</a><span class="nowrap">}}</span>: </p><p>3.<span style="line-height: 1.2em; padding-top: 0.2em; border: 1px solid transparent; border-top-color: black; border-top-left-radius: 50% 25%; border-top-right-radius: 50% 25%;">142857</span> </p> <div class="mw-heading mw-heading4"><h4 id="Triple_dot_\dddot" data-mw-thread-id="h-Triple_dot_\dddot-Unimplemented_elements_and_workarounds"><span id="Triple_dot_.5Cdddot"></span><span data-mw-comment-start="" id="h-Triple_dot_\dddot-Unimplemented_elements_and_workarounds"></span>Triple dot <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\dddot</span></code><span data-mw-comment-end="h-Triple_dot_\dddot-Unimplemented_elements_and_workarounds"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=57" title="Edit section: Triple dot \dddot"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\dddot</span></code> is not implemented. For a workaround use <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\overset</span><span class="nb">{</span>...<span class="nb">}{</span>x<span class="nb">}</span></code>, which gives </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overset {...}{x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mrow> <mo>.</mo> <mo>.</mo> <mo>.</mo> </mrow> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overset {...}{x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb8d15e6c0a847c78c77f7f791c74f3c33fb1f43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.372ex; height:2.509ex;" alt="{\displaystyle {\overset {...}{x}}}"/></span>. </p> <div class="mw-heading mw-heading4"><h4 id="Starred_operatorname_\operatorname*" data-mw-thread-id="h-Starred_operatorname_\operatorname*-Unimplemented_elements_and_workarounds"><span id="Starred_operatorname_.5Coperatorname.2A"></span><span data-mw-comment-start="" id="h-Starred_operatorname_\operatorname*-Unimplemented_elements_and_workarounds"></span>Starred operatorname <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\operatorname*</span></code><span data-mw-comment-end="h-Starred_operatorname_\operatorname*-Unimplemented_elements_and_workarounds"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=58" title="Edit section: Starred operatorname \operatorname*"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The starred version of <code>\operatorname</code> is not currently supported. A workaround for </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\operatorname*</span><span class="nb">{</span>median<span class="nb">}_{</span>j<span class="k">\,\ne\,</span>i<span class="nb">}</span> X<span class="nb">_{</span>i,j<span class="nb">}</span> </pre></div> <p>is either </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\operatorname</span><span class="nb">{</span><span class="k">\underset</span><span class="nb">{</span><span class="k">\mathit</span><span class="nb">{</span>j<span class="k">\,\ne\,</span>i<span class="nb">}}{</span>median<span class="nb">}}</span> X<span class="nb">_{</span>i,j<span class="nb">}</span> </pre></div> <p>or </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\mathop</span><span class="nb">{</span><span class="k">\operatorname</span><span class="nb">{</span>median<span class="nb">}}</span><span class="k">\limits</span><span class="nb">_{</span>j<span class="k">\,\ne\,</span>i<span class="nb">}</span> X<span class="nb">_{</span>i,j<span class="nb">}</span> </pre></div> <div class="mw-heading mw-heading4"><h4 id="Strikethrough" data-mw-thread-id="h-Strikethrough-Unimplemented_elements_and_workarounds"><span data-mw-comment-start="" id="h-Strikethrough-Unimplemented_elements_and_workarounds"></span>Strikethrough<span data-mw-comment-end="h-Strikethrough-Unimplemented_elements_and_workarounds"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=59" title="Edit section: Strikethrough"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Strikethrough like <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\sout</span></code> or <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\st</span></code> is not implemented, nor is overlapping like <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\rlap</span></code>. This means struck characters like ƛ are difficult to type, except the hardcoded <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\hbar</span></code>. A workaround suffix for a normal strikethrough is <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">q <span class="k">\!\!\!\frac</span><span class="nb">{}{</span><span class="k">\ </span><span class="nb">}</span></code>, and for elevated strikethrough is <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><span class="k">\lambda</span> <span class="k">\!\!\!</span><span class="nb">^{{}^</span><span class="k">\underline</span><span class="nb">{</span><span class="k">\ \ </span><span class="nb">}}</span></code>, which give </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q\!\!\!{\frac {}{\ }},\quad \lambda \!\!\!^{{}^{\underline {\ \ }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow></mrow> <mtext> </mtext> </mfrac> </mrow> <mo>,</mo> <mspace width="1em"></mspace> <mi>λ</mi> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <msup> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <munder> <mrow> <mtext> </mtext> <mtext> </mtext> </mrow> <mo>_</mo> </munder> </mrow> </msup> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q\!\!\!{\frac {}{\ }},\quad \lambda \!\!\!^{{}^{\underline {\ \ }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4036273a0b5d7d33764f867e395418648d8578b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.092ex; width:6.526ex; height:3.676ex;" alt="{\displaystyle q\!\!\!{\frac {}{\ }},\quad \lambda \!\!\!^{{}^{\underline {\ \ }}}}"/></span></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Formatting_in_\text" data-mw-thread-id="h-Formatting_in_\text-Unimplemented_elements_and_workarounds"><span id="Formatting_in_.5Ctext"></span><span data-mw-comment-start="" id="h-Formatting_in_\text-Unimplemented_elements_and_workarounds"></span>Formatting in \text<span data-mw-comment-end="h-Formatting_in_\text-Unimplemented_elements_and_workarounds"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=60" title="Edit section: Formatting in \text"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Formatting in <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">\text</code> is not supported. In other words, you can't use: </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\text</span><span class="nb">{</span><span class="k">\textsf</span><span class="nb">{</span>textual description of a variable<span class="nb">}}</span> </pre></div> <p>but have to use: </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\mathsf</span><span class="nb">{</span>textual<span class="k">\ </span>description<span class="k">\ </span>of<span class="k">\ </span>a<span class="k">\ </span>variable<span class="nb">}</span> </pre></div> <p>More specifically, in Mathoid's MathJax, no processing is done to the contents of <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">\text</code> at all. The texvcjs component blocks the use of macros, but another way this behavior leaks through is in the processing of quotation marks, where the Unicode version must be used instead of <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">`</code>: </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\text</span><span class="nb">{</span>`failed ``ascii'' quotes'<span class="nb">}</span>,<span class="k">\ \text</span><span class="nb">{</span>‘okay “unicode” quotes’<span class="nb">}</span> </pre></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{`failed ``ascii'' quotes'}},\ {\text{‘okay “unicode” quotes’}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>`failed ``ascii'' quotes'</mtext> </mrow> <mo>,</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>‘okay “unicode” quotes’</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{`failed ``ascii'' quotes'}},\ {\text{‘okay “unicode” quotes’}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ad1ab3840ba0e61c2a660324fc32ce17f0b64ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:48.484ex; height:2.509ex;" alt="{\displaystyle {\text{`failed ``ascii'' quotes'}},\ {\text{‘okay “unicode” quotes’}}}"/></span></dd></dl> <p>It is currently impossible to get <a href="/wiki/Quotation_mark#Typewriters_and_early_computers" title="Quotation mark">straight (typewriter) quotes</a> in MathJax. </p> <div class="mw-heading mw-heading4"><h4 id="Automatic_line-breaking" data-mw-thread-id="h-Automatic_line-breaking-Unimplemented_elements_and_workarounds"><span data-mw-comment-start="" id="h-Automatic_line-breaking-Unimplemented_elements_and_workarounds"></span>Automatic line-breaking<span data-mw-comment-end="h-Automatic_line-breaking-Unimplemented_elements_and_workarounds"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=61" title="Edit section: Automatic line-breaking"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The current image-based implementation precludes automatic line-breaking of inline formulae after binary operators and "=" as seen in TeX. The only workarounds are to <i>not</i> write long formulae inline, or to split the formula into separate parts at each acceptable break point. </p><p>Readers wishing to enable automatic line-breaking can try to <a href="https://www.mediawiki.org/wiki/Extension:Math/advancedSettings#CSS_for_the_MathML_with_SVG_fallback_mode" class="extiw" title="mw:Extension:Math/advancedSettings">have the browser render the MathML itself</a> or to use an alternate in-browser renderer. </p> <div class="mw-heading mw-heading3"><h3 id="Syntax_to_avoid" data-mw-thread-id="h-Syntax_to_avoid-Formatting_using_LaTeX"><span data-mw-comment-start="" id="h-Syntax_to_avoid-Formatting_using_LaTeX"></span>Syntax to avoid<span data-mw-comment-end="h-Syntax_to_avoid-Formatting_using_LaTeX"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=62" title="Edit section: Syntax to avoid"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Unicode_characters" data-mw-thread-id="h-Unicode_characters-Syntax_to_avoid"><span data-mw-comment-start="" id="h-Unicode_characters-Syntax_to_avoid"></span>Unicode characters<span data-mw-comment-end="h-Unicode_characters-Syntax_to_avoid"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=63" title="Edit section: Unicode characters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1264776157">.mw-parser-output .tracked{float:right;clear:right;margin:0 0 1em 1em;width:12em;border:1px solid var(--border-color-base,#a2a9b1);border-radius:2px;background-color:var(--background-color-interactive,#EAECF0);color:var(--color-base,#202122);font-size:85%;text-align:center;padding:0.5em}.mw-parser-output .tracked-url{font-weight:bold}.mw-parser-output .tracked-closure{color:var(--color-emphasized,#000);font-weight:bold;text-transform:uppercase}.mw-parser-output .tracked-resolved{color:var(--color-success,#14866d)}</style><div role="note" class="tracked plainlinks mw-trackedTemplate">Tracked in <a href="https://phabricator.wikimedia.org/" class="extiw" title="phabricator:">Phabricator</a><br/><span class="tracked-url"><a href="https://phabricator.wikimedia.org/T50032" class="extiw" title="phabricator:T50032"><span class="trakfab-T50032"> Task T50032</span></a></span><br/></div> <p>Non-ASCII Unicode characters like <span class="texhtml mvar" style="font-style:italic;">π</span> work in MathML, but not in Mathoid (server-side MathJax in SVG/PNG mode, <i>after</i> validation by texvcjs). They should be avoided for maximum compatibility. </p><p>MathJax itself supports Unicode characters in <code>\text{}</code>, but the texvcjs validator insists on blocking them (replicating old <a href="/w/index.php?title=Texvc&action=edit&redlink=1" class="new" title="Texvc (page does not exist)">texvc</a> behavior). A formal feature request and discussion is required to fix this. </p> <div class="mw-heading mw-heading5"><h5 id="Invisible_Unicode_characters" data-mw-thread-id="h-Invisible_Unicode_characters-Unicode_characters"><span data-mw-comment-start="" id="h-Invisible_Unicode_characters-Unicode_characters"></span>Invisible Unicode characters<span data-mw-comment-end="h-Invisible_Unicode_characters-Unicode_characters"></span></h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=64" title="Edit section: Invisible Unicode characters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A rare but very frustrating cause of inexplicable syntax errors is <i>invisible</i> Unicode characters copied from some other source. For example, the <a href="/wiki/Windows_Calculator" title="Windows Calculator">Windows Calculator</a> includes Unicode <a href="/wiki/Bidirectional_text" title="Bidirectional text">Bidirectional text</a> control characters in its output: U+202D (left-to-right override) at the beginning and U+202C (pop directional formatting) at the end. These characters can be invisibly pasted into the Wikipedia editor, but will cause <strong class="error">Failed to parse (syntax error):</strong> messages from the LaTeX renderer, despite the source <i>appearing</i> to be correct. It can usually be fixed by deleting and manually retyping the beginning and end of the pasted text. </p> <div class="mw-heading mw-heading4"><h4 id="Deprecated_syntax" data-mw-thread-id="h-Deprecated_syntax-Syntax_to_avoid"><span data-mw-comment-start="" id="h-Deprecated_syntax-Syntax_to_avoid"></span>Deprecated syntax<span data-mw-comment-end="h-Deprecated_syntax-Syntax_to_avoid"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=65" title="Edit section: Deprecated syntax"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The texvc processor accepted some non-standard control sequences. These are now deprecated for Wikipedia use because the MathJax-based renderers do not support them. This is part of an effort to update the math engine. See <a href="https://www.mediawiki.org/wiki/Extension:Math/Roadmap" class="extiw" title="mw:Extension:Math/Roadmap">mw:Extension:Math/Roadmap</a> for details. A bot <a href="/wiki/User:Texvc2LaTeXBot" title="User:Texvc2LaTeXBot">User:Texvc2LaTeXBot</a> will replace this syntax on the English Wikipedia. </p> <table class="wikitable"><tbody><tr style="vertical-align:top"><th scope="col" style=""> texvc syntax</th><th scope="col" style=""> Suggested replacement</th><th scope="col"> Comment</th></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> $</td><td style="font-family:monospace;"> \$</td><td> redefinition would involve changing the character code</td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> %</td><td style="font-family:monospace;"> \%</td><td> redefinition would involve changing the character code</td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \or</td><td style="font-family:monospace;"> \lor</td><td> causes the teubner TeX package to fail<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \and</td><td style="font-family:monospace;"> \land</td><td> causes normal align environment to fail</td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \pagecolor</td><td style="font-style:oblique;"> (remove)</td><td> not needed and not working anymore, done manually</td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \part</td><td style="font-family:monospace;"> \partial</td><td> acceptable if the document doesn't use sectioning with <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">\part</code>.</td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \ang</td><td style="font-family:monospace;"> \angle</td><td> this only conflicts with siunitx package.</td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \C</td><td style="font-family:monospace;"> \Complex</td><td> conflicts with puenc.def e.g. from hyperref package</td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \H</td><td style="font-family:monospace;"> \mathbb{H}</td><td> conflicts with text command <code>\H{o}</code>, which is ő.</td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \bold</td><td style="font-family:monospace;"> \mathbf</td><td></td></tr><tr style="vertical-align:top"><td style="font-family:monospace;"> \Bbb</td><td style="font-family:monospace;"> \mathbb</td><td></td></tr></tbody></table> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Chemistry" data-mw-thread-id="h-Chemistry"><span data-mw-comment-start="" id="h-Chemistry"></span>Chemistry<span data-mw-comment-end="h-Chemistry"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=66" title="Edit section: Chemistry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:MATHCHEM"></span></div><div class="module-shortcutboxplain noprint" role="note"><div class="module-shortcutlist"><a href="/wiki/Wikipedia:Shortcut" title="Wikipedia:Shortcut">Shortcut</a></div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Wikipedia:MATHCHEM&redirect=no">WP:MATHCHEM</a></span></li></ul></div></div> <p>There are three ways to render chemical sum formulas as used in <a href="/wiki/Chemical_equation" title="Chemical equation">chemical equations</a>: </p> <ul><li><code class="nowrap"><<a class="mw-selflink-fragment" href="#Chemistry">chem</a>>...</chem></code> (<code class="nowrap"><<a class="mw-selflink-fragment" href="#Chemistry">ce</a>>...</ce></code> is a deprecated alias for it)</li> <li><code class="nowrap"><<a href="https://www.mediawiki.org/wiki/Extension:Math" class="extiw" title="mw:Extension:Math">math</a> chem>...</math></code></li> <li><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> and <code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code></li></ul> <p><code class="nowrap"><<a class="mw-selflink-fragment" href="#Chemistry">chem</a>>X</chem></code> is short for <code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math</span><span class="w"> </span><span class="err">chem</span><span class="nt">></span>\ce{X}<span class="nt"></math></span></code> (where <code>X</code> is a chemical sum formula) </p><p>Technically, <code class="nowrap"><<a href="https://www.mediawiki.org/wiki/Extension:Math" class="extiw" title="mw:Extension:Math">math</a> chem></code> is a <code>math</code> tag with the extension <code>mhchem</code> enabled, according to the <a rel="nofollow" class="external text" href="http://docs.mathjax.org/en/latest/input/tex/extensions/mhchem.html">MathJax documentation</a>. </p><p><a href="/wiki/Wikipedia:Manual_of_Style/Chemistry" title="Wikipedia:Manual of Style/Chemistry">Wikipedia:Manual of Style/Chemistry</a> advises avoiding the <code class="nowrap"><<a class="mw-selflink-fragment" href="#Chemistry">chem</a>></code> and <code class="nowrap"><<a href="https://www.mediawiki.org/wiki/Extension:Math" class="extiw" title="mw:Extension:Math">math</a> chem></code> markup methods when possible. </p><p>Note that the commands <code>\cee</code> and <code>\cf</code> are disabled, because they are marked as deprecated in the <a rel="nofollow" class="external text" href="http://www.ctan.org/pkg/mhchem">mhchem LaTeX package documentation</a>. </p><p>If the formula reaches a certain "complexity", spaces might be ignored (<code><chem>A + B</chem></code> might be rendered as if it were <code><chem>A+B</chem></code> with a positive charge). In that case, write <code><chem>A{} + B</chem></code> (and <i>not</i> <code><chem>{A} + {B}</chem></code> as was previously suggested). This will allow auto-cleaning of formulas once the bug is fixed and/or a newer version of <code>mhchem</code> is available. </p><p>Please note that there are still <a class="external text" href="https://phabricator.wikimedia.org/T140217">major issues</a> with mhchem support in MediaWiki. Some issues can be solved by enabling the extension using <code class="nowrap"><<a href="https://www.mediawiki.org/wiki/Extension:Math" class="extiw" title="mw:Extension:Math">math</a> chem></code> and formatting individual items with <code>\ce</code>. For example, </p> <ul><li><code><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><math chem><span class="k">\ce</span><span class="nb">{</span>pIC<span class="nb">_{</span>50<span class="nb">}}</span> = -<span class="k">\log</span><span class="nb">_{</span>10<span class="nb">}</span> <span class="k">\ce</span><span class="nb">{</span>(IC<span class="nb">_{</span>50<span class="nb">}</span>)<span class="nb">}</span></math></code></code> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {pIC_{50}}}=-\log _{10}{\ce {(IC_{50})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>pIC</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>50</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msubsup> <mtext>IC</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>50</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {pIC_{50}}}=-\log _{10}{\ce {(IC_{50})}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ea65306461d194db53b0cb6d8a0b48937915c00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.418ex; height:3.009ex;" alt="{\displaystyle {\ce {pIC_{50}}}=-\log _{10}{\ce {(IC_{50})}}}"/></span></dd></dl></li></ul> <div class="mw-heading mw-heading3"><h3 id="Molecular_and_condensed_formula" data-mw-thread-id="h-Molecular_and_condensed_formula-Chemistry"><span data-mw-comment-start="" id="h-Molecular_and_condensed_formula-Chemistry"></span>Molecular and condensed formula<span data-mw-comment-end="h-Molecular_and_condensed_formula-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=67" title="Edit section: Molecular and condensed formula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>mhchem</th> <th><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code></th> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code></th> <th>Equivalent HTML </th></tr> <tr> <td style="vertical-align:bottom"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>H2O</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {H2O}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {H2O}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/373648858d1d59d300f88386b46dd95e01f04c5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.605ex; height:2.843ex;" alt="{\displaystyle {\ce {H2O}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>Sb2O3</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {Sb2O3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>Sb</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {Sb2O3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb4d8081a6e7e5f1eba95c6958722b511a3b6e2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.502ex; height:2.843ex;" alt="{\displaystyle {\ce {Sb2O3}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>(NH4)2S</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {(NH4)2S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msubsup> <mtext>NH</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>S</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {(NH4)2S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3db28a1bd8d78037b2d2c7c2d9280bec66b7fee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.697ex; height:3.009ex;" alt="{\displaystyle {\ce {(NH4)2S}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r1260720223">.mw-parser-output div.template-markup-wrapper>:first-child{margin-top:0}.mw-parser-output div.template-markup-wrapper>:last-child{margin-bottom:0}.mw-parser-output .template-markup{margin:0;border:none;word-wrap:break-word;white-space:pre-wrap}.mw-parser-output code.template-markup{padding:0}.mw-parser-output