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<ul id="toc-General_guidelines-sublist" class="vector-toc-list"> <li id="toc-When_should_an_article_exist?" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#When_should_an_article_exist?"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>When should an article exist?</span> </div> </a> <ul id="toc-When_should_an_article_exist?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Outline" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Outline"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Outline</span> </div> </a> <ul id="toc-Outline-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Infobox" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Infobox"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Infobox</span> </div> </a> <ul id="toc-Infobox-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symbolic_and_linguistic_representations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Symbolic_and_linguistic_representations"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Symbolic and linguistic representations</span> </div> </a> <ul id="toc-Symbolic_and_linguistic_representations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Assessing_mathematical_number_facts" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Assessing_mathematical_number_facts"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Assessing mathematical number facts</span> </div> </a> <button aria-controls="toc-Assessing_mathematical_number_facts-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 Assessing mathematical number facts subsection</span> </button> <ul id="toc-Assessing_mathematical_number_facts-sublist" class="vector-toc-list"> <li id="toc-Simple_facts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simple_facts"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Simple facts</span> </div> </a> <ul id="toc-Simple_facts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formulaic_facts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formulaic_facts"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Formulaic facts</span> </div> </a> <ul id="toc-Formulaic_facts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Off-topic_facts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Off-topic_facts"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Off-topic facts</span> </div> </a> <ul id="toc-Off-topic_facts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Connection" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Connection"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Connection</span> </div> </a> <ul id="toc-Connection-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-No_Wikipedia_page" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#No_Wikipedia_page"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>No Wikipedia page</span> </div> </a> <ul id="toc-No_Wikipedia_page-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-OEIS" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#OEIS"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>OEIS</span> </div> </a> <ul id="toc-OEIS-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-No_original_research_and_no_synthesis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#No_original_research_and_no_synthesis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>No original research and no synthesis</span> </div> </a> <ul id="toc-No_original_research_and_no_synthesis-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Assessing_content_outside_of_pure_mathematics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Assessing_content_outside_of_pure_mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Assessing content outside of pure mathematics</span> </div> </a> <button aria-controls="toc-Assessing_content_outside_of_pure_mathematics-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 Assessing content outside of pure mathematics subsection</span> </button> <ul id="toc-Assessing_content_outside_of_pure_mathematics-sublist" class="vector-toc-list"> <li id="toc-Applied_mathematics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Applied_mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Applied mathematics</span> </div> </a> <ul id="toc-Applied_mathematics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Philosophy_and_symbolism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Philosophy_and_symbolism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Philosophy and symbolism</span> </div> </a> <ul id="toc-Philosophy_and_symbolism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-What_not_to_include" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#What_not_to_include"> 