pre.template-markup{padding:2px 0 0}</style> </td> <td class="mw-collapsible mw-collapsed"> <p class="mw-empty-elt"> </p> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|H|2|O}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|Sb|2|O|3}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">Sb<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|({{chem|N|H|4}})|2|S}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">(<span class="chemf nowrap">NH<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span>)<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>S</span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <p class="mw-empty-elt"> </p> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|H2O}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><style data-mw-deduplicate="TemplateStyles:r1123817410">.mw-parser-output .template-chem2-su{display:inline-block;font-size:80%;line-height:1;vertical-align:-0.35em}.mw-parser-output .template-chem2-su>span{display:block;text-align:left}.mw-parser-output sub.template-chem2-sub{font-size:80%;vertical-align:-0.35em}.mw-parser-output sup.template-chem2-sup{font-size:80%;vertical-align:0.65em}</style><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>O</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|Sb2O3}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Sb<sub class="template-chem2-sub">2</sub>O<sub class="template-chem2-sub">3</sub></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|(NH4)2S}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">(NH<sub class="template-chem2-sub">4</sub>)<sub class="template-chem2-sub">2</sub>S</span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <p class="mw-empty-elt"> </p> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">H<sub>2</sub>O</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>H<sub>2</sub>O </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">Sb<sub>2</sub>O<sub>3</sub></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>Sb<sub>2</sub>O<sub>3</sub> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">(NH<sub>4</sub>)<sub>2</sub>S</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>(NH<sub>4</sub>)<sub>2</sub>S </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Bonds" data-mw-thread-id="h-Bonds-Chemistry"><span data-mw-comment-start="" id="h-Bonds-Chemistry"></span>Bonds<span data-mw-comment-end="h-Bonds-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=68" title="Edit section: Bonds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>mhchem</th> <th>Equivalent <code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> and HTML</th> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code> </th></tr> <tr> <td style="vertical-align:bottom"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>C6H5-CHO</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {C6H5-CHO}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mtext>CHO</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {C6H5-CHO}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8435c2507fe927c7129e593d933724df23353f93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.567ex; height:2.843ex;" alt="{\displaystyle {\ce {C6H5-CHO}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>A-B=C#D</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A-B=C#D}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mtext>B</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>≡</mo> </mrow> <mtext>D</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A-B=C#D}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31fe9d0bb3fb9e0dab5c3c572d2b09a84f7fa2c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.267ex; height:2.343ex;" alt="{\displaystyle {\ce {A-B=C#D}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|C|6|H|5}}-CHO <br/> C<sub>6</sub>H<sub>5</sub>-CHO</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">5</sub></span></span></span>-<span class="chemf nowrap">CHO</span> <br/> </p><p>C<sub>6</sub>H<sub>5</sub>-CHO </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">A-B=C≡D</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>N/A </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|C6H5\sCHO}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">5</sub>−CHO</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|1=A\sB=C≡D}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">A−B=C≡D</span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Charges" data-mw-thread-id="h-Charges-Chemistry"><span data-mw-comment-start="" id="h-Charges-Chemistry"></span>Charges<span data-mw-comment-end="h-Charges-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=69" title="Edit section: Charges"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>mhchem</th> <th><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code></th> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code></th> <th>Equivalent HTML </th></tr> <tr> <td style="vertical-align:bottom"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>H+</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {H+}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {H+}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/474f66456168f5fd00301be7b96b2539cf2760b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.254ex; height:2.509ex;" alt="{\displaystyle {\ce {H+}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>NO3-</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {NO3-}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>NO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msubsup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {NO3-}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02e54ddd1b0acf2c3e42d87536ab09fab46126d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.062ex; height:3.176ex;" alt="{\displaystyle {\ce {NO3-}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>CrO4^2-</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {CrO4^2-}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>CrO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>−</mo> </mrow> </msubsup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {CrO4^2-}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dc0bb99de334b2feb0e1e47c942f67119121643" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.731ex; height:3.176ex;" alt="{\displaystyle {\ce {CrO4^2-}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>AgCl2-</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {AgCl2-}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>AgCl</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msubsup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {AgCl2-}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d591eda1af49e75593fa8bb102cf29ff68ae675" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.741ex; height:3.009ex;" alt="{\displaystyle {\ce {AgCl2-}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>[AgCl2]-</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {[AgCl2]-}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>AgCl</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {[AgCl2]-}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05e7091d037f75d840bfe2e759043d37ee81a4b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.089ex; height:3.343ex;" alt="{\displaystyle {\ce {[AgCl2]-}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>Y^99+</chem> <chem>Y^{99+}</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {Y^99+}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>Y</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>99</mn> <mo>+</mo> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {Y^99+}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cff645b09b60dac9b1ba2716f941788c8b579b5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.898ex; height:2.676ex;" alt="{\displaystyle {\ce {Y^99+}}}"/></span><br/><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {Y^{99+}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>Y</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>99</mn> <mspace width="thinmathspace"></mspace> <mo>+</mo> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {Y^{99+}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c6797fc964d546d318693c71739fe6edeaa5391" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.285ex; height:2.676ex;" alt="{\displaystyle {\ce {Y^{99+}}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <p class="mw-empty-elt"> </p> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|H|+}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|N|O|3|-}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">NO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|Cr|O|4|2-}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">CrO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2−</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|Ag|Cl|2|-}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">AgCl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|[{{chem|Ag|Cl|2}}]|-}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">[<span class="chemf nowrap">AgCl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>]<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|Y|99+}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">Y<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">99+</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <p class="mw-empty-elt"> </p> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|H+}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sup class="template-chem2-sup">+</sup></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|NO3(-)}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<span class="template-chem2-su"><span>−</span><span>3</span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|CrO4(2-)}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">CrO<span class="template-chem2-su"><span>2−</span><span>4</span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|AgCl2(-)}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">AgCl<span class="template-chem2-su"><span>−</span><span>2</span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|[AgCl2](-)}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">[AgCl<sub class="template-chem2-sub">2</sub>]<sup>−</sup></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|Y(99+)}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Y<sup>99+</sup></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <p class="mw-empty-elt"> </p> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">H<sup>+</sup></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>H<sup>+</sup> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">NO<sub>3</sub><sup>−</sup></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>NO<sub>3</sub><sup>−</sup> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">CrO<sub>4</sub><sup>2-</sup></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>CrO<sub>4</sub><sup>2-</sup> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">AgCl<sub>2</sub><sup>−</sup></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>AgCl<sub>2</sub><sup>−</sup> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">[AgCl<sub>2</sub>]<sup>−</sup></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>[AgCl<sub>2</sub>]<sup>−</sup> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">Y<sup>99+</sup></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>Y<sup>99+</sup> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Addition_compounds_and_stoichiometric_numbers" data-mw-thread-id="h-Addition_compounds_and_stoichiometric_numbers-Chemistry"><span data-mw-comment-start="" id="h-Addition_compounds_and_stoichiometric_numbers-Chemistry"></span>Addition compounds and stoichiometric numbers<span data-mw-comment-end="h-Addition_compounds_and_stoichiometric_numbers-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=70" title="Edit section: Addition compounds and stoichiometric numbers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>mhchem</th> <th><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code></th> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code> </th></tr> <tr> <td style="vertical-align:middle"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0; vertical-align:middle"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>MgSO4.7H2O</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {MgSO4.7H2O}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>MgSO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo>⋅</mo> <mn>7</mn> <mspace width="thinmathspace"></mspace> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {MgSO4.7H2O}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0801e57fbe2700e474522acb3b08a04448186f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.282ex; height:2.843ex;" alt="{\displaystyle {\ce {MgSO4.7H2O}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>KCr(SO4)2*12H2O</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {KCr(SO4)2*12H2O}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>KCr</mtext> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msubsup> <mtext>SO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo>⋅</mo> <mn>12</mn> <mspace width="thinmathspace"></mspace> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {KCr(SO4)2*12H2O}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ce69af8634b3c89050142f6ab064ebf31c5dd17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.413ex; height:3.009ex;" alt="{\displaystyle {\ce {KCr(SO4)2*12H2O}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>CaSO4.1/2H2O + 1\!1/2 H2O -> CaSO4.2H2O</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {CaSO4.1/2H2O + 1\!1/2 H2O -> CaSO4.2H2O}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>CaSO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo>⋅</mo> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> <mo stretchy="false">⟶</mo> <msubsup> <mtext>CaSO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo>⋅</mo> <mn>2</mn> <mspace width="thinmathspace"></mspace> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {CaSO4.1/2H2O + 1\!1/2 H2O -> CaSO4.2H2O}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0cb858281ddb398822be7fb2e7bed0156752c1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:45.13ex; height:3.509ex;" alt="{\displaystyle {\ce {CaSO4.1/2H2O + 1\!1/2 H2O -> CaSO4.2H2O}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>25/2 O2 + C8H18 -> 8 CO2 + 9 H2O</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {25/2 O2 + C8H18 -> 8 CO2 + 9 H2O}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>25</mn> <mn>2</mn> </mfrac> </mstyle> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo>+</mo> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>18</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">⟶</mo> <mn>8</mn> <mspace width="thinmathspace"></mspace> <msubsup> <mtext>CO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo>+</mo> <mn>9</mn> <mspace width="thinmathspace"></mspace> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {25/2 O2 + C8H18 -> 8 CO2 + 9 H2O}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f73a96de1b4649f2d2403a7ead5e3abc8c607b7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:34.716ex; height:3.509ex;" alt="{\displaystyle {\ce {25/2 O2 + C8H18 -> 8 CO2 + 9 H2O}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0; vertical-align:middle"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr">{{chem|Mg|S|O|4}}<span class="ni">&middot;</span>7{{chem|H|2|O}}</code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">MgSO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span>·7<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr">{{chem|K|Cr|({{chem|S|O|4}})|2}}<span class="ni">&middot;</span>12{{chem|H|2|O}}</code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">KCr(<span class="chemf nowrap">SO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span>)<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>·12<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr">{{chem|Ca|S|O|4}}<span class="ni">&middot;&frac12;</span>{{chem|H|2|O}} + 1<span class="ni">&frac12;</span>{{chem|H|2|O}} → {{chem|Ca|S|O|4}}<span class="ni">&middot;</span>2{{chem|H|2|O}}</code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">CaSO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span>·½<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> + 1½<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> → <span class="chemf nowrap">CaSO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span>·2<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr">{{frac|25|2}}{{chem|O|2}} + {{chem|C|8|H|18}} → 8{{chem|C|O|2}} + 9{{chem|H|2|O}}</code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">25</span>⁄<span class="den">2</span></span><span class="chemf nowrap">O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> + <span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">8</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">18</sub></span></span></span> → 8<span class="chemf nowrap">CO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> + 9<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0; vertical-align:middle"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|MgSO4*7H2O}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">MgSO<sub class="template-chem2-sub">4</sub>·7H<sub>2</sub>O</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|KCr(SO4)2*12H2O}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">KCr(SO<sub class="template-chem2-sub">4</sub>)<sub class="template-chem2-sub">2</sub>·12H<sub>2</sub>O</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|2CaSO4*H2O + 3H2O -> 2CaSO4*2H2O}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2CaSO<sub class="template-chem2-sub">4</sub>·H<sub>2</sub>O + 3H<sub class="template-chem2-sub">2</sub>O → 2CaSO<sub class="template-chem2-sub">4</sub>·2H<sub>2</sub>O</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|25 O2 + 2 C8H18 -> 16 CO2 + 18 H2O}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">25 O<sub class="template-chem2-sub">2</sub> + 2 C<sub class="template-chem2-sub">8</sub>H<sub class="template-chem2-sub">18</sub> → 16 CO<sub class="template-chem2-sub">2</sub> + 18 H<sub class="template-chem2-sub">2</sub>O</span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Wiki_linking" data-mw-thread-id="h-Wiki_linking-Chemistry"><span data-mw-comment-start="" id="h-Wiki_linking-Chemistry"></span>Wiki linking<span data-mw-comment-end="h-Wiki_linking-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=71" title="Edit section: Wiki linking"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="width:100%"> <tbody><tr> <th><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup">25 {{chem|link=oxygen|O|2}} + 2 {{chem|link=octane|C|8|H|18}} → 16 {{chem|link=Carbon dioxide|C|O|2}} + 18 {{chem|link=water|H|2|O}}</pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper">25 <span class="chemf nowrap"><a href="/wiki/Oxygen" title="Oxygen">O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></a></span> + 2 <span class="chemf nowrap"><a href="/wiki/Octane" title="Octane">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">8</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">18</sub></span></span></a></span> → 16 <span class="chemf nowrap"><a href="/wiki/Carbon_dioxide" title="Carbon dioxide">CO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></a></span> + 18 <span class="chemf nowrap"><a href="/wiki/Water" title="Water">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</a></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code> </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup">{{chem2|25 [[oxygen|O2]] + 2 [[octane|C8H18]] -> 16 [[Carbon dioxide|CO2]] + 18 [[water|H2O]]}}</pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">25 <a href="/wiki/Oxygen" title="Oxygen">O<sub class="template-chem2-sub">2</sub></a> + 2 <a href="/wiki/Octane" title="Octane">C<sub class="template-chem2-sub">8</sub>H<sub class="template-chem2-sub">18</sub></a> → 16 <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">CO<sub class="template-chem2-sub">2</sub></a> + 18 <a href="/wiki/Water" title="Water">H<sub class="template-chem2-sub">2</sub>O</a></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="(Italic)_Math" data-mw-thread-id="h-(Italic)_Math-Chemistry"><span id=".28Italic.29_Math"></span><span data-mw-comment-start="" id="h-(Italic)_Math-Chemistry"></span>(Italic) Math<span data-mw-comment-end="h-(Italic)_Math-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=72" title="Edit section: (Italic) Math"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="width:100%"> <tbody><tr> <th>mhchem </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><chem><span class="nb">{</span>C<span class="nb">_</span><span class="k">\mathit</span><span class="nb">{</span>x<span class="nb">}</span>H<span class="nb">_</span><span class="k">\mathit</span><span class="nb">{</span>y<span class="nb">}}</span> + <span class="k">\mathit</span><span class="nb">{</span>z<span class="nb">}</span>O2 -> <span class="nb">{</span><span class="k">\mathit</span><span class="nb">{</span>x<span class="nb">}</span>CO2<span class="nb">}</span> + <span class="k">\frac</span><span class="nb">{</span><span class="k">\mathit</span><span class="nb">{</span>y<span class="nb">}}{</span>2<span class="nb">}</span>H2O</chem></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {{C_{\mathit {x}}H_{\mathit {y}}}+{\mathit {z}}O2->{{\mathit {x}}CO2}+{\frac {\mathit {y}}{2}}H2O}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">x</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">y</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">z</mtext> </mrow> </mrow> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">⟶</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">x</mtext> </mrow> </mrow> <msubsup> <mtext>CO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">y</mtext> </mrow> <mrow> <mn>2</mn> <mspace width="thinmathspace"></mspace> </mrow> </mfrac> </mrow> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {{C_{\mathit {x}}H_{\mathit {y}}}+{\mathit {z}}O2->{{\mathit {x}}CO2}+{\frac {\mathit {y}}{2}}H2O}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/332c1ec61868d27d389180e7db90d5c4ed1c27ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:32.648ex; height:4.843ex;" alt="{\displaystyle {\ce {{C_{\mathit {x}}H_{\mathit {y}}}+{\mathit {z}}O2->{{\mathit {x}}CO2}+{\frac {\mathit {y}}{2}}H2O}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup">{{chem|C|''x''|H|''y''}} + ''z''{{chem|O|2}} → ''x''{{chem|C|O|2}} + {{frac|''y''|2}}{{chem|H|2|O}}</pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>x</i></sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><i>y</i></sub></span></span></span> + <i>z</i><span class="chemf nowrap">O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> → <i>x</i><span class="chemf nowrap">CO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>y</i></span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span><span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code> </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup">{{chem2|C_{''x''}H_{''y''} + ''z'' O2 -> ''x'' CO2}} + {{sfrac|''y''|2}} {{chem2| H2O}}</pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub"><i>x</i></sub>H<sub class="template-chem2-sub"><i>y</i></sub> + <i>z</i> O<sub class="template-chem2-sub">2</sub> → <i>x</i> CO<sub class="template-chem2-sub">2</sub></span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>y</i></span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>O</span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Oxidation_states" data-mw-thread-id="h-Oxidation_states-Chemistry"><span data-mw-comment-start="" id="h-Oxidation_states-Chemistry"></span>Oxidation states<span data-mw-comment-end="h-Oxidation_states-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=73" title="Edit section: Oxidation states"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>mhchem </th> <td style="vertical-align:bottom"> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><chem>Fe^{II}Fe^{III}2O4</chem></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {Fe^{II}Fe^{III}2O4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>Fe</mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>II</mtext> </mrow> </msup> <msubsup> <mtext>Fe</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>III</mtext> </mrow> </msubsup> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {Fe^{II}Fe^{III}2O4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9156733e38a48aab48693dbb461d6580af79c8b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:11.396ex; height:3.343ex;" alt="{\displaystyle {\ce {Fe^{II}Fe^{III}2O4}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> with <code class="nowrap" style=""><sup>...