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class="vector-toc-numb">4.1</span> <span>Naming compliance</span> </div> </a> <ul id="toc-Naming_compliance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Referencing"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Referencing</span> </div> </a> <ul id="toc-Referencing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Edit_summaries" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Edit_summaries"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Edit summaries</span> </div> </a> <ul id="toc-Edit_summaries-sublist" class="vector-toc-list"> </ul> </li> </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"> 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data-ooui='{"_":"OO.ui.ToggleSwitchWidget","href":"\/w\/index.php?title=Wikipedia:WikiProject_Numbers\/Guidelines&diff=prev&oldid=1240601872&diff-type=inline","value":false,"title":"Switches between inline format and two-column format"}'><span class='oo-ui-toggleSwitchWidget-glow'></span><a href='/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&diff=prev&oldid=1240601872&diff-type=inline'><span class='oo-ui-toggleSwitchWidget-grip'></span></a></div></div></div></div></div></div><table class="diff diff-type-table diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" class="diff-otitle diff-side-deleted"><div id="mw-diff-otitle1"><strong><a href="/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&oldid=1240601765" title="Wikipedia:WikiProject Numbers/Guidelines">Revision as of 08:20, 16 August 2024</a> <span class="mw-diff-edit"><a href="/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&action=edit&oldid=1240601765" title="Wikipedia:WikiProject Numbers/Guidelines">edit</a></span><span class="mw-diff-timestamp" data-timestamp="2024-08-16T08:20:57Z"></span></strong></div><div id="mw-diff-otitle2"><a href="/wiki/User:Polyamorph" class="mw-userlink" title="User:Polyamorph" data-mw-revid="1240601765"><bdi>Polyamorph</bdi></a> <span class="mw-usertoollinks">(<a href="/wiki/User_talk:Polyamorph" class="mw-usertoollinks-talk" title="User talk:Polyamorph">talk</a> | <a href="/wiki/Special:Contributions/Polyamorph" class="mw-usertoollinks-contribs" title="Special:Contributions/Polyamorph">contribs</a>)</span><div class="mw-diff-usermetadata"><div class="mw-diff-userroles"><a href="/wiki/Wikipedia:Extended_confirmed_editors" class="mw-redirect" title="Wikipedia:Extended confirmed editors">Extended confirmed users</a>, <a href="/wiki/Wikipedia:Page_mover" title="Wikipedia:Page mover">Page movers</a>, <a href="/wiki/Wikipedia:Reviewing_pending_changes" title="Wikipedia:Reviewing pending changes">Pending changes reviewers</a>, <a href="/wiki/Wikipedia:Rollback" title="Wikipedia:Rollback">Rollbackers</a></div><div class="mw-diff-usereditcount"><span>29,769</span> edits</div></div></div><div id="mw-diff-otitle3"> <span class="comment comment--without-parentheses"><span class="autocomment"><a href="#Off-topic_facts">→<bdi dir="ltr">Off-topic facts</bdi></a>: </span> revise</span></div><div id="mw-diff-otitle5"></div><div id="mw-diff-otitle4"><a href="/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&diff=prev&oldid=1240601765" title="Wikipedia:WikiProject Numbers/Guidelines" id="differences-prevlink">← Previous edit</a></div></td> <td colspan="2" class="diff-ntitle diff-side-added"><div id="mw-diff-ntitle1"><strong><a href="/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&oldid=1240601872" title="Wikipedia:WikiProject Numbers/Guidelines">Revision as of 08:22, 16 August 2024</a> <span class="mw-diff-edit"><a href="/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&action=edit&oldid=1240601872" title="Wikipedia:WikiProject Numbers/Guidelines">edit</a></span><span class="mw-diff-timestamp" data-timestamp="2024-08-16T08:22:10Z"></span> <span class="mw-diff-undo"><a href="/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&action=edit&undoafter=1240601765&undo=1240601872" title=""Undo" reverts this edit and opens the edit form in preview mode. It allows adding a reason in the summary.">undo</a></span></strong></div><div id="mw-diff-ntitle2"><a href="/wiki/User:Polyamorph" class="mw-userlink" title="User:Polyamorph" data-mw-revid="1240601872"><bdi>Polyamorph</bdi></a> <span class="mw-usertoollinks">(<a href="/wiki/User_talk:Polyamorph" class="mw-usertoollinks-talk" title="User talk:Polyamorph">talk</a> | <a href="/wiki/Special:Contributions/Polyamorph" class="mw-usertoollinks-contribs" title="Special:Contributions/Polyamorph">contribs</a>)</span><div class="mw-diff-usermetadata"><div