</sup></code> </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup">{{chem|Fe|<sup>II</sup>|Fe|<sup>III</sup>|2|O|4}}</pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="chemf nowrap">Fe<sup>II</sup>Fe<sup>III</sup><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code> </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup">{{chem2|Fe^{II}Fe^{III}2O4}}</pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Fe<sup class="template-chem2-sup">II</sup>Fe<sup class="template-chem2-sup">III</sup><sub class="template-chem2-sub">2</sub>O<sub class="template-chem2-sub">4</sub></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Greek_characters" data-mw-thread-id="h-Greek_characters-Chemistry"><span data-mw-comment-start="" id="h-Greek_characters-Chemistry"></span>Greek characters<span data-mw-comment-end="h-Greek_characters-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=74" title="Edit section: Greek characters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center;"> <tbody><tr> <th>mhchem</th> <th>Equivalent <code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> and HTML</th> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code> </th></tr> <tr> <td style="vertical-align:center;"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0; vertical-align:center"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><chem><span class="k">\mu</span>-Cl</chem></code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {\mu-Cl}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mtext>Cl</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {\mu-Cl}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73adf6346efc46f129a5bad2bbc9c310520510ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.535ex; height:2.676ex;" alt="{\displaystyle {\ce {\mu-Cl}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><chem>[Fe(<span class="k">\eta</span><span class="nb">^</span>5-C5H5)2]</chem></code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {[Fe(\eta^5-C5H5)2]}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>Fe</mtext> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>η</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {[Fe(\eta^5-C5H5)2]}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/223bb3e6afc787238e9493f63b468360da2884bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:16.273ex; height:3.509ex;" alt="{\displaystyle {\ce {[Fe(\eta^5-C5H5)2]}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0; vertical-align:center"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr">''μ''-Cl</code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><i>μ</i>-Cl </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><div class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr"><pre><span></span>[{{chem|Fe|(''η''<span class="p"><</span><span class="nt">sup</span><span class="p">></span>5<span class="p"></</span><span class="nt">sup</span><span class="p">></span>-{{chem|C|5|H|5}})|2}}] <span class="p"><</span><span class="nt">br</span><span class="p">/></span> [Fe(''η''<span class="p"><</span><span class="nt">sup</span><span class="p">></span>5<span class="p"></</span><span class="nt">sup</span><span class="p">></span>-C<span class="p"><</span><span class="nt">sub</span><span class="p">></span>5<span class="p"></</span><span class="nt">sub</span><span class="p">></span>H<span class="p"><</span><span class="nt">sub</span><span class="p">></span>5<span class="p"></</span><span class="nt">sub</span><span class="p">></span>)<span class="p"><</span><span class="nt">sub</span><span class="p">></span>2<span class="p"></</span><span class="nt">sub</span><span class="p">></span>] </pre></div></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>[<span class="chemf nowrap">Fe(<i>η</i><sup>5</sup>-<span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">5</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">5</sub></span></span></span>)<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>]<br/> [Fe(<i>η</i><sup>5</sup>-C<sub>5</sub>H<sub>5</sub>)<sub>2</sub>] </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <p class="mw-empty-elt"> </p> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|''μ''\sCl}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><i>μ</i>−Cl</span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem2|[Fe(''\h''^{5}\sC5H5)2]}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">[Fe(<i>η</i><sup class="template-chem2-sup">5</sup>−C<sub class="template-chem2-sub">5</sub>H<sub class="template-chem2-sub">5</sub>)<sub class="template-chem2-sub">2</sub>]</span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Isotopes" data-mw-thread-id="h-Isotopes-Chemistry"><span data-mw-comment-start="" id="h-Isotopes-Chemistry"></span>Isotopes<span data-mw-comment-end="h-Isotopes-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=75" title="Edit section: Isotopes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center;"> <tbody><tr> <th>mhchem</th> <th>Equivalent <code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> and HTML </th></tr> <tr> <td style="vertical-align:center;"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0; vertical-align:center"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><chem><span class="nb">^{</span>227<span class="nb">}_{</span>90<span class="nb">}</span>Th+</chem></code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {^{227}_{90}Th+}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>Th</mtext> <none></none> <mo>+</mo> <mprescripts></mprescripts> <mn>90</mn> <mn>227</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {^{227}_{90}Th+}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1335877af9156621b8926eeb2d495e0e24a8c831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.238ex; height:3.343ex;" alt="{\displaystyle {\ce {^{227}_{90}Th+}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><chem><span class="nb">^</span>0<span class="nb">_{</span>-1<span class="nb">}</span>n-</chem></code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {^0_{-1}n-}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mmultiscripts> <mtext>n</mtext> <none></none> <mo>−</mo> <mprescripts></mprescripts> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mn>0</mn> </mmultiscripts> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {^0_{-1}n-}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd3b63ad15d73416fcf5e61e4c871274f5cde92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.194ex; height:3.509ex;" alt="{\displaystyle {\ce {^0_{-1}n-}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0; vertical-align:center"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|227|90|Th|+}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">227</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">90</sub></span></span>Th<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|0|-1}}n<sup>−</sup></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">0</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">-1</sub></span></span></span>n<sup>−</sup> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="States" data-mw-thread-id="h-States-Chemistry"><span data-mw-comment-start="" id="h-States-Chemistry"></span>States<span data-mw-comment-end="h-States-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=76" title="Edit section: States"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Subscripting states is not an IUPAC recommendation. </p> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>mhchem</th> <th><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> </th></tr> <tr> <td style="vertical-align:bottom;"> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>H2_{(aq)}</chem> </pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {H2_{(aq)}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mtext>aq</mtext> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {H2_{(aq)}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f1ccdf06f51e906d4778bdd923f4db4fcc19bd3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:5.767ex; height:3.343ex;" alt="{\displaystyle {\ce {H2_{(aq)}}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>CO3^{2-}(aq)</chem> </pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {CO3^{2-}(aq)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>CO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mtext>aq</mtext> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {CO3^{2-}(aq)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8246e73424b4d53294b4db3e036a7da8265b644" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.405ex; height:3.343ex;" alt="{\displaystyle {\ce {CO3^{2-}(aq)}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td> <td class="mw-collapsible mw-collapsed"> <p class="mw-empty-elt"> </p> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|H|2(aq)}}</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2(aq)</sub></span></span></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup">{{chem|C|O|3|2-}}(aq)</pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="chemf nowrap">CO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2−</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span></span>(aq) </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Precipitate_and_gas_formation" data-mw-thread-id="h-Precipitate_and_gas_formation-Chemistry"><span data-mw-comment-start="" id="h-Precipitate_and_gas_formation-Chemistry"></span><a href="/wiki/Precipitate" class="mw-redirect" title="Precipitate">Precipitate</a> and gas formation<span data-mw-comment-end="h-Precipitate_and_gas_formation-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=77" title="Edit section: Precipitate and gas formation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="width:100%"> <tbody><tr> <th>mhchem </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><chem>Ba^2+ + SO4^{2-} -> BaSO4(v)</chem></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {Ba^2+ + SO4^{2-}-> BaSO4(v)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>Ba</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>+</mo> </mrow> </msup> <mo>+</mo> <msubsup> <mtext>SO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mrow> </msubsup> <mo stretchy="false">⟶</mo> <msubsup> <mtext>BaSO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↓</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {Ba^2+ + SO4^{2-}-> BaSO4(v)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/230b643a2c41d475177530057a715e05adaceb5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.023ex; height:3.343ex;" alt="{\displaystyle {\ce {Ba^2+ + SO4^{2-}-> BaSO4(v)}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th><code>{{<a href="/wiki/Template:Chem" title="Template:Chem">chem</a>}}</code> </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup">{{chem|Ba|2+}} + {{chem|S|O|4|2-}} → {{chem|Ba|S|O|4}}↓</pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="chemf nowrap">Ba<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2+</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span class="chemf nowrap">SO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2−</sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span> → <span class="chemf nowrap">BaSO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br/><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span>↓</div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th><code>{{<a href="/wiki/Template:Chem2" title="Template:Chem2">chem2</a>}}</code> </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup">{{chem2|Ba(2+) + SO4(2-) -> BaSO4↓}}</pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Ba<sup>2+</sup> + SO<span class="template-chem2-su"><span>2−</span><span>4</span></span> → BaSO<sub class="template-chem2-sub">4</sub>↓</span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th>Equivalent HTML </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-html mw-content-ltr" dir="ltr">Ba<span class="p"><</span><span class="nt">sup</span><span class="p">></span>2+<span class="p"></</span><span class="nt">sup</span><span class="p">></span> + SO<span class="p"><</span><span class="nt">sub</span><span class="p">></span>4<span class="p"></</span><span class="nt">sub</span><span class="p">><</span><span class="nt">sup</span><span class="p">></span>2<span class="ni">&minus;</span><span class="p"></</span><span class="nt">sup</span><span class="p">></span> <span class="ni">&rarr;</span> BaSO<span class="p"><</span><span class="nt">sub</span><span class="p">></span>4<span class="p"></</span><span class="nt">sub</span><span class="p">></span><span class="ni">&darr;</span></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper">Ba<sup>2+</sup> + SO<sub>4</sub><sup>2−</sup> → BaSO<sub>4</sub>↓</div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr> <tr> <th>mhchem </th> <td> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><chem>2HCl + Zn -> ZnCl2 + H2 ^</chem></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {2HCl + Zn -> ZnCl2 + H2 ^}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mtext>HCl</mtext> <mo>+</mo> <mtext>Zn</mtext> <mo stretchy="false">⟶</mo> <msubsup> <mtext>ZnCl</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo>+</mo> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↑</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {2HCl + Zn -> ZnCl2 + H2 ^}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc5014e2744d4ce85c0e706fb68facdb76f6871d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.159ex; height:2.843ex;" alt="{\displaystyle {\ce {2HCl + Zn -> ZnCl2 + H2 ^}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Reaction_arrows" data-mw-thread-id="h-Reaction_arrows-Chemistry"><span data-mw-comment-start="" id="h-Reaction_arrows-Chemistry"></span>Reaction arrows<span data-mw-comment-end="h-Reaction_arrows-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=78" title="Edit section: Reaction arrows"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0; vertical-align:middle"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>A -> B</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A -> B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mo stretchy="false">⟶</mo> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A -> B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/466ec84f149e0a394af6fe8c160e9389133fa23b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.485ex; height:2.176ex;" alt="{\displaystyle {\ce {A -> B}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>A <- B</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A <- B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mo stretchy="false">⟵</mo> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A <- B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e21f2473ac5870a2b0ef6888b96ec4f5a4c109c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.417ex; height:2.176ex;" alt="{\displaystyle {\ce {A <- B}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>A <-> B</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A <-> B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mo stretchy="false">⟷</mo> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A <-> B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12b79a79afc17b6469e3dfff60b54b206da979c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.998ex; height:2.176ex;" alt="{\displaystyle {\ce {A <-> B}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>A <--> B</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p>Unsupported<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>A <=> B</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A <=> B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mpadded height="0" depth="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↽</mo> </mrow> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mpadded> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⇀</mo> </mrow> </mrow> </mstyle> </mrow> </mover> </mrow> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A <=> B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4dc08872cf438765f61ac2dd004609976b28311" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.002ex; margin-bottom: -0.502ex; width:8.037ex; height:2.843ex;" alt="{\displaystyle {\ce {A <=> B}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>A <=>> B</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A <=>> B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mstyle mathsize="0.85em"> <mrow class="MJX-TeXAtom-ORD"> <mpadded height="0" depth="0"> <mo stretchy="false">↽</mo> </mpadded> </mrow> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⇀</mo> </mrow> </mstyle> </mrow> </mover> </mrow> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A <=>> B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03a6adc4502ff931632382d9f733986de69e8c9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.002ex; margin-bottom: -0.336ex; width:8.037ex; height:2.676ex;" alt="{\displaystyle {\ce {A <=>> B}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><chem>A <<=> B</chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A <<=> B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↽</mo> </mrow> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mstyle> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⇀</mo> </mrow> </mover> </mrow> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A <<=> B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc1183159a3d104b40c35db2e84cdc2808732d6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:8.037ex; height:3.009ex;" alt="{\displaystyle {\ce {A <<=> B}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><chem>A ->[<span class="nb">{}</span><span class="k">\atop</span> x] B</chem></code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A->[{} \atop x]B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mfrac linethickness="0"> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mi>x</mi> </mfrac> </mpadded> </mover> </mrow> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A->[{} \atop x]B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b416227fa232a53f329a424cf6c39c6e3829522d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.028ex; margin-top: -0.347ex; margin-bottom: -0.477ex; width:7.323ex; height:3.843ex;" alt="{\displaystyle {\ce {A->[{} \atop x]B}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><chem>A ->[<span class="k">\text</span><span class="nb">{</span>text above<span class="nb">}</span>][<span class="k">\text</span><span class="nb">{</span>text below<span class="nb">}</span>] B</chem></code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A->[{\text{text above}}][{\text{text below}}]B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mrow class="MJX-TeXAtom-REL"> <munderover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset="-.24em"> <mrow class="MJX-TeXAtom-ORD"> <mtext>text below</mtext> </mrow> </mpadded> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mrow class="MJX-TeXAtom-ORD"> <mtext>text above</mtext> </mrow> </mpadded> </munderover> </mrow> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A->[{\text{text above}}][{\text{text below}}]B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c4298e79e43789e1e847e4aba3885e82120b264" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.81ex; margin-top: -0.309ex; margin-bottom: -0.528ex; width:13.616ex; height:5.676ex;" alt="{\displaystyle {\ce {A->[{\text{text above}}][{\text{text below}}]B}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><chem>A ->[<span class="nb">{}</span><span class="k">\atop\ce</span><span class="nb">{</span>+H2O<span class="nb">}</span>] B</chem></code></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {A->[{} \atop {\ce {+H2O}}]B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mfrac linethickness="0"> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mtext>O</mtext> </mrow> </mfrac> </mpadded> </mover> </mrow> <mtext>B</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A->[{} \atop {\ce {+H2O}}]B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48456d226ca3dfd38e00bae1b62c3ea1fcb5599b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.028ex; margin-top: -0.294ex; margin-bottom: -0.477ex; width:10.437ex; height:4.509ex;" alt="{\displaystyle {\ce {A->[{} \atop {\ce {+H2O}}]B}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading4"><h4 id="Comparison_of_arrow_symbols" data-mw-thread-id="h-Comparison_of_arrow_symbols-Reaction_arrows"><span data-mw-comment-start="" id="h-Comparison_of_arrow_symbols-Reaction_arrows"></span>Comparison of arrow symbols<span data-mw-comment-end="h-Comparison_of_arrow_symbols-Reaction_arrows"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=79" title="Edit section: Comparison of arrow symbols"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table style="margin-top:0;margin-left:0; border-width:medium; padding:0;"> <tbody><tr> <th scope="col" style="width:50%;">Markup</th> <th scope="col" style="width:50%;">Renders as </th></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><math>\rightarrow</math></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e574cc3aa5b4bf5f3f5906caf121a378eef08b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightarrow }"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><math>\rightleftarrows</math></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightleftarrows }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇄</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightleftarrows }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdbaea31afa0894aa82079b04d6a5e7566da7195" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle \rightleftarrows }"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><math>\rightleftharpoons</math></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightleftharpoons }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo class="MJX-variant" stretchy="false">⇌</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightleftharpoons }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c37b981df851b9e54e489e017b1481e37d418f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightleftharpoons }"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><math>\leftrightarrow</math></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><math>\longrightarrow</math> <chem>-></chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \longrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⟶</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \longrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ffb6a294b21bebe64570c4088d77a884dec95ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.806ex; height:1.843ex;" alt="{\displaystyle \longrightarrow }"/></span><br/><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {->}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⟶</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {->}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ec7affe508f808c307bf7a219abfe179b143ce8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.806ex; height:1.843ex;" alt="{\displaystyle {\ce {->}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><math>\rightleftharpoons</math> <chem><=></chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightleftharpoons }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo class="MJX-variant" stretchy="false">⇌</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightleftharpoons }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c37b981df851b9e54e489e017b1481e37d418f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightleftharpoons }"/></span><br/><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {<=>}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mpadded height="0" depth="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↽</mo> </mrow> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mpadded> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mspace width="negativethinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⇀</mo> </mrow> </mrow> </mstyle> </mrow> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {<=>}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961c77b79c6c5277df106f207db09fb691d7bf72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0; margin-bottom: -0.505ex; width:3.358ex; height:2.843ex;" alt="{\displaystyle {\ce {<=>}}}"/></span> </p> </div> </td></tr> <tr> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div class="template-markup-wrapper"><pre style="" class="template-markup"><math>\longleftrightarrow</math> <chem><-></chem></pre></div> </td> <td style="background:#f8f9fa; background:var(--background-color-interactive-subtle, #f8f9fa); color:var(--color-base, #000); border:1px solid #eaecf0; padding:5px; vertical-align:top;"><div style="" class="template-markup-wrapper"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \longleftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⟷</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \longleftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fa5e5cff7293679ce41a5afa73a372963be52cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.319ex; height:1.843ex;" alt="{\displaystyle \longleftrightarrow }"/></span><br/><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {<->}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⟷</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {<->}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9de3f27462eb69d14516d66d0da13d787a8ddcc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.319ex; height:1.843ex;" alt="{\displaystyle {\ce {<->}}}"/></span> </p> </div> </td></tr> <tr> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td> <td style="border-width:1px;border-style: none none none;border-color:#ddd; padding:5px; vertical-align:top;"> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Further_examples_using_ordinary_LaTeX_tags" data-mw-thread-id="h-Further_examples_using_ordinary_LaTeX_tags-Chemistry"><span data-mw-comment-start="" id="h-Further_examples_using_ordinary_LaTeX_tags-Chemistry"></span>Further examples using ordinary LaTeX tags<span data-mw-comment-end="h-Further_examples_using_ordinary_LaTeX_tags-Chemistry"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=80" title="Edit section: Further examples using ordinary LaTeX tags"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><math chem><span class="k">\begin</span><span class="nb">{</span>align<span class="nb">}</span> <span class="k">\overbrace</span><span class="nb">{</span><span class="k">\ce</span><span class="nb">{</span>2Fe3O4<span class="nb">}}^{</span><span class="k">\text</span><span class="nb">{</span>magnetite<span class="nb">}}</span> + <span class="k">\ce</span><span class="nb">{</span>1/2 O2 -><span class="nb">}</span><span class="k">\ </span><span class="nb">&{</span><span class="k">\color</span><span class="nb">{</span>Brown<span class="nb">}</span><span class="k">\overbrace</span><span class="nb">{</span><span class="k">\ce</span><span class="nb">{</span>3(<span class="k">\lambda</span><span class="nb">{</span>-<span class="nb">}</span>Fe2O3)<span class="nb">}}^{</span><span class="k">\text</span><span class="nb">{</span>maghemite<span class="nb">}}}</span><span class="k">\\</span> <span class="k">\underbrace</span><span class="nb">{</span><span class="k">\ce</span><span class="nb">{</span>2Fe3O4<span class="nb">}}_{</span><span class="k">\text</span><span class="nb">{</span>magnetite<span class="nb">}}</span> + <span class="k">\ce</span><span class="nb">{</span>1/2 O2 -><span class="nb">}</span><span class="k">\ </span><span class="nb">&{</span><span class="k">\color</span><span class="nb">{</span>Red<span class="nb">}</span><span class="k">\underbrace</span><span class="nb">{</span><span class="k">\ce</span><span class="nb">{</span>3(<span class="k">\alpha</span><span class="nb">{</span>-<span class="nb">}</span>Fe2O3)<span class="nb">}}_{</span><span class="k">\text</span><span class="nb">{</span>hematite<span class="nb">}}}</span> <span class="k">\end</span><span class="nb">{</span>align<span class="nb">}</span></math> </pre></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\overbrace {{\ce {2Fe3O4}}} ^{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {Brown}\overbrace {{\ce {3(\lambda{-}Fe2O3)}}} ^{\text{maghemite}}}\\\underbrace {{\ce {2Fe3O4}}} _{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {BrickRed}\underbrace {{\ce {3(\alpha{-}Fe2O3)}}} _{\text{hematite}}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace"></mspace> <msubsup> <mtext>Fe</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> </mrow> <mo>⏞</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>magnetite</mtext> </mrow> </mover> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">⟶</mo> </mrow> <mtext> </mtext> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#792500"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mrow> <msubsup> <mtext>Fe</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> </mrow> <mo>⏞</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>maghemite</mtext> </mrow> </mover> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace"></mspace> <msubsup> <mtext>Fe</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>magnetite</mtext> </mrow> </munder> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">⟶</mo> </mrow> <mtext> </mtext> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle mathcolor="#B6321C"> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mrow> <msubsup> <mtext>Fe</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em"></mspace> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>hematite</mtext> </mrow> </munder> </mstyle> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\overbrace {{\ce {2Fe3O4}}} ^{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {Brown}\overbrace {{\ce {3(\lambda{-}Fe2O3)}}} ^{\text{maghemite}}}\\\underbrace {{\ce {2Fe3O4}}} _{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {BrickRed}\underbrace {{\ce {3(\alpha{-}Fe2O3)}}} _{\text{hematite}}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3516eceb7cec5f437cc3139f9ce6fa0ea2b678af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.505ex; width:34.282ex; height:14.176ex;" alt="{\displaystyle {\begin{aligned}\overbrace {{\ce {2Fe3O4}}} ^{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {Brown}\overbrace {{\ce {3(\lambda{-}Fe2O3)}}} ^{\text{maghemite}}}\\\underbrace {{\ce {2Fe3O4}}} _{\text{magnetite}}+{\ce {1/2 O2 ->}}\ &{\color {BrickRed}\underbrace {{\ce {3(\alpha{-}Fe2O3)}}} _{\text{hematite}}}\end{aligned}}}"/></span></dd></dl> <p>To align the equations or color them, use <code class="nowrap"><<a class="mw-selflink-fragment" href="#Chemistry">math chem</a>></code> and <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">\ce</code>. </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Commutative_diagrams" data-mw-thread-id="h-Commutative_diagrams"><span data-mw-comment-start="" id="h-Commutative_diagrams"></span>Commutative diagrams<span data-mw-comment-end="h-Commutative_diagrams"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=81" title="Edit section: Commutative diagrams"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="1_step_method" data-mw-thread-id="h-1_step_method-Commutative_diagrams"><span data-mw-comment-start="" id="h-1_step_method-Commutative_diagrams"></span>1 step method<span data-mw-comment-end="h-1_step_method-Commutative_diagrams"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=82" title="Edit section: 1 step method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <pre><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{lcl}&X&{\overset {f}{\rightarrow }}&Z&\\&g\downarrow &&\downarrow g'\\&Y&{\underset {f'}{\rightarrow }}&W&\\\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left center left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd></mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo stretchy="false">→</mo> <mi>f</mi> </mover> </mrow> </mtd> <mtd> <mi>Z</mi> </mtd> <mtd></mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi>g</mi> <mo stretchy="false">↓</mo> </mtd> <mtd></mtd> <mtd> <mo stretchy="false">↓</mo> <msup> <mi>g</mi> <mo>′</mo> </msup> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi>Y</mi> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <munder> <mo stretchy="false">→</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> </munder> </mrow> </mtd> <mtd> <mi>W</mi> </mtd> <mtd></mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{lcl}&X&{\overset {f}{\rightarrow }}&Z&\\&g\downarrow &&\downarrow g'\\&Y&{\underset {f'}{\rightarrow }}&W&\\\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2e505b777320ad777926030a16bbf27c4be44fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:18.9ex; height:12.509ex;" alt="{\displaystyle {\begin{array}{lcl}&X&{\overset {f}{\rightarrow }}&Z&\\&g\downarrow &&\downarrow g'\\&Y&{\underset {f'}{\rightarrow }}&W&\\\end{array}}}"/></span> </pre> <div class="mw-highlight mw-highlight-lang-tex mw-content-ltr" dir="ltr"><pre><span></span><math> <span class="k">\begin</span><span class="nb">{</span>array<span class="nb">}{</span>lcl<span class="nb">}</span> <span class="nb">&</span> X <span class="nb">&</span> <span class="k">\overset</span><span class="nb">{</span>f<span class="nb">}</span><span class="k">\rightarrow</span> <span class="nb">&</span> Z <span class="nb">&</span> <span class="k">\\</span> <span class="nb">&</span> g <span class="k">\downarrow</span> <span class="nb">&&</span> <span class="k">\downarrow</span> g'<span class="k">\\</span> <span class="nb">&</span> Y <span class="nb">&</span> <span class="k">\underset</span><span class="nb">{</span>f'<span class="nb">}</span><span class="k">\rightarrow</span> <span class="nb">&</span> W <span class="nb">&</span> <span class="k">\\</span> <span class="k">\end</span><span class="nb">{</span>array<span class="nb">}</span> </math> </pre></div> <div class="mw-heading mw-heading3"><h3 id="3_step_method" data-mw-thread-id="h-3_step_method-Commutative_diagrams"><span data-mw-comment-start="" id="h-3_step_method-Commutative_diagrams"></span>3 step method<span data-mw-comment-end="h-3_step_method-Commutative_diagrams"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=83" title="Edit section: 3 step method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:First_isomorphism_theorem_(plain).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/First_isomorphism_theorem_%28plain%29.svg/220px-First_isomorphism_theorem_%28plain%29.svg.png" decoding="async" width="220" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/First_isomorphism_theorem_%28plain%29.svg/330px-First_isomorphism_theorem_%28plain%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/First_isomorphism_theorem_%28plain%29.svg/440px-First_isomorphism_theorem_%28plain%29.svg.png 2x" data-file-width="113" data-file-height="80"/></a><figcaption>A sample commutative diagram, created in the manner described</figcaption></figure> <p>To make a <a href="/wiki/Commutative_diagram" title="Commutative diagram">commutative diagram</a>, there are three steps: </p> <ol><li>write the diagram in <a href="/wiki/TeX" title="TeX">TeX</a></li> <li><a href="#Convert_to_SVG">convert to SVG</a></li> <li><a href="https://commons.wikimedia.org/wiki/Commons:First_steps/Upload_form" class="extiw" title="commons:Commons:First steps/Upload form">upload the file</a> to <a href="https://commons.wikimedia.org/wiki/" class="extiw" title="commons:">Wikimedia Commons</a></li></ol> <div class="mw-heading mw-heading4"><h4 id="Diagrams_in_TeX" data-mw-thread-id="h-Diagrams_in_TeX-3_step_method"><span data-mw-comment-start="" id="h-Diagrams_in_TeX-3_step_method"></span>Diagrams in TeX<span data-mw-comment-end="h-Diagrams_in_TeX-3_step_method"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=84" title="Edit section: Diagrams in TeX"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a rel="nofollow" class="external text" href="http://www.tug.org/applications/Xy-pic/">Xy-pic</a><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> (<a rel="nofollow" class="external text" href="http://tex.loria.fr/graph-pack/doc-xypic/xyguide-html/xyguide-html.html">online manual</a>) is the most powerful and general-purpose diagram package in <a href="/wiki/TeX" title="TeX">TeX</a>. Diagrams created using it can be found at <a href="https://commons.wikimedia.org/wiki/Category:Xy-pic_diagrams" class="extiw" title="commons:Category:Xy-pic diagrams">Commons: Category:Xy-pic diagrams</a>. </p><p>Simpler packages include: </p> <ul><li><a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">AMS's</a> <a rel="nofollow" class="external text" href="http://www.dante.de/CTAN//help/Catalogue/entries/amscd.html">amscd</a></li> <li>Paul Taylor's <a rel="nofollow" class="external text" href="http://www.ctan.org/tex-archive/macros/generic/diagrams/taylor/">diagrams</a></li> <li>François Borceux <a rel="nofollow" class="external text" href="http://www.ctan.org/tex-archive/help/Catalogue/entries/borceux.html">Diagrams</a></li></ul> <p>The following is a template for Xy-pic: </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\documentclass</span><span class="na">[border=10pt]</span><span class="nb">{</span>standalone<span class="nb">}</span> <span class="c">% Crop to size, remove page numbers, leave margin</span> <span class="k">\usepackage</span><span class="na">[all]</span><span class="nb">{</span>xy<span class="nb">}</span> <span class="c">% Loading the XY-Pic package</span> <span class="k">\begin</span><span class="nb">{</span>document<span class="nb">}</span> <span class="k">\SelectTips</span><span class="nb">{</span>eu<span class="nb">}{}</span> <span class="c">% Euler (shorter) arrowheads (tips)</span> <span class="sb">$$</span> <span class="nv">\xymatrix</span><span class="nb">{</span> <span class="c">%%% Diagram goes here %%%</span> <span class="nb">}</span> <span class="s">$$</span> <span class="k">\end</span><span class="nb">{</span>document<span class="nb">}</span> </pre></div> <p>Using postscript drivers may in some cases give smoother curves and will handle fonts differently: </p> <div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><span class="k">\usepackage</span><span class="na">[all, ps, dvips]</span><span class="nb">{</span>xy<span class="nb">}</span> </pre></div> <div class="mw-heading mw-heading4"><h4 id="Convert_to_SVG" data-mw-thread-id="h-Convert_to_SVG-3_step_method"><span data-mw-comment-start="" id="h-Convert_to_SVG-3_step_method"></span>Convert to SVG<span data-mw-comment-end="h-Convert_to_SVG-3_step_method"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=85" title="Edit section: Convert to SVG"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Once you have produced your diagram in LaTeX (or TeX), you can convert it to an SVG file using the following sequence of commands: </p> <div class="mw-highlight mw-highlight-lang-bash mw-content-ltr" dir="ltr"><pre><span></span>pdflatex<span class="w"> </span>file.tex pdf2svg<span class="w"> </span>file.pdf<span class="w"> </span>file.svg </pre></div> <p>The <a rel="nofollow" class="external text" href="http://pdfcrop.sourceforge.net">pdfcrop</a> and <a rel="nofollow" class="external text" href="http://www.cityinthesky.co.uk/opensource/pdf2svg">pdf2svg</a> utilities are needed for this procedure. You can alternatively use <a rel="nofollow" class="external text" href="http://www.pdftron.com/pdf2svg/">pdf2svg</a> from PDFTron for the last step. </p><p>If you do not have <a href="/wiki/PdfTeX" title="PdfTeX">pdfTeX</a> (which is unlikely) you can use the following commands to replace the first step (TeX → PDF): </p> <div class="mw-highlight mw-highlight-lang-bash mw-content-ltr" dir="ltr"><pre><span></span>latex<span class="w"> </span>file.tex dvipdfm<span class="w"> </span>file.dvi </pre></div> <p>In general, you will not be able to get anywhere with diagrams without TeX and Ghostscript, and the <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">inkscape</code> program is a useful tool for creating or modifying your diagrams by hand. There is also a utility <code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr">pstoedit</code> which supports direct conversion from Postscript files to many vector graphics formats, but it requires a non-free plugin to convert to SVG, and regardless of the format, <a href="/wiki/User:Ryan_Reich" title="User:Ryan Reich">this editor</a> has not been successful in using it to convert diagrams with diagonal arrows from TeX-created files. </p><p>These programs are: </p> <ul><li>a working TeX distribution, such as <a href="/wiki/TeX_Live" title="TeX Live">TeX Live</a></li> <li><a href="/wiki/Ghostscript" title="Ghostscript">Ghostscript</a></li> <li><a href="/wiki/Pstoedit" title="Pstoedit">pstoedit</a></li> <li><a href="/wiki/Inkscape" title="Inkscape">Inkscape</a></li></ul> <div class="mw-heading mw-heading4"><h4 id="Upload_the_file" data-mw-thread-id="h-Upload_the_file-3_step_method"><span data-mw-comment-start="" id="h-Upload_the_file-3_step_method"></span>Upload the file<span data-mw-comment-end="h-Upload_the_file-3_step_method"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=86" title="Edit section: Upload the file"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Help:Contents/Images_and_media" class="mw-redirect" title="Help:Contents/Images and media">Help:Contents/Images and media</a></div> <p>As the diagram is your own work, upload it to <a href="https://commons.wikimedia.org/wiki/" class="extiw" title="commons:">Wikimedia Commons</a>, so that all projects (notably, all languages) can use it without having to copy it to their language's Wiki. (If you've previously uploaded a file to somewhere other than Commons, to Commons.) </p> <dl><dt>Check size</dt> <dd>Before uploading, check that the default size of the image is neither too large nor too small by opening in an <a href="/wiki/SVG#Support_in_applications" title="SVG">SVG application</a> and viewing at default size (100% scaling), otherwise adjust the <code>-y</code> option to <code>dvips</code>.</dd> <dt>Name</dt> <dd>Make sure the file has a <a href="/wiki/Wikipedia:Naming_conventions" class="mw-redirect" title="Wikipedia:Naming conventions">meaningful name</a>.</dd> <dt>Upload</dt> <dd><a href="https://commons.wikimedia.org/wiki/Special:Userlogin" class="extiw" title="commons:Special:Userlogin">Login to Wikimedia Commons</a>, then <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/w/index.php?title=Special:Upload&uselang=ownwork">upload the file</a></span>; for the <b>Summary</b>, give a brief description.</dd></dl> <p>Now go to the <a href="/wiki/Help:Image_page" class="mw-redirect" title="Help:Image page">image page</a> and add a <a href="https://commons.wikimedia.org/wiki/Commons:First_steps/Quality_and_description#Good_file_descriptions" class="extiw" title="commons:Commons:First steps/Quality and description">description</a>, including the <b>source code</b>, using this template: </p> <div class="mw-highlight mw-highlight-lang-wikitext mw-content-ltr" dir="ltr"><pre><span></span><span class="p">{{</span><span class="nt">Information</span> <span class="p">|</span><span class="nl">description </span><span class="o">=</span> <span class="p">{{</span><span class="nt">en</span><span class="p">|</span><span class="nl">1</span><span class="o">=</span> <span class="gs">'''Description </span><span class="p">[[</span><span class="nn">:en</span><span class="p">:</span><span class="nt">Link to WP page</span><span class="p">|</span>topic<span class="p">]]</span><span class="gs">'''</span><span class="p">}}</span> <span class="p">|</span><span class="nl">source </span><span class="o">=</span> <span class="p">{{</span><span class="nt">own</span><span class="p">}}</span>, created as per: <span class="p">[[</span><span class="nn">:en:Help</span><span class="p">:</span><span class="nt">Displaying a formula</span><span class="p">#</span><span class="nl">Commutative diagrams</span><span class="p">]]</span>; source code below. <span class="p">|</span><span class="nl">date </span><span class="o">=</span> <span class="gs">'''The Creation Date, like 1999-12-31'''</span> <span class="p">|</span><span class="nl">author </span><span class="o">=</span> <span class="gs">'''</span><span class="p">[[</span><span class="nn">User</span><span class="p">:</span><span class="nt">YourUserName</span><span class="p">|</span>Your Real Name<span class="p">]]</span><span class="gs">'''</span> <span class="p">|</span><span class="nl">permission </span><span class="o">=</span> <span class="p">{{</span><span class="nt">self</span><span class="p">|</span>PD-self <span class="gs">'''(or </span><span class="p">[[</span><span class="nn">commons</span><span class="p">:</span><span class="nt">Licensing</span><span class="p">#</span><span class="nl">Well-known licenses</span><span class="p">|</span>other license<span class="p">]]</span><span class="gs">)'''</span> <span class="p">|</span><span class="nl">author </span><span class="o">=</span> <span class="gs">'''</span><span class="p">[[</span><span class="nn">User</span><span class="p">:</span><span class="nt">YourUserName</span><span class="p">|</span>Your Real Name<span class="p">]]</span><span class="gs">'''</span><span class="p">}}</span> <span class="p">}}</span> <span class="gu">====TeX source====</span> <span class="p"><</span><span class="nt">syntaxhighlight</span><span class="w"> </span><span class="na">lang</span><span class="o">=</span><span class="s2">"latex"</span><span class="p">></span> <span class="c">% TeX source here</span> <span class="p"></</span><span class="nt">syntaxhighlight</span><span class="p">></span> <span class="p">[[</span><span class="nn">Category</span><span class="p">:</span><span class="nt">Commutative diagrams</span><span class="p">]]</span> <span class="p">[[</span><span class="nn">Category</span><span class="p">:</span><span class="nt">Xy-pic diagrams</span><span class="p">]]</span> <span class="p">[[</span><span class="nn">Category</span><span class="p">:</span><span class="nt">Images with LaTeX source code</span><span class="p">]]</span> </pre></div> <dl><dt>Source code</dt> <dd> <ul><li>Include the source code in the <a href="/wiki/Help:Image_page" class="mw-redirect" title="Help:Image page">image page</a>, in the <style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">Source</span> section of the <code>{{<a href="https://commons.wikimedia.org/wiki/Template:Information" class="extiw" title="commons:Template:Information">Information</a>}}</code> template, so that the diagram can be edited in future.</li> <li>Include the complete <code>.tex</code> file, not just the fragment, so future editors do not need to reconstruct a compilable file.</li> <li>You may optionally make the source code section collapsible, using the <code>{{<a href="https://commons.wikimedia.org/wiki/Template:cot" class="extiw" title="commons:Template:cot">cot</a>}}</code> or <code>{{<a href="https://commons.wikimedia.org/wiki/Template:cob" class="extiw" title="commons:Template:cob">cob</a>}}</code> templates.</li> <li>(Don't include it in the Summary section, which is just supposed to be a summary.)</li></ul></dd></dl> <dl><dt>License</dt> <dd>The most common license for commutative diagrams is <code><a href="https://commons.wikimedia.org/wiki/Template:PD-self" class="extiw" title="commons:Template:PD-self">PD-self</a></code>; some use <code><a href="https://commons.wikimedia.org/wiki/Template:PD-self" class="extiw" title="commons:Template:PD-self">PD-ineligible</a></code>, especially for simple diagrams, or other licenses. Please <i>do not</i> use the <a rel="nofollow" class="external text" href="http://www.gnu.org/copyleft/fdl.html">GFDL</a>, as it requires the entire text of the GFDL to be attached to any document that uses the diagram.</dd> <dt>Description</dt> <dd>If possible, link to a Wikipedia page relevant to the diagram. (The <code>1=</code> is necessary if you use nest templates within the description, and harmless otherwise.)</dd> <dt>Category</dt> <dd>Include <code>[[Category:Commutative diagrams]]</code>, so that it appears in <a href="https://commons.wikimedia.org/wiki/Category:Commutative_diagrams" class="extiw" title="commons:Category:Commutative diagrams">commons:Category:Commutative diagrams</a>. There are also subcategories, which you may choose to use.</dd> <dt>Include image</dt> <dd>Now include the image on the original page via <code>[[File:Diagram.svg]]</code>. Use <code>[[File:Diagram.svg|class=skin-invert]]</code> to invert colors in dark mode.</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Examples_2" data-mw-thread-id="h-Examples_2-3_step_method"><span data-mw-comment-start="" id="h-Examples_2-3_step_method"></span>Examples<span data-mw-comment-end="h-Examples_2-3_step_method"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=87" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A sample conforming diagram is <a href="https://commons.wikimedia.org/wiki/File:PSU-PU.svg" class="extiw" title="commons:File:PSU-PU.svg">commons:File:PSU-PU.svg</a>. </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Semantics_and_links" data-mw-thread-id="h-Semantics_and_links"><span data-mw-comment-start="" id="h-Semantics_and_links"></span>Semantics and links<span data-mw-comment-end="h-Semantics_and_links"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=88" title="Edit section: Semantics and links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While links from formulas using LaTeX macros such as <i>\href</i> or <i>\url</i> or are currently not supported, one can link individual math expressions to Wikidata items to explain the meaning of individual terms of mathematical expressions. For example, </p> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><span class="nt"><math</span><span class="w"> </span><span class="na">qid=</span><span class="s">Q35875</span><span class="nt">></span>E=mc^2<span class="nt"></math></span></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element" data-qid="Q35875"><a href="/w/index.php?title=Special:MathWikibase&qid=Q35875" style="color:inherit;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=mc^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=mc^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f73dbd37a0cac34406ee89057fa1b36a1e6a18e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.976ex; height:2.676ex;" alt="{\displaystyle E=mc^{2}}"/></a></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <p>links to <a class="external text" href="https://en.wikipedia.org/wiki/Special:MathWikibase?qid=Q35875">a special page that displays additional information on that formula</a>. To change the information shown on the special page, navigate to the Wikidata item linked at the bottom of the special page. Use the <i>has part</i> property to link parts of the equation to other Wikidata items with their respective Wikipedia articles. This is not limited to individual identifiers, but can also be used to link more complex terms. </p><p>A condensed version of that special page might be shown in the future as a popup: <a href="https://phabricator.wikimedia.org/T239357" class="extiw" title="phab:T239357">phab:T239357</a>. </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Examples_of_implemented_TeX_formulas" data-mw-thread-id="h-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Examples_of_implemented_TeX_formulas"></span>Examples of implemented TeX formulas<span data-mw-comment-end="h-Examples_of_implemented_TeX_formulas"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=89" title="Edit section: Examples of implemented TeX formulas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Quadratic_polynomial" data-mw-thread-id="h-Quadratic_polynomial-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Quadratic_polynomial-Examples_of_implemented_TeX_formulas"></span>Quadratic polynomial<span data-mw-comment-end="h-Quadratic_polynomial-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=90" title="Edit section: Quadratic polynomial"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math>ax<span class="nb">^</span>2 + bx + c = 0</math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ax^{2}+bx+c=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ax^{2}+bx+c=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23e70cfa003f402d108ec04d97983fb62f69536e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:16.89ex; height:2.843ex;" alt="{\displaystyle ax^{2}+bx+c=0}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Quadratic_formula" data-mw-thread-id="h-Quadratic_formula-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Quadratic_formula-Examples_of_implemented_TeX_formulas"></span>Quadratic formula<span data-mw-comment-end="h-Quadratic_formula-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=91" title="Edit section: Quadratic formula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math>x=<span class="k">\frac</span><span class="nb">{</span>-b<span class="k">\pm\sqrt</span><span class="nb">{</span>b<span class="nb">^</span>2-4ac<span class="nb">}}{</span>2a<span class="nb">}</span></math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>b</mi> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mi>a</mi> <mi>c</mi> </msqrt> </mrow> </mrow> <mrow> <mn>2</mn> <mi>a</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00c22777378f9c594c71158fea8946f2495f2a28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.525ex; height:6.176ex;" alt="{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Tall_parentheses_and_fractions" data-mw-thread-id="h-Tall_parentheses_and_fractions-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Tall_parentheses_and_fractions-Examples_of_implemented_TeX_formulas"></span>Tall parentheses and fractions<span data-mw-comment-end="h-Tall_parentheses_and_fractions-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=92" title="Edit section: Tall parentheses and fractions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math>2 = <span class="k">\left</span>( <span class="k">\frac</span><span class="nb">{</span><span class="k">\left</span>(3-x<span class="k">\right</span>) <span class="k">\times</span> 2<span class="nb">}{</span>3-x<span class="nb">}</span> <span class="k">\right</span>)</math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2=\left({\frac {\left(3-x\right)\times 2}{3-x}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mn>2</mn> </mrow> <mrow> <mn>3</mn> <mo>−</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2=\left({\frac {\left(3-x\right)\times 2}{3-x}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68773852a0ff9e1187b88b150c55ee568c5ae4a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:19.663ex; height:6.343ex;" alt="{\displaystyle 2=\left({\frac {\left(3-x\right)\times 2}{3-x}}\right)}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math>S<span class="nb">_{</span><span class="k">\text</span><span class="nb">{</span>new<span class="nb">}}</span> = S<span class="nb">_{</span><span class="k">\text</span><span class="nb">{</span>old<span class="nb">}}</span> - <span class="k">\frac</span><span class="nb">{</span> <span class="k">\left</span>( 5-T <span class="k">\right</span>) <span class="nb">^</span>2<span class="nb">}</span> <span class="nb">{</span>2<span class="nb">}</span></math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{\text{new}}=S_{\text{old}}-{\frac {\left(5-T\right)^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>new</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>old</mtext> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow> <mo>(</mo> <mrow> <mn>5</mn> <mo>−</mo> <mi>T</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{\text{new}}=S_{\text{old}}-{\frac {\left(5-T\right)^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d5ba6c1b3898710bba0edcd7f80c142714a549c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.616ex; height:6.009ex;" alt="{\displaystyle S_{\text{new}}=S_{\text{old}}-{\frac {\left(5-T\right)^{2}}{2}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Integrals" data-mw-thread-id="h-Integrals-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Integrals-Examples_of_implemented_TeX_formulas"></span>Integrals<span data-mw-comment-end="h-Integrals-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=93" title="Edit section: Integrals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\int</span><span class="nb">_</span>a<span class="nb">^</span>x <span class="k">\int</span><span class="nb">_</span>a<span class="nb">^</span>s f(y)<span class="k">\,</span>dy<span class="k">\,</span>ds = <span class="k">\int</span><span class="nb">_</span>a<span class="nb">^</span>x f(y)(x-y)<span class="k">\,</span>dy</math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{a}^{x}\int _{a}^{s}f(y)\,dy\,ds=\int _{a}^{x}f(y)(x-y)\,dy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msubsup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>y</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>s</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{a}^{x}\int _{a}^{s}f(y)\,dy\,ds=\int _{a}^{x}f(y)(x-y)\,dy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74f95965f55c5c89cf0cdb3e444af410c54b2025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:38.832ex; height:5.843ex;" alt="{\displaystyle \int _{a}^{x}\int _{a}^{s}f(y)\,dy\,ds=\int _{a}^{x}f(y)(x-y)\,dy}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\int</span><span class="nb">_</span>e<span class="nb">^{</span><span class="k">\infty</span><span class="nb">}</span><span class="k">\frac</span> <span class="nb">{</span>1<span class="nb">}{</span>t(<span class="k">\ln</span> t)<span class="nb">^</span>2<span class="nb">}</span>dt = <span class="k">\left</span>. <span class="k">\frac</span><span class="nb">{</span>-1<span class="nb">}{</span><span class="k">\ln</span> t<span class="nb">}</span> <span class="k">\right\vert</span><span class="nb">_</span>e<span class="nb">^</span><span class="k">\infty</span> = 1</math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{e}^{\infty }{\frac {1}{t(\ln t)^{2}}}dt=\left.{\frac {-1}{\ln t}}\right\vert _{e}^{\infty }=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>t</mi> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>t</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <msubsup> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mi>ln</mi> <mo>⁡</mo> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{e}^{\infty }{\frac {1}{t(\ln t)^{2}}}dt=\left.{\frac {-1}{\ln t}}\right\vert _{e}^{\infty }=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0eaba10e7f3d7f76477ef013900dbfb32ba4154" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.371ex; height:6.176ex;" alt="{\displaystyle \int _{e}^{\infty }{\frac {1}{t(\ln t)^{2}}}dt=\left.{\frac {-1}{\ln t}}\right\vert _{e}^{\infty }=1}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Matrices_and_determinants" data-mw-thread-id="h-Matrices_and_determinants-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Matrices_and_determinants-Examples_of_implemented_TeX_formulas"></span>Matrices and determinants<span data-mw-comment-end="h-Matrices_and_determinants-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=94" title="Edit section: Matrices and determinants"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\det</span>(<span class="k">\mathsf</span><span class="nb">{</span>A<span class="nb">}</span>-<span class="k">\lambda\mathsf</span><span class="nb">{</span>I<span class="nb">}</span>) = 0</math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \det({\mathsf {A}}-\lambda {\mathsf {I}})=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">det</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">A</mi> </mrow> </mrow> <mo>−</mo> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">I</mi> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \det({\mathsf {A}}-\lambda {\mathsf {I}})=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2d4e2286fc8c6989c53581f75f69efadcbda53d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.693ex; height:2.843ex;" alt="{\displaystyle \det({\mathsf {A}}-\lambda {\mathsf {I}})=0}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Summation" data-mw-thread-id="h-Summation-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Summation-Examples_of_implemented_TeX_formulas"></span>Summation<span data-mw-comment-end="h-Summation-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=95" title="Edit section: Summation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\sum</span><span class="nb">_{</span>i=0<span class="nb">}^{</span>n-1<span class="nb">}</span> i</math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=0}^{n-1}i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=0}^{n-1}i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d44072a2aee1afe485c67a227c2642a7ba37577" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:4.545ex; height:7.343ex;" alt="{\displaystyle \sum _{i=0}^{n-1}i}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\sum</span><span class="nb">_{</span>m=1<span class="nb">}^</span><span class="k">\infty\sum</span><span class="nb">_{</span>n=1<span class="nb">}^</span><span class="k">\infty\frac</span><span class="nb">{</span>m<span class="nb">^</span>2 n<span class="nb">}{</span>3<span class="nb">^</span>m<span class="k">\left</span>(m 3<span class="nb">^</span>n + n 3<span class="nb">^</span>m<span class="k">\right</span>)<span class="nb">}</span></math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}n}{3^{m}\left(m3^{n}+n3^{m}\right)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> </mrow> <mrow> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mi>m</mi> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>+</mo> <mi>n</mi> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}n}{3^{m}\left(m3^{n}+n3^{m}\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53f3fb71cc5f871053868e85497ae5e1914b0289" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.036ex; height:6.843ex;" alt="{\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}n}{3^{m}\left(m3^{n}+n3^{m}\right)}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Differential_equation" data-mw-thread-id="h-Differential_equation-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Differential_equation-Examples_of_implemented_TeX_formulas"></span>Differential equation<span data-mw-comment-end="h-Differential_equation-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=96" title="Edit section: Differential equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math>u'' + p(x)u' + q(x)u=f(x),<span class="k">\quad</span> x>a</math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u''+p(x)u'+q(x)u=f(x),\quad x>a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>u</mi> <mo>″</mo> </msup> <mo>+</mo> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <msup> <mi>u</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>u</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em"></mspace> <mi>x</mi> <mo>></mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u''+p(x)u'+q(x)u=f(x),\quad x>a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1dee5f64232e0531f58ee6ecb8a3cba5c5ee97e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.539ex; height:3.009ex;" alt="{\displaystyle u''+p(x)u'+q(x)u=f(x),\quad x>a}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Complex_numbers" data-mw-thread-id="h-Complex_numbers-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Complex_numbers-Examples_of_implemented_TeX_formulas"></span>Complex numbers<span data-mw-comment-end="h-Complex_numbers-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=97" title="Edit section: Complex numbers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><math>|<span class="k">\bar</span><span class="nb">{</span>z<span class="nb">}</span>| = |z|, |(<span class="k">\bar</span><span class="nb">{</span>z<span class="nb">}</span>)<span class="nb">^</span>n| = |z|<span class="nb">^</span>n, <span class="k">\arg</span>(z<span class="nb">^</span>n) = n <span class="k">\arg</span>(z)</math> </pre></div></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>z</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>z</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>,</mo> <mi>arg</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mi>arg</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a4dbfbd1ca54e2af592a5c1b1e7a583910e9000" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.823ex; height:3.009ex;" alt="{\displaystyle |{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Limits" data-mw-thread-id="h-Limits-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Limits-Examples_of_implemented_TeX_formulas"></span>Limits<span data-mw-comment-end="h-Limits-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=98" title="Edit section: Limits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\lim</span><span class="nb">_{</span>z<span class="k">\to</span> z<span class="nb">_</span>0<span class="nb">}</span> f(z)=f(z<span class="nb">_</span>0)</math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{z\to z_{0}}f(z)=f(z_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> <mo stretchy="false">→</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </munder> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{z\to z_{0}}f(z)=f(z_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/298dc78a7b89f34c6ad2ba16f58dceb8d793b6b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.893ex; height:4.176ex;" alt="{\displaystyle \lim _{z\to z_{0}}f(z)=f(z_{0})}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Integral_equation" data-mw-thread-id="h-Integral_equation-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Integral_equation-Examples_of_implemented_TeX_formulas"></span>Integral equation<span data-mw-comment-end="h-Integral_equation-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=99" title="Edit section: Integral equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><math><span class="k">\phi</span><span class="nb">_</span>n(<span class="k">\kappa</span>) = <span class="k">\frac</span><span class="nb">{</span>1<span class="nb">}{</span>4<span class="k">\pi</span><span class="nb">^</span>2<span class="k">\kappa</span><span class="nb">^</span>2<span class="nb">}</span> <span class="k">\int</span><span class="nb">_</span>0<span class="nb">^</span><span class="k">\infty</span> <span class="k">\frac</span><span class="nb">{</span><span class="k">\sin</span>(<span class="k">\kappa</span> R)<span class="nb">}{</span><span class="k">\kappa</span> R<span class="nb">}</span> <span class="k">\frac</span><span class="nb">{</span><span class="k">\partial</span><span class="nb">}{</span><span class="k">\partial</span> R<span class="nb">}</span> <span class="k">\left</span> [ R<span class="nb">^</span>2<span class="k">\frac</span><span class="nb">{</span><span class="k">\partial</span> D<span class="nb">_</span>n(R)<span class="nb">}{</span><span class="k">\partial</span> R<span class="nb">}</span> <span class="k">\right</span> ] <span class="k">\,</span>dR</math> </pre></div></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{n}(\kappa )={\frac {1}{4\pi ^{2}\kappa ^{2}}}\int _{0}^{\infty }{\frac {\sin(\kappa R)}{\kappa R}}{\frac {\partial }{\partial R}}\left[R^{2}{\frac {\partial D_{n}(R)}{\partial R}}\right]\,dR}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>κ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>κ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>κ</mi> <mi>R</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>κ</mi> <mi>R</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>R</mi> </mrow> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>R</mi> </mrow> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi _{n}(\kappa )={\frac {1}{4\pi ^{2}\kappa ^{2}}}\int _{0}^{\infty }{\frac {\sin(\kappa R)}{\kappa R}}{\frac {\partial }{\partial R}}\left[R^{2}{\frac {\partial D_{n}(R)}{\partial R}}\right]\,dR}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f6695154ee0e388c6ea1da20c2e19810282251a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:51.552ex; height:6.343ex;" alt="{\displaystyle \phi _{n}(\kappa )={\frac {1}{4\pi ^{2}\kappa ^{2}}}\int _{0}^{\infty }{\frac {\sin(\kappa R)}{\kappa R}}{\frac {\partial }{\partial R}}\left[R^{2}{\frac {\partial D_{n}(R)}{\partial