class="mw-diff-userroles"><a href="/wiki/Wikipedia:Extended_confirmed_editors" class="mw-redirect" title="Wikipedia:Extended confirmed editors">Extended confirmed users</a>, <a href="/wiki/Wikipedia:Page_mover" title="Wikipedia:Page mover">Page movers</a>, <a href="/wiki/Wikipedia:Reviewing_pending_changes" title="Wikipedia:Reviewing pending changes">Pending changes reviewers</a>, <a href="/wiki/Wikipedia:Rollback" title="Wikipedia:Rollback">Rollbackers</a></div><div class="mw-diff-usereditcount"><span>29,769</span> edits</div></div></div><div id="mw-diff-ntitle3"> <span class="comment comment--without-parentheses"><span class="autocomment"><a href="#Assessing_mathematical_number_facts">→<bdi dir="ltr">Assessing mathematical number facts</bdi></a>: </span> revise</span></div><div id="mw-diff-ntitle5"></div><div id="mw-diff-ntitle4"><a href="/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&diff=next&oldid=1240601872" title="Wikipedia:WikiProject Numbers/Guidelines" id="differences-nextlink">Next edit →</a></div></td> </tr><tr> <td colspan="2" class="diff-lineno">Line 54:</td> <td colspan="2" class="diff-lineno">Line 54:</td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>== Assessing mathematical number facts ==</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>== Assessing mathematical number facts ==</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>The purpose of number articles is to provide a broad overview of a number's history, <del class="diffchange diffchange-inline">properties</del>, and uses, without going into excessive detail (see [[WP:Summary]]). While there is an endless array of true mathematical facts about a given number, not all of them are appropriate for inclusion. This section provides several criteria for assessing the suitability of a mathematical number fact.</div></td> <td class="diff-marker" data-marker="+"></td> <td class="diff-addedline diff-side-added"><div>The purpose of number articles is to provide a broad overview of a number's history, <ins class="diffchange diffchange-inline">mathematical</ins>,<ins class="diffchange diffchange-inline"> scientific, or cultural properties</ins> and uses, without going into excessive detail (see [[WP:Summary]]). While there is an endless array of true mathematical facts about a given number, not all of them are appropriate for inclusion. This section provides several criteria for assessing the suitability of a mathematical number fact.</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>=== Simple facts === </div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>=== Simple facts === </div></td> </tr> </table><hr class='diff-hr' id='mw-oldid' /> <h2 class='diff-currentversion-title'>Revision as of 08:22, 16 August 2024</h2> <div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><a href="/w/index.php?title=Template:WikiProject_numbers_tabs&action=edit&redlink=1" class="new" title="Template:WikiProject numbers tabs (page does not exist)">Template:WikiProject numbers tabs</a> </p> <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:NUM/G"></span></div><div class="module-shortcutboxplain noprint" role="note"><div class="module-shortcutlist"><a href="/wiki/Wikipedia:Shortcut" title="Wikipedia:Shortcut">Shortcut</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:NUM/G&redirect=no">WP:NUM/G</a></span></li></ul></div></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"><a href="/wiki/File:Essay.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Essay.svg/30px-Essay.svg.png" decoding="async" width="30" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Essay.svg/45px-Essay.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Essay.svg/60px-Essay.svg.png 2x" data-file-width="35" data-file-height="42"/></a></span></td><td class="mbox-text"><div style="padding-top: 6px; padding-bottom: 5px;"><b>This is an <a href="/wiki/Wikipedia:Essays#WikiProject_advice_pages" title="Wikipedia:Essays">essay</a> on <a href="/wiki/Wikipedia:Core_content_policies" title="Wikipedia:Core content policies">article content</a>.</b> It contains the advice and/or opinions of one or more <a href="/wiki/Wikipedia:WikiProject" title="Wikipedia:WikiProject">WikiProjects</a> on how the <a href="/wiki/Wikipedia:List_of_policies#Content" title="Wikipedia:List of policies">content policies</a> may be interpreted within their area of interest.<br/><div style="font-size: 90%;"><b><a href="/wiki/Wikipedia:WikiProject_Council/Guide#Advice_pages" title="Wikipedia:WikiProject Council/Guide">This information</a></b> is not a formal <a href="/wiki/Wikipedia:Policies_and_guidelines" title="Wikipedia:Policies and guidelines">Wikipedia policy or guideline</a>, as it has not been <a href="/wiki/Wikipedia:Local_consensus" class="mw-redirect" title="Wikipedia:Local consensus">thoroughly vetted by the community</a>.