R}}\right]\,dR}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Example" data-mw-thread-id="h-Example-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Example-Examples_of_implemented_TeX_formulas"></span>Example<span data-mw-comment-end="h-Example-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=100" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><math><span class="k">\phi</span><span class="nb">_</span>n(<span class="k">\kappa</span>) = 0.033C<span class="nb">_</span>n<span class="nb">^</span>2<span class="k">\kappa</span><span class="nb">^{</span>-11/3<span class="nb">}</span>,<span class="k">\quad</span> <span class="k">\frac</span><span class="nb">{</span>1<span class="nb">}{</span>L<span class="nb">_</span>0<span class="nb">}</span><span class="k">\ll\kappa\ll\frac</span><span class="nb">{</span>1<span class="nb">}{</span>l<span class="nb">_</span>0<span class="nb">}</span></math> </pre></div></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{n}(\kappa )=0.033C_{n}^{2}\kappa ^{-11/3},\quad {\frac {1}{L_{0}}}\ll \kappa \ll {\frac {1}{l_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>κ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.033</mn> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msup> <mi>κ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>11</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> <mo>,</mo> <mspace width="1em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>≪</mo> <mi>κ</mi> <mo>≪</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi _{n}(\kappa )=0.033C_{n}^{2}\kappa ^{-11/3},\quad {\frac {1}{L_{0}}}\ll \kappa \ll {\frac {1}{l_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7380be42e0d9b67971f2b646ccfac392fa54d9ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:41.146ex; height:5.676ex;" alt="{\displaystyle \phi _{n}(\kappa )=0.033C_{n}^{2}\kappa ^{-11/3},\quad {\frac {1}{L_{0}}}\ll \kappa \ll {\frac {1}{l_{0}}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Continuation_and_cases" data-mw-thread-id="h-Continuation_and_cases-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Continuation_and_cases-Examples_of_implemented_TeX_formulas"></span>Continuation and cases<span data-mw-comment-end="h-Continuation_and_cases-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=101" title="Edit section: Continuation and cases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><math>f(x) = <span class="k">\begin</span><span class="nb">{</span>cases<span class="nb">}</span> 1 <span class="nb">&</span> -1 <span class="k">\le</span> x < 0 <span class="k">\\</span> <span class="k">\frac</span><span class="nb">{</span>1<span class="nb">}{</span>2<span class="nb">}</span> <span class="nb">&</span> x = 0 <span class="k">\\</span> 1 - x<span class="nb">^</span>2 <span class="nb">&</span> <span class="k">\text</span><span class="nb">{</span>otherwise<span class="nb">}</span> <span class="k">\end</span><span class="nb">{</span>cases<span class="nb">}</span></math> </pre></div></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&{\text{otherwise}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> <mo>≤</mo> <mi>x</mi> <mo><</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> <mtd> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>otherwise</mtext> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&{\text{otherwise}}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21bb89612023ceb640cb699c40bed94359bb8674" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:30.702ex; height:9.176ex;" alt="{\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&{\text{otherwise}}\end{cases}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Prefixed_subscript" data-mw-thread-id="h-Prefixed_subscript-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Prefixed_subscript-Examples_of_implemented_TeX_formulas"></span>Prefixed subscript<span data-mw-comment-end="h-Prefixed_subscript-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=102" title="Edit section: Prefixed subscript"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span> <math><span class="nb">{}_</span>pF<span class="nb">_</span>q(a<span class="nb">_</span>1,<span class="k">\dots</span>,a<span class="nb">_</span>p;c<span class="nb">_</span>1,<span class="k">\dots</span>,c<span class="nb">_</span>q;z) = <span class="k">\sum</span><span class="nb">_{</span>n=0<span class="nb">}^</span><span class="k">\infty</span> <span class="k">\frac</span><span class="nb">{</span>(a<span class="nb">_</span>1)<span class="nb">_</span>n<span class="k">\cdots</span>(a<span class="nb">_</span>p)<span class="nb">_</span>n<span class="nb">}{</span>(c<span class="nb">_</span>1)<span class="nb">_</span>n<span class="k">\cdots</span>(c<span class="nb">_</span>q)<span class="nb">_</span>n<span class="nb">}</span> <span class="k">\frac</span><span class="nb">{</span>z<span class="nb">^</span>n<span class="nb">}{</span>n!<span class="nb">}</span></math> </pre></div></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {}_{p}F_{q}(a_{1},\dots ,a_{p};c_{1},\dots ,c_{q};z)=\sum _{n=0}^{\infty }{\frac {(a_{1})_{n}\cdots (a_{p})_{n}}{(c_{1})_{n}\cdots (c_{q})_{n}}}{\frac {z^{n}}{n!}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> <mo>;</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>⋯</mo> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>⋯</mo> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mrow> <mi>n</mi> <mo>!</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {}_{p}F_{q}(a_{1},\dots ,a_{p};c_{1},\dots ,c_{q};z)=\sum _{n=0}^{\infty }{\frac {(a_{1})_{n}\cdots (a_{p})_{n}}{(c_{1})_{n}\cdots (c_{q})_{n}}}{\frac {z^{n}}{n!}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba820c14abacac6d502ef6a55725ca15803014c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-left: -0.063ex; width:52.504ex; height:6.843ex;" alt="{\displaystyle {}_{p}F_{q}(a_{1},\dots ,a_{p};c_{1},\dots ,c_{q};z)=\sum _{n=0}^{\infty }{\frac {(a_{1})_{n}\cdots (a_{p})_{n}}{(c_{1})_{n}\cdots (c_{q})_{n}}}{\frac {z^{n}}{n!}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Fraction_and_small_fraction" data-mw-thread-id="h-Fraction_and_small_fraction-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Fraction_and_small_fraction-Examples_of_implemented_TeX_formulas"></span>Fraction and small fraction<span data-mw-comment-end="h-Fraction_and_small_fraction-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=103" title="Edit section: Fraction and small fraction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math><span class="k">\frac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span><span class="k">\ \tfrac</span><span class="nb">{</span>a<span class="nb">}{</span>b<span class="nb">}</span></math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {a}{b}}\ {\tfrac {a}{b}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a}{b}}\ {\tfrac {a}{b}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c6c8d9c6e92fbf6dd3c638c30c6f96afca8d887" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:4.352ex; height:4.843ex;" alt="{\displaystyle {\frac {a}{b}}\ {\tfrac {a}{b}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Area_of_a_quadrilateral" data-mw-thread-id="h-Area_of_a_quadrilateral-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Area_of_a_quadrilateral-Examples_of_implemented_TeX_formulas"></span>Area of a quadrilateral<span data-mw-comment-end="h-Area_of_a_quadrilateral-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=104" title="Edit section: Area of a quadrilateral"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math>S=dD<span class="k">\sin\alpha</span></math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=dD\sin \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mi>d</mi> <mi>D</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=dD\sin \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b291e616745149acceadb21a75ac036059914b46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.855ex; height:2.176ex;" alt="{\displaystyle S=dD\sin \alpha }"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Volume_of_a_sphere-stand" data-mw-thread-id="h-Volume_of_a_sphere-stand-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Volume_of_a_sphere-stand-Examples_of_implemented_TeX_formulas"></span>Volume of a sphere-stand<span data-mw-comment-end="h-Volume_of_a_sphere-stand-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=105" title="Edit section: Volume of a sphere-stand"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><code class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><math> V = <span class="k">\frac</span><span class="nb">{</span>1<span class="nb">}{</span>6<span class="nb">}</span> <span class="k">\pi</span> h <span class="k">\left</span> [ 3 <span class="k">\left</span> ( r<span class="nb">_</span>1<span class="nb">^</span>2 + r<span class="nb">_</span>2<span class="nb">^</span>2 <span class="k">\right</span> ) + h<span class="nb">^</span>2 <span class="k">\right</span> ] </math></code></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {1}{6}}\pi h\left[3\left(r_{1}^{2}+r_{2}^{2}\right)+h^{2}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mi>π</mi> <mi>h</mi> <mrow> <mo>[</mo> <mrow> <mn>3</mn> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {1}{6}}\pi h\left[3\left(r_{1}^{2}+r_{2}^{2}\right)+h^{2}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/480eb74247c5f48886e4558d4eb5dd09e6649745" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:27.841ex; height:5.176ex;" alt="{\displaystyle V={\frac {1}{6}}\pi h\left[3\left(r_{1}^{2}+r_{2}^{2}\right)+h^{2}\right]}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading3"><h3 id="Multiple_equations" data-mw-thread-id="h-Multiple_equations-Examples_of_implemented_TeX_formulas"><span data-mw-comment-start="" id="h-Multiple_equations-Examples_of_implemented_TeX_formulas"></span>Multiple equations<span data-mw-comment-end="h-Multiple_equations-Examples_of_implemented_TeX_formulas"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=106" title="Edit section: Multiple equations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The altered newline code <code>\\[0.6ex]</code> below adds a vertical space between the two lines of length equal to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0.6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0.6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0.6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c0001ac9c2a3bfc0abcfa25e7375e7bc62f5a15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.972ex; height:2.176ex;" alt="{\displaystyle 0.6}"/></span> times the height of a single '<code>x</code>' character. </p> <table class="wikitable" style=""> <tbody><tr> <th>Markup </th> <td><div class="template-markup-wrapper"><pre class="template-markup"><div class="mw-highlight mw-highlight-lang-latex mw-content-ltr" dir="ltr"><pre><span></span><math><span class="k">\begin</span><span class="nb">{</span>align<span class="nb">}</span> u <span class="nb">&</span> = <span class="k">\tfrac</span><span class="nb">{</span>1<span class="nb">}{</span><span class="k">\sqrt</span><span class="nb">{</span>2<span class="nb">}}</span>(x+y) <span class="k">\qquad</span> <span class="nb">&</span> x <span class="nb">&</span>= <span class="k">\tfrac</span><span class="nb">{</span>1<span class="nb">}{</span><span class="k">\sqrt</span><span class="nb">{</span>2<span class="nb">}}</span>(u+v) <span class="k">\\</span><span class="na">[0.6ex]</span> v <span class="nb">&</span> = <span class="k">\tfrac</span><span class="nb">{</span>1<span class="nb">}{</span><span class="k">\sqrt</span><span class="nb">{</span>2<span class="nb">}}</span>(x-y) <span class="k">\qquad</span> <span class="nb">&</span> y <span class="nb">&</span>= <span class="k">\tfrac</span><span class="nb">{</span>1<span class="nb">}{</span><span class="k">\sqrt</span><span class="nb">{</span>2<span class="nb">}}</span>(u-v) <span class="k">\end</span><span class="nb">{</span>align<span class="nb">}</span></math> </pre></div></pre></div> </td></tr> <tr> <th>Renders as </th> <td><div class="template-markup-wrapper"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}u&={\tfrac {1}{\sqrt {2}}}(x+y)\qquad &x&={\tfrac {1}{\sqrt {2}}}(u+v)\\[0.6ex]v&={\tfrac {1}{\sqrt {2}}}(x-y)\qquad &y&={\tfrac {1}{\sqrt {2}}}(u-v)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.558em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>u</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mspace width="2em"></mspace> </mtd> <mtd> <mi>x</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>u</mi> <mo>+</mo> <mi>v</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mi>v</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mspace width="2em"></mspace> </mtd> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>u</mi> <mo>−</mo> <mi>v</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}u&={\tfrac {1}{\sqrt {2}}}(x+y)\qquad &x&={\tfrac {1}{\sqrt {2}}}(u+v)\\[0.6ex]v&={\tfrac {1}{\sqrt {2}}}(x-y)\qquad &y&={\tfrac {1}{\sqrt {2}}}(u-v)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e0308a3a70f9d0b044c9dd0541c27a130ddbeac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:39.194ex; height:9.176ex;" alt="{\displaystyle {\begin{aligned}u&={\tfrac {1}{\sqrt {2}}}(x+y)\qquad &x&={\tfrac {1}{\sqrt {2}}}(u+v)\\[0.6ex]v&={\tfrac {1}{\sqrt {2}}}(x-y)\qquad &y&={\tfrac {1}{\sqrt {2}}}(u-v)\end{aligned}}}"/></span></div> </td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1260720223"> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="See_also" data-mw-thread-id="h-See_also"><span data-mw-comment-start="" id="h-See_also"></span>See also<span data-mw-comment-end="h-See_also"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=107" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="nowrap">{{</span><a href="/wiki/Template:Math" title="Template:Math">Math</a><span class="nowrap">}}</span></li> <li><a href="/wiki/MathJax" title="MathJax">MathJax</a>—<a href="/wiki/Javascript" class="mw-redirect" title="Javascript">Javascript</a> library that converts LaTeX to <a href="/wiki/MathML" title="MathML">MathML</a></li> <li><a href="/wiki/Wikipedia:Manual_of_Style/Mathematics#Typesetting_of_mathematical_formulas" title="Wikipedia:Manual of Style/Mathematics">Typesetting of mathematical formulas</a></li> <li><a href="/wiki/Help:Score" title="Help:Score">Help:Score</a> (a tag for <a href="/wiki/Tablature" title="Tablature">tablatures</a>, "sheet music") and <a href="/wiki/Help:Musical_symbols" title="Help:Musical symbols">Help:Musical symbols</a></li> <li><a href="/wiki/List_of_mathematical_symbols" class="mw-redirect" title="List of mathematical symbols">List of mathematical symbols</a></li> <li><a href="/wiki/Wikipedia:Rendering_math" title="Wikipedia:Rendering math">WP:Rendering math</a></li> <li><a href="/wiki/Wikipedia_talk:WikiProject_Mathematics/Archive_10#blahtex:_a_LaTeX_to_MathML_converter" class="mw-redirect" title="Wikipedia talk:WikiProject Mathematics/Archive 10">blahtex: a LaTeX to MathML converter for Wikipedia</a></li> <li><a href="https://commons.wikimedia.org/wiki/Category:Images_which_should_use_TeX" class="extiw" title="commons:Category:Images which should use TeX">commons:Category:Images which should use TeX</a></li> <li><a href="/wiki/Handwriting_recognition" title="Handwriting recognition">Handwriting recognition</a>, another way to put formulas, in a visual manner.</li></ul> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="References" data-mw-thread-id="h-References"><span data-mw-comment-start="" id="h-References"></span>References<span data-mw-comment-end="h-References"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=108" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Footnotes" data-mw-thread-id="h-Footnotes-References"><span data-mw-comment-start="" id="h-Footnotes-References"></span>Footnotes<span data-mw-comment-end="h-Footnotes-References"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=109" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-lower-alpha" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Expected result is <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Bi-dir_reaction_arrows.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Bi-dir_reaction_arrows.svg/32px-Bi-dir_reaction_arrows.svg.png" decoding="async" width="32" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Bi-dir_reaction_arrows.svg/48px-Bi-dir_reaction_arrows.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Bi-dir_reaction_arrows.svg/64px-Bi-dir_reaction_arrows.svg.png 2x" data-file-width="32" data-file-height="13"/></a></span> (longer <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">\rightleftarrows</code>)</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Use the barr option for commutative diagrams, e.g., <code>\usepackage[cmtip,all,barr]{xy}</code>.</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Citations" data-mw-thread-id="h-Citations-References"><span data-mw-comment-start="" id="h-Citations-References"></span>Citations<span data-mw-comment-end="h-Citations-References"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=110" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-:0-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFEd_Sanders2016" class="citation web cs1">Ed Sanders (December 18, 2016). <a class="external text" href="https://phabricator.wikimedia.org/T153606">"Consider a longer, less ambiguous name for <ce>"</a>. <a href="/wiki/Wikimedia_Foundation" title="Wikimedia Foundation">Wikimedia Foundation</a><span class="reference-accessdate">. Retrieved <span class="nowrap">April 24,</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Consider+a+longer%2C+less+ambiguous+name+for+%3Cce%3E&rft.pub=Wikimedia+Foundation&rft.date=2016-12-18&rft.au=Ed+Sanders&rft_id=https%3A%2F%2Fphabricator.wikimedia.org%2FT153606&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHelp%3ADisplaying+a+formula" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://html.spec.whatwg.org/#attributes-2">"HTML Living Standard"</a>. <i>Web Hypertext Application Technology Working Group (WHATWG)</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Web+Hypertext+Application+Technology+Working+Group+%28WHATWG%29&rft.atitle=HTML+Living+Standard&rft_id=https%3A%2F%2Fhtml.spec.whatwg.org%2F%23attributes-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHelp%3ADisplaying+a+formula" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ._A._WheelerC._MisnerK._S._Thorne1973" class="citation book cs1">J. A. Wheeler; C. Misner; K. S. Thorne (1973). <i>Gravitation</i> (2nd ed.). W. H. Freeman & Co. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-0344-0" title="Special:BookSources/0-7167-0344-0"><bdi>0-7167-0344-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gravitation&rft.edition=2nd&rft.pub=W.+H.+Freeman+%26+Co&rft.date=1973&rft.isbn=0-7167-0344-0&rft.au=J.+A.+Wheeler&rft.au=C.+Misner&rft.au=K.+S.+Thorne&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHelp%3ADisplaying+a+formula" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://tex.stackexchange.com/questions/418490">"Redefine \or form within a nested if statement? - TeX - LaTeX Stack Exchange"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Redefine+%5Cor+form+within+a+nested+if+statement%3F+-+TeX+-+LaTeX+Stack+Exchange&rft_id=https%3A%2F%2Ftex.stackexchange.com%2Fquestions%2F418490&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHelp%3ADisplaying+a+formula" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="External_links" data-mw-thread-id="h-External_links"><span data-mw-comment-start="" id="h-External_links"></span>External links<span data-mw-comment-end="h-External_links"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Help:Displaying_a_formula&action=edit&section=111" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikibooks-logo-en-noslogan.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/80px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400"/></a></span></div> <div class="side-box-text plainlist">Wikibooks has a book on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/LaTeX" class="extiw" title="wikibooks:LaTeX">LaTeX</a></b></i></div></div> </div> <ul><li><a class="external text" href="https://phabricator.wikimedia.org/T45058">Task:Creating a visual VisualEditor plugin tool to add/edit maths blocks</a> in <a href="https://phabricator.wikimedia.org/" class="extiw" title="phab:">Wikimedia Phabricator</a></li> <li><a rel="nofollow" class="external text" href="http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/">A LaTeX tutorial</a></li> <li><a rel="nofollow" class="external text" href="http://www.codecogs.com/latex/eqneditor.php">LaTex online editor</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2">Doob, Michael, <a rel="nofollow" class="external text" href="http://www.ctan.org/tex-archive/info/gentle/gentle.pdf"><i>A Gentle Introduction to TeX: A Manual for Self-study</i></a> <span class="cs1-format">(PDF)</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Gentle+Introduction+to+TeX%3A+A+Manual+for+Self-study&rft.aulast=Doob&rft.aufirst=Michael&rft_id=http%3A%2F%2Fwww.ctan.org%2Ftex-archive%2Finfo%2Fgentle%2Fgentle.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHelp%3ADisplaying+a+formula" class="Z3988"></span>. A paper introducing TeX — see page 39 onwards for a good introduction to the maths side of things.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2">Oetiker, Tobias; Partl, Hubert; Hyna, Irene; Schlegl, Elisabeth (December 13, 2009), <a rel="nofollow" class="external text" href="http://www.ctan.org/tex-archive/info/lshort/english/lshort.pdf"><i>The Not So Short Introduction to LaTeX 2<sub>ε</sub></i></a> <span class="cs1-format">(PDF)</span> (4.27 ed.)</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Not+So+Short+Introduction+to+LaTeX+2%3Csub%3E%26epsilon%3B%3C%2Fsub%3E&rft.edition=4.27&rft.date=2009-12-13&rft.aulast=Oetiker&rft.aufirst=Tobias&rft.au=Partl%2C+Hubert&rft.au=Hyna%2C+Irene&rft.au=Schlegl%2C+Elisabeth&rft_id=http%3A%2F%2Fwww.ctan.org%2Ftex-archive%2Finfo%2Flshort%2Fenglish%2Flshort.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHelp%3ADisplaying+a+formula" class="Z3988"></span>. A paper introducing LaTeX — skip to page 49 for the math section. See page 63 for a complete reference list of symbols included in LaTeX and AMS-LaTeX.</li> <li><a rel="nofollow" class="external text" href="http://ctan.org/tex-archive/info/symbols/comprehensive/symbols-letter.pdf">The Comprehensive LaTeX Symbol List</a>—symbols not found here may be documented there.</li> <li><a rel="nofollow" class="external text" href="http://mirrors.ctan.org/macros/latex/contrib/esint/esint-doc.pdf">The esint package for closed double integrals</a></li> <li><a rel="nofollow" class="external text" href="http://www.ams.org/tex/amslatex.html">AMS-LaTeX guide</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mathpix.com/handwriting-recognition">"Handwriting Recognition"</a>. Mathpix.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Handwriting+Recognition&rft.pub=Mathpix&rft_id=https%3A%2F%2Fmathpix.com%2Fhandwriting-recognition&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHelp%3ADisplaying+a+formula" class="Z3988"></span> Optical character recognition of handwritten mathematical formulas into LaTeX and other formats, offering 10 free snips a month (registration required).</li> <li>cancel package <a rel="nofollow" class="external text" href="http://www.ctan.org/pkg/cancel">homepage</a> and <a rel="nofollow" class="external text" href="http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf">PDF documentation</a></li> <li><a rel="nofollow" class="external text" href="http://us.metamath.org/symbols/symbols.html">A set of public domain fixed-size math symbol bitmaps</a>.</li> <li><a rel="nofollow" class="external text" href="http://milde.users.sourceforge.net/LUCR/Math/unimathsymbols.html">List of mathematical symbols with their Unicode characters and their LaTeX commands</a></li> <li><a href="/wiki/MathML" title="MathML">MathML</a>: A product of the <a href="/wiki/W3C" class="mw-redirect" title="W3C">W3C</a> <a rel="nofollow" class="external text" href="http://www.w3.org/Math/">Math working group</a>, is a low-level specification for describing mathematics as a basis for machine-to-machine communication</li> <li><a rel="nofollow" class="external text" href="https://www.w3.org/MarkUp/html3/maths.html">HTML Math and the <MATH> tag</a>, <a href="/wiki/W3C" class="mw-redirect" title="W3C">W3C</a>.</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Wikipedia_help_pages2185" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Wikipedia_help_pages" title="Template:Wikipedia help pages"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Wikipedia_help_pages" title="Template talk:Wikipedia help pages"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Wikipedia_help_pages" title="Special:EditPage/Template:Wikipedia help pages"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Wikipedia_help_pages2185" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Directory" title="Help:Directory">Wikipedia help pages</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div> <ul><li><b>Visit the <i><a href="/wiki/Wikipedia:Teahouse" title="Wikipedia:Teahouse">Teahouse</a></i> or the <i><a href="/wiki/Wikipedia:Help_desk" title="Wikipedia:Help desk">Help desk</a></i> for an interactive <abbr title="questions and answers">Q & A</abbr> forum.</b></li></ul> <hr/> <ul><li><b><a href="/wiki/Wikipedia:FAQ" title="Wikipedia:FAQ">FAQs</a></b> <b><abbr title="This is a list of frequently asked questions about using and contributing to Wikipedia.">(?)</abbr></b></li> <li><b><a href="/wiki/Wikipedia:Reference_desk" title="Wikipedia:Reference desk">Reference desks</a></b> <b><abbr title="Works like a library reference desk. Ask a question here and Wikipedia volunteers will try to answer it.">(?)</abbr></b></li> <li><b><a href="/wiki/Wikipedia:Noticeboards" title="Wikipedia:Noticeboards">Noticeboards</a></b> <b><abbr title="Pages where editors can ask questions and request assistance from people who are familiar with the policies and guidelines covered by each individual board.">(?)</abbr></b></li> <li><b><a href="/wiki/Help:Cheatsheet" title="Help:Cheatsheet">Cheatsheet</a></b> <b><abbr title="For a list of the most commonly used Wiki markup and templates.">(?)</abbr></b></li> <li><b> <a href="/wiki/Wikipedia:Directories_and_indexes" title="Wikipedia:Directories and indexes">Directories</a></b> <b><abbr title="For a list of Wikipedia's directories and indexes.">(?)</abbr></b></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Wikipedia:About" title="Wikipedia:About">About Wikipedia</a> <abbr title="Wikipedia's governess and customs">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:Administration" title="Wikipedia:Administration">Administration</a> <ul><li><a href="/wiki/Wikipedia:Purpose" title="Wikipedia:Purpose">Purpose</a></li> <li><a href="/wiki/Wikipedia:Five_pillars" title="Wikipedia:Five pillars">Principles</a></li></ul></li> <li><a href="/wiki/Wikipedia:Policies_and_guidelines" title="Wikipedia:Policies and guidelines">Policies and guidelines</a></li> <li><a href="/wiki/Wikipedia:What_Wikipedia_is_not" title="Wikipedia:What Wikipedia is not">What Wikipedia is not</a></li> <li><a href="/wiki/Wikipedia:General_disclaimer" title="Wikipedia:General disclaimer">Disclaimer</a> (<a href="/wiki/Wikipedia:Advice_for_parents" title="Wikipedia:Advice for parents">parental advice</a>)</li> <li><a href="/wiki/Wikipedia:Request_directory" title="Wikipedia:Request directory">Making requests</a></li> <li><a href="/wiki/Wikipedia:Who_writes_Wikipedia%3F" title="Wikipedia:Who writes Wikipedia?">Who writes Wikipedia?</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Wikipedia:Reader%27s_index_to_Wikipedia" title="Wikipedia:Reader's index to Wikipedia">Help for readers</a> <abbr title="Concerns and questions readers may have about Wikipedia">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:FAQ/Readers" title="Wikipedia:FAQ/Readers">FAQ</a></li> <li><a href="/wiki/Wikipedia:Wikipedia_book_creator_status" class="mw-redirect" title="Wikipedia:Wikipedia book creator status">Books</a></li> <li><a href="/wiki/Help:Copyright" title="Help:Copyright">Copyright</a></li> <li><a href="/wiki/Help:Glossary" class="mw-redirect" title="Help:Glossary">Glossary</a></li> <li><a href="/wiki/Help:Mobile_access" title="Help:Mobile access">Mobile access</a></li> <li><a href="/wiki/Help:Navigation" title="Help:Navigation">Navigation</a></li> <li><a href="/wiki/Help:Other_languages" title="Help:Other languages">Other languages</a></li> <li><a href="/wiki/Help:Searching" title="Help:Searching">Searching</a></li> <li><a href="/wiki/Help:Student_help" title="Help:Student help">Students</a></li> <li><a href="/wiki/Help:Viewing_media" title="Help:Viewing media">Viewing media</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Wikipedia:Contributing_to_Wikipedia" title="Wikipedia:Contributing to Wikipedia">Contributing<br/>to Wikipedia</a> <abbr title="Overviews and resources needed to comprehend, comment on, and edit">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:Guidance_for_younger_editors" title="Wikipedia:Guidance for younger editors">Advice for young editors</a></li> <li><a href="/wiki/Wikipedia:Avoiding_common_mistakes" title="Wikipedia:Avoiding common mistakes">Avoiding common mistakes</a></li> <li><a href="/wiki/Wikipedia:Etiquette" title="Wikipedia:Etiquette">Etiquette</a></li> <li><a href="/wiki/Wikipedia:Simplified_Manual_of_Style" title="Wikipedia:Simplified Manual of Style">Simplified Manual of Style</a></li> <li><a href="/wiki/Wikipedia:Simplified_ruleset" title="Wikipedia:Simplified ruleset">Simplified rule-set</a> <ul><li><a href="/wiki/Wikipedia:Ignore_all_rules" title="Wikipedia:Ignore all rules">"Ignore all rules"</a></li> <li><a href="/wiki/Wikipedia:The_rules_are_principles" title="Wikipedia:The rules are principles">"The rules are principles"</a></li></ul></li> <li><a href="/wiki/Wikipedia:Styletips" title="Wikipedia:Styletips">Style-tips</a></li> <li><a href="/wiki/Wikipedia:Tip_of_the_day" title="Wikipedia:Tip of the day">Tip of the day</a></li> <li><a href="/wiki/Help:Your_first_article" title="Help:Your first article">Your first article</a> (<a href="/wiki/Wikipedia:Article_wizard" title="Wikipedia:Article wizard">article wizard</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Help:Getting_started" title="Help:Getting started">Getting started</a> <abbr title="Introductions and tutorials">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:Why_create_an_account%3F" title="Wikipedia:Why create an account?">Why create an account?</a></li> <li><a href="/wiki/Help:Introduction" title="Help:Introduction">Introductions by topic</a></li> <li><a href="/wiki/Wikipedia:Graphics_tutorials" title="Wikipedia:Graphics tutorials">Graphics tutorials</a> <ul><li><a href="/wiki/Help:Pictures" title="Help:Pictures">Picture tutorial</a></li> <li><a href="/wiki/Wikipedia:IRC/Tutorial" title="Wikipedia:IRC/Tutorial">IRC <span style="font-size:85%;">(live chat)</span> tutorial</a></li></ul></li> <li><a href="/wiki/Wikipedia:VisualEditor/User_guide" class="mw-redirect" title="Wikipedia:VisualEditor/User guide">VisualEditor user guide</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Wikipedia:Dos_and_don%27ts" title="Wikipedia:Dos and don'ts">Dos and don'ts</a> <abbr title="Wikipedia policies, guidelines, and formatting standards in bullet points">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:Accessibility_dos_and_don%27ts" title="Wikipedia:Accessibility dos and don'ts">Accessibility</a></li> <li><a href="/wiki/Wikipedia:Biography_dos_and_don%27ts" title="Wikipedia:Biography dos and don'ts">Biographies</a></li> <li><a href="/wiki/Wikipedia:Biographies_of_living_persons_dos_and_don%27ts" title="Wikipedia:Biographies of living persons dos and don'ts">Biographies (living)</a></li> <li><a href="/wiki/Wikipedia:Categorization_dos_and_don%27ts" title="Wikipedia:Categorization dos and don'ts">Categorization</a></li> <li><a href="/wiki/Wikipedia:Consensus_dos_and_don%27ts" title="Wikipedia:Consensus dos and don'ts">Consensus</a></li> <li><a href="/wiki/Wikipedia:Talk_dos_and_don%27ts" title="Wikipedia:Talk dos and don'ts">Discussions</a></li> <li><a href="/wiki/Wikipedia:Disambiguation_dos_and_don%27ts" title="Wikipedia:Disambiguation dos and don'ts">Disambiguation</a></li> <li><a href="/wiki/Wikipedia:Image_dos_and_don%27ts" title="Wikipedia:Image dos and don'ts">Images</a></li> <li><a href="/wiki/Wikipedia:Lead_dos_and_don%27ts" title="Wikipedia:Lead dos and don'ts">Leads</a></li> <li><a href="/wiki/Wikipedia:Linking_dos_and_don%27ts" title="Wikipedia:Linking dos and don'ts">Links</a></li> <li><a href="/wiki/Wikipedia:List_dos_and_don%27ts" title="Wikipedia:List dos and don'ts">Lists</a></li> <li><a href="/wiki/Wikipedia:References_dos_and_don%27ts" title="Wikipedia:References dos and don'ts">References</a></li> <li><a href="/wiki/Wikipedia:Table_dos_and_don%27ts" title="Wikipedia:Table dos and don'ts">Tables</a></li> <li><a href="/wiki/Wikipedia:Article_title_dos_and_don%27ts" title="Wikipedia:Article title dos and don'ts">Titles (of articles)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Category:Wikipedia_how-to" title="Category:Wikipedia how-to">How-to pages</a> and<br/><a href="/wiki/Category:Wikipedia_information_pages" title="Category:Wikipedia information pages">information pages</a> <abbr title="Topic specific informative and instructional pages">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:Guide_to_appealing_blocks" title="Wikipedia:Guide to appealing blocks">Appealing blocks</a></li> <li><a href="/wiki/Wikipedia:Guide_to_deletion" title="Wikipedia:Guide to deletion">Article deletion</a></li> <li><a href="/wiki/Help:Category" title="Help:Category">Categories</a></li> <li><a href="/wiki/Help:Citations_quick_reference" title="Help:Citations quick reference">Citations/references</a> <ul><li><a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">Referencing for beginners</a></li> <li><a href="/wiki/Help:Citation_Style_1" title="Help:Citation Style 1">Citation Style 1</a></li> <li><a href="/wiki/Help:Cite_errors" title="Help:Cite errors">Cite errors</a></li> <li><a href="/wiki/Help:References_and_page_numbers" title="Help:References and page numbers">References and page numbers</a></li></ul></li> <li><a href="/wiki/Help:Convert" title="Help:Convert">Convert</a></li> <li><a href="/wiki/Help:Diff" title="Help:Diff">Diff</a></li> <li><a href="/wiki/Help:Editing" title="Help:Editing">Editing</a> <ul><li><a href="/wiki/Help:Minor_edit" title="Help:Minor edit">Minor edit</a></li> <li><a href="/wiki/Help:Edit_toolbar" title="Help:Edit toolbar">toolbar</a></li> <li><a href="/wiki/Help:Edit_conflict" title="Help:Edit conflict">edit conflict</a></li></ul></li> <li><a href="/wiki/Help:Find_sources" title="Help:Find sources">Find sources</a></li> <li><a href="/wiki/Help:Files" title="Help:Files">Files</a></li> <li><a href="/wiki/Help:Footnotes" title="Help:Footnotes">Footnotes</a></li> <li><a href="/wiki/Wikipedia:Guide_to_image_deletion" title="Wikipedia:Guide to image deletion">Image deletion</a></li> <li><a href="/wiki/Help:Infobox" title="Help:Infobox">Infoboxes</a></li> <li><a href="/wiki/Help:Link" title="Help:Link">Linking</a> (<a href="/wiki/Help:Link_color" title="Help:Link color">link color</a>)</li> <li><a href="/wiki/Help:Logging_in" title="Help:Logging in">Logging in</a></li> <li><a href="/wiki/Wikipedia:Merging" title="Wikipedia:Merging">Merging</a></li> <li><a href="/wiki/Help:Page_name" title="Help:Page name">Page name</a> <ul><li><a href="/wiki/Help:How_to_move_a_page" title="Help:How to move a page">Renaming pages</a></li></ul></li> <li><a href="/wiki/Help:Redirect" title="Help:Redirect">Redirect</a></li> <li><a href="/wiki/Help:Reset_password" title="Help:Reset password">Passwords</a> <ul><li><a href="/wiki/Help:Email_confirmation" title="Help:Email confirmation">Email confirmation</a></li></ul></li> <li><a href="/wiki/Help:Reverting" title="Help:Reverting">Reverting</a> <ul><li><a href="/wiki/Help:Simple_guide_to_vandalism_cleanup" title="Help:Simple guide to vandalism cleanup">Simple vandalism cleanup</a></li></ul></li> <li><a href="/wiki/Help:Talk_pages" title="Help:Talk pages">Talk pages</a> (<a href="/wiki/Help:Archiving_a_talk_page" title="Help:Archiving a talk page">archiving</a></li> <li><a href="/wiki/Help:Archiving_(plain_and_simple)" title="Help:Archiving (plain and simple)">simple archiving</a>)</li> <li><a href="/wiki/Help:User_contributions" title="Help:User contributions">User contributions</a></li> <li><a href="/wiki/Help:WP_search_protocol" title="Help:WP search protocol">WP search protocol</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Wiki_markup" class="mw-redirect" title="Wiki markup">Coding</a> <abbr title="Wikitext information consists of the syntax used to format a page">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Help:Wikitext" title="Help:Wikitext">Wiki markup</a></li> <li><a href="/wiki/Help:Barchart" title="Help:Barchart">Barcharts</a></li> <li><a href="/wiki/Help:Calculation" title="Help:Calculation">Calculations</a></li> <li><a href="/wiki/Help:Special_characters" title="Help:Special characters">Characters</a></li> <li><a href="/wiki/Help:Columns" title="Help:Columns">Columns</a></li> <li><a href="/wiki/Help:Elevation" title="Help:Elevation">Elevation</a></li> <li><a href="/wiki/Wikipedia:Manual_of_Style/Hidden_text" title="Wikipedia:Manual of Style/Hidden text">Hidden text</a></li> <li><a href="/wiki/Help:HTML_in_wikitext" title="Help:HTML in wikitext">HTML</a></li> <li><a href="/wiki/Help:List" title="Help:List">Lists</a></li> <li><a href="/wiki/Help:Magic_words" title="Help:Magic words">Magic words</a></li> <li><a href="/wiki/Help:Musical_symbols" title="Help:Musical symbols">Music symbols</a></li> <li><a href="/wiki/Help:Section" title="Help:Section">Sections</a></li> <li><a href="/wiki/Help:Sound_file_markup" title="Help:Sound file markup">Sounds</a></li> <li><a href="/wiki/Help:Table" title="Help:Table">Tables</a></li> <li><a href="/wiki/Help:Template" title="Help:Template">Templates</a></li> <li><a href="/wiki/Wikipedia:Transclusion" class="mw-redirect" title="Wikipedia:Transclusion">Transclusion</a></li> <li><a href="/wiki/Help:URL" title="Help:URL">URL</a></li> <li><a href="/wiki/Help:Visual_file_markup" title="Help:Visual file markup">Visual files</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Wikipedia:Directories_and_indexes" title="Wikipedia:Directories and indexes">Directories</a> <abbr title="Wikipedia's directories and indexes">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:Wikipedia_abbreviations" title="Wikipedia:Wikipedia abbreviations">Abbreviations</a></li> <li><a href="/wiki/Wikipedia:Contents" title="Wikipedia:Contents">Contents</a> <small>(Encyclopedia proper)</small></li> <li><a href="/wiki/Wikipedia:Department_directory" title="Wikipedia:Department directory">Departments</a></li> <li><a href="/wiki/Wikipedia:Editor%27s_index_to_Wikipedia" title="Wikipedia:Editor's index to Wikipedia">Editor's index</a></li> <li><a href="/wiki/Wikipedia:Essay_directory" title="Wikipedia:Essay directory">Essays</a></li> <li><a href="/wiki/Wikipedia:FAQ/Index" class="mw-redirect" title="Wikipedia:FAQ/Index">FAQs</a></li> <li><a href="/wiki/Wikipedia:Glossary" title="Wikipedia:Glossary">Glossary</a></li> <li><a href="/wiki/Wikipedia:List_of_guidelines" title="Wikipedia:List of guidelines">Guidelines</a></li> <li><a href="/wiki/Wikipedia:Manual_of_Style/Contents" title="Wikipedia:Manual of Style/Contents">Manual of Style </a></li> <li><a href="/wiki/Wikipedia:List_of_policies" title="Wikipedia:List of policies">Policies</a></li> <li><a href="/wiki/Wikipedia:Maintenance" title="Wikipedia:Maintenance">Tasks</a></li> <li><a href="/wiki/Wikipedia:Tips" title="Wikipedia:Tips">Tips</a></li> <li><a href="/wiki/Wikipedia:Tools" title="Wikipedia:Tools">Tools</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div><b> <a href="/wiki/Help:Wikipedia:_The_Missing_Manual" title="Help:Wikipedia: The Missing Manual">Missing Manual</a></b> <hr/> <span class="noprint plainlinks" title="Edit Special:MyTalk"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Special:MyTalk&action=edit&section=new&preload=Help:Contents/helpmepreload&preloadtitle=Help+me%21"><b>Ask for help on your talk page</b></a></span> <b><abbr title="If you need help, you can use this link to ask a question on your talk page; a volunteer will visit you there shortly!">(?)</abbr></b></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Wikipedia_technical_help1389" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align: center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Wikipedia_technical_help" title="Template:Wikipedia technical help"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Wikipedia_technical_help" title="Template talk:Wikipedia technical help"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Wikipedia_technical_help" title="Special:EditPage/Template:Wikipedia technical help"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Wikipedia_technical_help1389" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Directory#Technical_help" title="Help:Directory">Wikipedia technical help</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align: center;"><div><b>Get personal technical help at <a href="/wiki/Wikipedia:Teahouse" title="Wikipedia:Teahouse">the Teahouse</a>, <a href="/wiki/Wikipedia:Help_desk" title="Wikipedia:Help desk">help desk</a>, <a href="/wiki/Wikipedia:Village_pump_(technical)" title="Wikipedia:Village pump (technical)">village pump (technical)</a>, <a href="/wiki/Help:Introduction_to_talk_pages/1" title="Help:Introduction to talk pages/1">talk pages</a> or <a href="/wiki/Wikipedia:IRC" title="Wikipedia:IRC">IRC</a>.</b></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Wikipedia:FAQ/Technical" title="Wikipedia:FAQ/Technical">General<br/>technical help</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:Browser_notes" title="Wikipedia:Browser notes">Browser notes</a> <ul><li><a href="/wiki/Wikipedia:Bypass_your_cache" title="Wikipedia:Bypass your cache">Bypass cache</a></li> <li><a href="/wiki/Help:Keyboard_shortcuts" title="Help:Keyboard shortcuts">Keyboard shortcuts</a></li></ul></li> <li><a href="/wiki/Help:Editing" title="Help:Editing">Editing</a> <ul><li><a href="/wiki/Help:CharInsert" title="Help:CharInsert">CharInsert</a></li> <li><a href="/wiki/Help:Edit_conflict" title="Help:Edit conflict">Edit conflict</a></li> <li><a href="/wiki/Help:Edit_toolbar" title="Help:Edit toolbar">Edit toolbar</a></li> <li><a href="/wiki/Help:Reverting" title="Help:Reverting">Reverting</a></li></ul></li> <li><a href="/wiki/Wikipedia:How_to_create_a_page" title="Wikipedia:How to create a page">How to create a page</a></li> <li><a href="/wiki/Wikipedia:IRC" title="Wikipedia:IRC">IRC</a> <ul><li><a href="/wiki/Wikipedia:IRC/Tutorial" title="Wikipedia:IRC/Tutorial">Tutorial</a></li></ul></li> <li><a href="/wiki/Help:Mobile_access" title="Help:Mobile access">Mobile access</a></li> <li><a href="/wiki/Help:Multilingual_support" title="Help:Multilingual support">Multilingual support</a></li> <li><a href="/wiki/Help:Page_history" title="Help:Page history">Page history</a></li> <li><a href="/wiki/Help:Page_information" title="Help:Page information">Page information</a></li> <li><a href="/wiki/Wikipedia:Page_name" title="Wikipedia:Page name">Page name</a> <ul><li><a href="/wiki/Help:Page_name" title="Help:Page name">Help</a></li></ul></li> <li><a href="/wiki/Help:Printing" title="Help:Printing">Printing</a></li> <li><a href="/wiki/Wikipedia:Software_notices" title="Wikipedia:Software notices">Software notices</a> <ul><li><a href="/wiki/Wikipedia:Editnotice" title="Wikipedia:Editnotice">Editnotice</a></li></ul></li> <li><a href="/wiki/Help:Special_characters" title="Help:Special characters">Special Characters</a> <ul><li><a href="/wiki/Help:Entering_special_characters" title="Help:Entering special characters">Entering</a></li></ul></li> <li><a href="/wiki/Wikipedia:User_access_levels" title="Wikipedia:User access levels">User access levels</a></li> <li><a href="/wiki/Wikipedia:VisualEditor" title="Wikipedia:VisualEditor">VisualEditor</a> <ul><li><a href="/wiki/Help:VisualEditor" title="Help:VisualEditor">Help</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Special:SpecialPages" title="Special:SpecialPages">Special<br/>page</a>-related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Help:Special_page" title="Help:Special page">Special page help</a></li> <li><a href="/wiki/Help:AllPages" title="Help:AllPages">AllPages</a></li> <li><a href="/wiki/Wikipedia:Edit_filter" title="Wikipedia:Edit filter">Edit filter</a></li> <li><a href="/wiki/Wikipedia:Emailing_users" title="Wikipedia:Emailing users">Emailing users</a></li> <li><a href="/wiki/Help:Logging_in" title="Help:Logging in">Logging in</a> <ul><li><a href="/wiki/Help:Reset_password" title="Help:Reset password">Reset passwords</a></li></ul></li> <li><a href="/wiki/Help:Log" title="Help:Log">Logs</a></li> <li><a href="/wiki/Wikipedia:Moving_a_page" title="Wikipedia:Moving a page">Moving a page</a> <ul><li><a href="/wiki/Wikipedia:History_merging" title="Wikipedia:History merging">History merging</a></li> <li><a href="/wiki/Help:When_to_place_technical_requests_in_%22Administrator_needed%22" title="Help:When to place technical requests in "Administrator needed"">Non-admin and admin-only page moves</a></li></ul></li> <li><a href="/wiki/Help:Notifications" title="Help:Notifications">Notifications/Echo</a> <ul><li><a href="/wiki/Help:Notifications/FAQ" title="Help:Notifications/FAQ">FAQ</a></li></ul></li> <li><a href="/wiki/Wikipedia:Page_Curation/Help" title="Wikipedia:Page Curation/Help">Page Curation</a></li> <li><a href="/wiki/Help:Import" title="Help:Import">Page import</a></li> <li><a href="/wiki/Wikipedia:Pending_changes" title="Wikipedia:Pending changes">Pending changes</a></li> <li><a href="/wiki/Wikipedia:Random" title="Wikipedia:Random">Random pages</a></li> <li><a href="/wiki/Help:Recent_changes" title="Help:Recent changes">Recent changes</a></li> <li><a href="/wiki/Help:Related_changes" title="Help:Related changes">Related changes</a></li> <li><a href="/wiki/Help:Searching" title="Help:Searching">Searching</a> <ul><li><a href="/wiki/Help:Linksearch" title="Help:Linksearch">Linksearch</a></li></ul></li> <li><a href="/wiki/Wikipedia:Tags" title="Wikipedia:Tags">Tags</a></li> <li><a href="/wiki/Help:User_contributions" title="Help:User contributions">User contributions</a></li> <li><a href="/wiki/Help:Watchlist" title="Help:Watchlist">Watchlist</a></li> <li><a href="/wiki/Help:What_links_here" title="Help:What links here">What links here</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Help:Wikitext" title="Help:Wikitext">Wikitext</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Help:Wikitext" title="Help:Wikitext">Wikitext</a> <ul><li><a href="/wiki/Help:Cheatsheet" title="Help:Cheatsheet">Cheatsheet</a></li></ul></li> <li><a href="/wiki/Help:Columns" title="Help:Columns">Columns</a></li> <li><a href="/wiki/Help:Line-break_handling" title="Help:Line-break handling">Line-break handling</a></li> <li><a href="/wiki/Help:List" title="Help:List">Lists</a></li> <li><a href="/wiki/Help:Magic_words" title="Help:Magic words">Magic words</a> <ul><li><a href="/wiki/Help:Magic_words_for_beginners" title="Help:Magic words for beginners">For beginners</a></li> <li><a href="/wiki/Help:Conditional_expressions" title="Help:Conditional expressions">Conditional expressions</a></li> <li><a href="/wiki/Help:Switch_parser_function" title="Help:Switch parser function">Switch parser function</a></li> <li><a href="/wiki/Help:Time_function" title="Help:Time function">Time function</a></li></ul></li> <li><a href="/wiki/Help:Redirect" title="Help:Redirect">Redirects</a></li> <li><a href="/wiki/Help:Section" title="Help:Section">Sections and TOCs</a></li> <li><a href="/wiki/Help:Table" title="Help:Table">Tables</a> <ul><li><a href="/wiki/Help:Introduction_to_tables_with_Wiki_Markup/1" title="Help:Introduction to tables with Wiki Markup/1">Introduction</a></li> <li><a href="/wiki/Help:Basic_table_markup" title="Help:Basic table markup">Basics</a></li> <li><a href="/wiki/Help:Advanced_table_formatting" title="Help:Advanced table formatting">Advanced table formatting</a></li> <li><a href="/wiki/Help:Collapsing_tables_and_more" title="Help:Collapsing tables and more">Collapsing</a></li> <li><a href="/wiki/Help:Conditional_tables" title="Help:Conditional tables">Conditional tables</a></li> <li><a href="/wiki/Help:Sortable_tables" title="Help:Sortable tables">Sortable tables</a></li></ul></li> <li><a href="/wiki/Help:Using_colours" title="Help:Using colours">Using colours</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Help:Link" title="Help:Link">Links</a> and <a href="/wiki/Help:Diff" title="Help:Diff">diffs</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Help:Link" title="Help:Link">Links</a> <ul><li><a href="/wiki/Help:Interlanguage_links" title="Help:Interlanguage links">Interlanguage</a></li> <li><a href="/wiki/Help:Interwiki_linking" title="Help:Interwiki linking">Interwiki</a></li> <li><a href="/wiki/Help:Permanent_link" title="Help:Permanent link">Permanent</a></li></ul></li> <li><a href="/wiki/Help:Diff" title="Help:Diff">Diffs</a> <ul><li><a href="/wiki/Wikipedia:Simplest_diff_guide" title="Wikipedia:Simplest diff guide">Simplest diff guide</a></li> <li><a href="/wiki/Wikipedia:Simple_diff_and_link_guide" title="Wikipedia:Simple diff and link guide">Simple diff and link guide</a></li> <li><a href="/wiki/Wikipedia:Complete_diff_and_link_guide" title="Wikipedia:Complete diff and link guide">Complete diff and link guide</a></li></ul></li> <li><a href="/wiki/Help:Colon_trick" title="Help:Colon trick">Colon trick</a></li> <li><a href="/wiki/Help:Link_color" title="Help:Link color">Link color</a></li> <li><a href="/wiki/Help:Pipe_trick" title="Help:Pipe trick">Pipe trick</a></li> <li><a href="/wiki/Help:URL" title="Help:URL">URLs</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Wikipedia:Media" class="mw-disambig" title="Wikipedia:Media">Media</a> files: images,<br/>videos and sounds</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Help:Media" title="Help:Media">Media help</a></li> <li><a href="/wiki/Help:Files" title="Help:Files">Files</a> <ul><li><a href="/wiki/Help:Creation_and_usage_of_media_files" title="Help:Creation and usage of media files">Creation and usage</a></li> <li><a href="/wiki/Wikipedia:Moving_files_to_Commons" title="Wikipedia:Moving files to Commons">Moving files to Commons</a></li></ul></li> <li><a href="/wiki/Wikipedia:Images" title="Wikipedia:Images">Images</a> <ul><li><a href="/wiki/Help:Introduction_to_images_with_Wiki_Markup/1" title="Help:Introduction to images with Wiki Markup/1">Introduction to images</a></li> <li><a href="/wiki/Help:Pictures" title="Help:Pictures">Picture tutorial</a></li> <li><a href="/wiki/Wikipedia:Preparing_images_for_upload" title="Wikipedia:Preparing images for upload">Preparing images for upload</a></li> <li><a href="/wiki/Wikipedia:Uploading_images" title="Wikipedia:Uploading images">Uploading images</a></li> <li><a href="/wiki/Help:Options_to_hide_an_image" title="Help:Options to hide an image">Options to hide an image</a></li> <li><a href="/wiki/Wikipedia:Extended_image_syntax" title="Wikipedia:Extended image syntax">Extended image syntax</a></li> <li><a href="/wiki/Wikipedia:SVG_help" title="Wikipedia:SVG help">SVG help</a></li></ul></li> <li><a href="/wiki/Help:Gallery_tag" title="Help:Gallery tag">Gallery tag</a></li> <li><a href="/wiki/Wikipedia:Graphics_tutorials" title="Wikipedia:Graphics tutorials">Graphics tutorials</a> <ul><li><a href="/wiki/Wikipedia:Basic_bitmap_image_editing" title="Wikipedia:Basic bitmap image editing">Basic bitmap image editing</a></li> <li><a href="/wiki/Wikipedia:How_to_improve_image_quality" title="Wikipedia:How to improve image quality">How to improve image quality</a></li> <li><a href="/wiki/Wikipedia:Graphics_Lab/Resources" title="Wikipedia:Graphics Lab/Resources">Graphics Lab resources</a></li></ul></li> <li><a href="/wiki/Help:Sound_file_markup" title="Help:Sound file markup">Sound file markup</a></li> <li><a href="/wiki/Help:Visual_file_markup" title="Help:Visual file markup">Visual file markup</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Other graphics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Help:Family_trees" title="Help:Family trees">Family trees</a></li> <li><a href="/wiki/Wikipedia:Graphs_and_charts" title="Wikipedia:Graphs and charts">Graphs and charts</a> <ul><li><a href="/wiki/Wikipedia:How_to_create_charts_for_Wikipedia_articles" title="Wikipedia:How to create charts for Wikipedia articles">How to create</a></li> <li><a href="/wiki/Help:Barchart" title="Help:Barchart">Barcharts</a></li> <li><a href="/wiki/Wikipedia:To_scale_charts" title="Wikipedia:To scale charts">To scale charts</a></li></ul></li> <li><a class="mw-selflink selflink">Math formulas</a> <ul><li><a class="mw-selflink-fragment" href="#Use_of_HTML_templates">Math symbols</a></li></ul></li> <li><a href="/wiki/Help:Score" title="Help:Score">Musical scores</a> <ul><li><a href="/wiki/Help:Musical_symbols" title="Help:Musical symbols">Musical symbols</a></li></ul></li> <li><a href="/wiki/Wikipedia:Timeline" title="Wikipedia:Timeline">Timeline</a> <ul><li><a href="/wiki/Help:EasyTimeline_syntax" title="Help:EasyTimeline syntax">EasyTimeline syntax</a></li></ul></li> <li><a href="/wiki/Help:WikiHiero_syntax" title="Help:WikiHiero syntax">WikiHiero syntax</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Help:A_quick_guide_to_templates" title="Help:A quick guide to templates">Templates</a> and<br/><a href="/wiki/Lua_(programming_language)" title="Lua (programming language)">Lua</a> modules</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Help:Template" title="Help:Template">Templates</a></li> <li><a href="/wiki/Wikipedia:Advanced_template_coding" title="Wikipedia:Advanced template coding">Advanced template coding</a></li> <li><a href="/wiki/Wikipedia:Template_documentation" title="Wikipedia:Template documentation">Template documentation</a></li> <li><a href="/wiki/Wikipedia:Template_index" title="Wikipedia:Template index">Template index</a></li> <li><a href="/wiki/Help:Template_limits" title="Help:Template limits">Template limits</a></li> <li><a href="/wiki/Wikipedia:Template_sandbox_and_test_cases" title="Wikipedia:Template sandbox and test cases">Template sandbox and test cases</a></li> <li><a href="/wiki/Wikipedia:Citation_templates" title="Wikipedia:Citation templates">Citation templates</a></li> <li><a href="/wiki/Help:Lua" title="Help:Lua">Lua help</a></li> <li><a href="/wiki/Wikipedia:Lua" title="Wikipedia:Lua">Lua project</a> <ul><li><a href="/wiki/Wikipedia:Lua/Resources" title="Wikipedia:Lua/Resources">Resources</a></li> <li><a href="/wiki/Wikipedia:Lua/To_do" title="Wikipedia:Lua/To do">To do</a></li></ul></li> <li><a href="/wiki/Help:Substitution" title="Help:Substitution">Substitution</a></li> <li><a href="/wiki/Help:Purge" title="Help:Purge">Purge</a> <ul><li><a href="/wiki/Help:Job_queue" title="Help:Job queue">Job queue</a></li></ul></li> <li><a href="/wiki/Help:Transclusion" title="Help:Transclusion">Transclusion</a> <ul><li><a href="/wiki/Help:Labeled_section_transclusion" title="Help:Labeled section transclusion">Labeled section</a></li> <li><a href="/wiki/Wikipedia:Transclusion_costs_and_benefits" title="Wikipedia:Transclusion costs and benefits">Costs and benefits</a></li></ul></li> <li><a href="/wiki/Wikipedia:Guide_to_Scribbling" title="Wikipedia:Guide to Scribbling">Guide to Scribbling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Wikipedia:Administration#Data_structure_and_development" title="Wikipedia:Administration">Data structure</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:Namespace" title="Wikipedia:Namespace">Namespaces</a></li> <li><a href="/wiki/Wikipedia:What_is_an_article%3F" title="Wikipedia:What is an article?">Main/Article</a></li> <li><a href="/wiki/Help:Category" title="Help:Category">Category</a></li> <li><a href="/wiki/Wikipedia:Drafts" title="Wikipedia:Drafts">Draft</a></li> <li><a href="/wiki/Help:Files" title="Help:Files">File</a> <ul><li><a href="/wiki/Help:File_description_page" title="Help:File description page">File description page</a></li></ul></li> <li><a href="/wiki/Wikipedia:Help_namespace" title="Wikipedia:Help namespace">Help</a></li> <li><a href="/wiki/Wikipedia:Portal" title="Wikipedia:Portal">Portal</a></li> <li><a href="/wiki/Wikipedia:Project_namespace" title="Wikipedia:Project namespace">Project/Wikipedia</a></li> <li><a href="/wiki/Help:Talk_pages" title="Help:Talk pages">Talk</a> <ul><li><a href="/wiki/Help:Archiving_a_talk_page" title="Help:Archiving a talk page">Archiving</a> <ul><li><a href="/wiki/Help:Archiving_(plain_and_simple)" title="Help:Archiving (plain and simple)">Simple</a></li></ul></li></ul></li> <li><a href="/wiki/Wikipedia:Template_namespace" title="Wikipedia:Template namespace">Template</a></li> <li><a href="/wiki/Wikipedia:User_pages" title="Wikipedia:User pages">User</a> <ul><li><a href="/wiki/Wikipedia:User_page_design_guide" title="Wikipedia:User page design guide">User page design</a></li></ul></li> <li><a href="/wiki/Help:MediaWiki_namespace" title="Help:MediaWiki namespace">MediaWiki</a> 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title="Wikipedia:Scripts">IRC Scripts</a></li> <li><a href="/wiki/Wikipedia:User_scripts" title="Wikipedia:User scripts">User scripts</a> <ul><li><a href="/wiki/Wikipedia:User_scripts/Guide" title="Wikipedia:User scripts/Guide">Guide</a></li> <li><a href="/wiki/Wikipedia:User_scripts/List" title="Wikipedia:User scripts/List">List</a></li> <li><a href="/wiki/Wikipedia:User_scripts/Techniques" title="Wikipedia:User scripts/Techniques">Techniques</a></li></ul></li> <li><a href="/wiki/Help:User_style" title="Help:User style">User style</a></li> <li><a href="/wiki/Wikipedia:Tools" title="Wikipedia:Tools">Tools</a> <ul><li><a href="/wiki/Wikipedia:Tools/Alternative_browsing" title="Wikipedia:Tools/Alternative browsing">Alternative browsing</a></li> <li><a href="/wiki/Wikipedia:Tools/Browser_tools" title="Wikipedia:Tools/Browser tools">Browser tools</a></li> <li><a href="/wiki/Wikipedia:Tools/Editing_tools" title="Wikipedia:Tools/Editing tools">Editing tools</a></li> <li><a href="/wiki/Wikipedia:Tools/Navigation_shortcuts" title="Wikipedia:Tools/Navigation shortcuts">Navigation shortcuts</a></li> <li><a href="/wiki/Wikipedia:Tools/Optimum_tool_set" title="Wikipedia:Tools/Optimum tool set">Optimum tool set</a></li></ul></li> <li><a href="/wiki/Wikipedia:Wikimedia_Cloud_Services" title="Wikipedia:Wikimedia Cloud Services">Wikimedia Cloud Services</a></li> <li><a href="https://www.mediawiki.org/wiki/Beta_Features" class="extiw" title="mw:Beta Features">Beta Features at MediaWiki</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Automated editing</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wikipedia:WikiProject_Articles_for_creation/Helper_script" title="Wikipedia:WikiProject Articles for creation/Helper script">AfC helper script</a></li> <li><a href="/wiki/Wikipedia:AntiVandal" title="Wikipedia:AntiVandal">AntiVandal</a></li> <li><a href="/wiki/Wikipedia:AutoWikiBrowser" title="Wikipedia:AutoWikiBrowser">AutoWikiBrowser</a></li> <li><a href="/wiki/Wikipedia:Bots" title="Wikipedia:Bots">Bots</a> <ul><li><a href="/wiki/Help:Creating_a_bot" title="Help:Creating a bot">Creating</a></li> <li><a href="/wiki/Wikipedia:History_of_Wikipedia_bots" title="Wikipedia:History of Wikipedia bots">history</a></li></ul></li> <li><a href="/wiki/Wikipedia:HotCat" title="Wikipedia:HotCat">HotCat</a></li> <li><a href="/wiki/Wikipedia:Huggle" title="Wikipedia:Huggle">Huggle</a></li> <li><a href="/wiki/Wikipedia:Tools/Navigation_popups" title="Wikipedia:Tools/Navigation popups">Navigation popups</a></li> <li><a href="/wiki/Wikipedia:RedWarn" title="Wikipedia:RedWarn">RedWarn</a></li> <li><a href="/wiki/Wikipedia:Twinkle" title="Wikipedia:Twinkle">Twinkle</a></li> <li><a href="/wiki/Wikipedia:Ultraviolet" title="Wikipedia:Ultraviolet">Ultraviolet</a></li> <li><a href="/wiki/Wikipedia:WPCleaner" title="Wikipedia:WPCleaner">WPCleaner</a></li> <li>Inactive <ul><li><a href="/wiki/Wikipedia:Igloo" title="Wikipedia:Igloo">igloo</a></li> <li><a href="/wiki/Wikipedia:STiki" title="Wikipedia:STiki">STiki</a></li></ul></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align: center;"><div> <ul><li>See also: <b><a href="/wiki/Category:Wikipedia_how-to" title="Category:Wikipedia how-to">Category:Wikipedia how-to</a></b></li> <li><b><a href="/wiki/Category:Wikipedia_information_pages" title="Category:Wikipedia information pages">Category:Wikipedia information pages</a></b><br/>Further navigation at: <a href="/wiki/Template:Wikipedia_help_pages" title="Template:Wikipedia help pages">Help pages</a> <ul><li><a href="/wiki/Template:Administrators%27_guide" title="Template:Administrators' guide">Administrators</a></li></ul></li> <li><a href="/wiki/Wikipedia:WikiProject_Accessibility/Navigation_menu" title="Wikipedia:WikiProject Accessibility/Navigation menu">Accessibility</a></li> <li><a href="/wiki/Template:Wikipedia_accounts" title="Template:Wikipedia accounts">Accounts</a></li> <li><a href="/wiki/Template:Botnav" title="Template:Botnav">Bots</a></li> <li><a href="/wiki/Template:Wikipedia_referencing" title="Template:Wikipedia referencing">Referencing</a> <ul><li><a href="/wiki/Template:Citation_metadata_navbox" title="Template:Citation metadata navbox">Citation metadata</a></li></ul></li> <li><a href="/wiki/Template:Wikipedia_templates" title="Template:Wikipedia templates">Templates</a></li> <li><a href="/wiki/Wikipedia:User_scripts/Navbox" title="Wikipedia:User scripts/Navbox">User scripts</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Common_mathematical_notation,_symbols,_and_formulas167" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Mathematical_symbols_notation_language" title="Template:Mathematical symbols notation language"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Mathematical_symbols_notation_language" title="Template talk:Mathematical symbols notation language"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Mathematical_symbols_notation_language" title="Special:EditPage/Template:Mathematical symbols notation language"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Common_mathematical_notation,_symbols,_and_formulas167" style="font-size:114%;margin:0 4em">Common <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> <a href="/wiki/Mathematical_notation" title="Mathematical notation">notation</a>, <a href="/wiki/List_of_mathematical_symbols_by_subject" class="mw-redirect" title="List of mathematical symbols by subject">symbols</a>, and <a class="mw-selflink selflink">formulas</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible expanded navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Lists_of_Unicode_and_LaTeX_mathematical_symbols167" style="font-size:114%;margin:0 4em">Lists of <a href="/wiki/Unicode" title="Unicode">Unicode</a> and <a href="/wiki/LaTeX" title="LaTeX">LaTeX</a> mathematical symbols</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_mathematical_symbols_by_subject" class="mw-redirect" title="List of mathematical symbols by subject">List of mathematical symbols by subject</a></li> <li><a href="/wiki/Glossary_of_mathematical_symbols" title="Glossary of mathematical symbols">Glossary of mathematical symbols</a></li> <li><a href="/wiki/List_of_logic_symbols" title="List of logic symbols">List of logic symbols</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible expanded navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Lists_of_Unicode_symbols167" style="font-size:114%;margin:0 4em">Lists of <a href="/wiki/Unicode" title="Unicode">Unicode</a> symbols</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_Unicode_characters" title="List of Unicode characters">List of Unicode characters</a></li> <li><a href="/wiki/Unicode_block" title="Unicode block">Unicode block</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Alphanumeric</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematical_Alphanumeric_Symbols" title="Mathematical Alphanumeric Symbols">Mathematical Alphanumeric Symbols</a></li> <li><a href="/wiki/Blackboard_bold#Usage" title="Blackboard bold">Blackboard bold</a></li> <li><a href="/wiki/Letterlike_Symbols" title="Letterlike Symbols">Letterlike Symbols</a></li> <li><a href="/wiki/Symbols_for_zero" title="Symbols for zero">Symbols for zero</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Arrow_(symbol)" title="Arrow (symbol)">Arrows</a> and <a href="/wiki/Geometric_Shapes_(Unicode_block)" title="Geometric Shapes (Unicode block)">Geometric Shapes</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arrow_(symbol)" title="Arrow (symbol)">Arrows</a></li> <li><a href="/wiki/Miscellaneous_Symbols_and_Arrows" title="Miscellaneous Symbols and Arrows">Miscellaneous Symbols and Arrows</a></li> <li><a href="/wiki/Geometric_Shapes_(Unicode_block)" title="Geometric Shapes (Unicode block)">Geometric Shapes (Unicode block)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Operators</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematical_operators_and_symbols_in_Unicode" title="Mathematical operators and symbols in Unicode">Mathematical operators and symbols</a></li> <li><a href="/wiki/Mathematical_Operators_(Unicode_block)" title="Mathematical Operators (Unicode block)">Mathematical Operators (Unicode block)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Supplemental_Mathematical_Operators" title="Supplemental Mathematical Operators">Supplemental Math Operators</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Supplemental_Mathematical_Operators" title="Supplemental Mathematical Operators">Supplemental Mathematical Operators</a></li> <li><a href="/wiki/Number_Forms" title="Number Forms">Number Forms</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Miscellaneous_Mathematical_Symbols-A" title="Miscellaneous Mathematical Symbols-A">A</a></li> <li><a href="/wiki/Miscellaneous_Mathematical_Symbols-B" title="Miscellaneous Mathematical Symbols-B">B</a></li> <li><a href="/wiki/Miscellaneous_Technical" title="Miscellaneous Technical">Technical</a></li> <li><a href="/wiki/ISO_31-11" title="ISO 31-11">ISO 31-11</a> (Mathematical signs and symbols for use in physical sciences and technology)</li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible expanded navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Typographical_conventions_and_notations167" style="font-size:114%;margin:0 4em">Typographical conventions and notations</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Language_of_mathematics" title="Language of mathematics">Language</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/APL_syntax_and_symbols#Monadic_functions" title="APL syntax and symbols">APL syntax and symbols</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Letters</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Diacritic" title="Diacritic">Diacritic</a></li> <li><a href="/wiki/List_of_letters_used_in_mathematics,_science,_and_engineering" title="List of letters used in mathematics, science, and engineering">Letters in STEM</a> <ul><li><a href="/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering" title="Greek letters used in mathematics, science, and engineering">Greek letters in STEM</a></li> <li><a href="/wiki/Latin_letters_used_in_mathematics,_science,_and_engineering" title="Latin letters used in mathematics, science, and engineering">Latin letters in STEM</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Notation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematical_notation" title="Mathematical notation">Mathematical notation</a></li> <li><a href="/wiki/List_of_mathematical_abbreviations" title="List of mathematical abbreviations">Abbreviations</a></li> <li><a href="/wiki/Notation_in_probability_and_statistics" title="Notation in probability and statistics">Notation in probability and statistics</a></li> <li><a href="/wiki/List_of_common_physics_notations" title="List of common physics notations">List of common physics notations</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible expanded navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Meanings_of_symbols167" style="font-size:114%;margin:0 4em">Meanings of symbols</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glossary_of_mathematical_symbols" title="Glossary of mathematical symbols">Glossary of mathematical symbols</a></li> <li><a href="/wiki/List_of_mathematical_constants" title="List of mathematical constants">List of mathematical constants</a></li> <li><a href="/wiki/Physical_constant" title="Physical constant">Physical constants</a></li> <li><a href="/wiki/Table_of_mathematical_symbols_by_introduction_date" title="Table of mathematical symbols by introduction date">Table of mathematical symbols by introduction date</a></li> <li><a href="/wiki/List_of_typographical_symbols_and_punctuation_marks" title="List of typographical symbols and punctuation marks">List of typographical symbols and punctuation marks</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Help:Displaying_a_formula&oldid=1271901721">https://en.wikipedia.org/w/index.php?title=Help:Displaying_a_formula&oldid=1271901721</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Wikipedia_how-to" title="Category:Wikipedia how-to">Wikipedia how-to</a></li><li><a href="/wiki/Category:Wikipedia_text_help" title="Category:Wikipedia text help">Wikipedia 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