</div></div></td></tr></tbody></table> <meta property="mw:PageProp/toc"/> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="General_guidelines" data-mw-thread-id="h-General_guidelines"><span data-mw-comment-start="" id="h-General_guidelines"></span>General guidelines<span data-mw-comment-end="h-General_guidelines"></span></h2></div> <div class="mw-heading mw-heading3"><h3 id="When_should_an_article_exist?" data-mw-thread-id="h-When_should_an_article_exist?-General_guidelines"><span id="When_should_an_article_exist.3F"></span><span data-mw-comment-start="" id="h-When_should_an_article_exist?-General_guidelines"></span>When should an article exist?<span data-mw-comment-end="h-When_should_an_article_exist?-General_guidelines"></span></h3></div> <p>See <a href="/wiki/Wikipedia:Notability_(numbers)#Notability_of_specific_individual_numbers" title="Wikipedia:Notability (numbers)">Wikipedia:Notability (numbers) § Notability of specific individual numbers</a> for guidelines on when an article on a number should exist. </p><p>The sections <a href="#Assessing_mathematical_number_facts">#Assessing mathematical number facts</a> and <a href="#Assessing_content_outside_of_pure_mathematics">#Assessing content outside of pure mathematics</a> on this page have guidelines for what content should go on such articles. </p> <div class="mw-heading mw-heading3"><h3 id="Outline" data-mw-thread-id="h-Outline-General_guidelines"><span data-mw-comment-start="" id="h-Outline-General_guidelines"></span>Outline<span data-mw-comment-end="h-Outline-General_guidelines"></span></h3></div> <p>Articles can be divided into sections based on how much content there is for each area they reference. A section devoted to mathematics is common, however it is optional when there is only mathematical content present (aside from references, or external links). Mathematical content should come before content that does not deal in <a href="/wiki/Pure_mathematics" title="Pure mathematics">pure mathematics</a>, including practical uses in <a href="/wiki/Applied_mathematics" title="Applied mathematics">applied fields</a> such as science, and extending to cultural associations, and the history of symbols associated with numbers. Mathematical coverage should open with simple mathematical properties of the number, and list some simple associated properties (whether they are <a href="/wiki/Prime_number" title="Prime number">prime</a>, or not, <a href="/wiki/Abundant_number" title="Abundant number">abundant</a>, etc). Then, articles should move on to discuss deeper mathematics that is associated with the numbers, such as properties arising from being a member of specific <a href="/wiki/List_of_prime_numbers#_Lists_of_primes_by_type" title="List of prime numbers">classes of primes</a>, or properties that stem from relationships with particular <a href="/wiki/Geometric_figure" class="mw-redirect" title="Geometric figure">geometric figures</a>; any relevant mathematical history of the number as it relates to these properties is also worth covering. </p><p>The advise for assessing mathematical content specifically distinguishes between content that is simple (or basic), formulaic, and off-topic. Referencing the <i><a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">On-Line Encyclopedia of Integer Sequences</a></i> (OEIS) is largely admissible and encouraged, within limits; criteria generally follows merits of <a href="/wiki/Uniqueness_quantification" title="Uniqueness quantification">uniqueness</a> of the numbers in question within the sequences and any other relevant associated sequences. Assessing deeper connections of integers to other <a href="/wiki/Mathematical_object" title="Mathematical object">mathematical objects</a> of interest is also relevant and an important part of coverage of mathematical properties ascribed to the numbers. This guideline also emphasizes, per Wikipedia policy, that original research (inclusive of synthesis of published information) is not permitted. </p> <div class="mw-heading mw-heading3"><h3 id="Infobox" data-mw-thread-id="h-Infobox-General_guidelines"><span data-mw-comment-start="" id="h-Infobox-General_guidelines"></span>Infobox<span data-mw-comment-end="h-Infobox-General_guidelines"></span></h3></div> <table style="float: right; border-spacing: 3px; border: 1px solid darkgray; border-collapse: separate; background: #F7F8F9; margin-left: 1em; font-size:smaller;"> <caption align="top" style="caption-side: top; height:2em"><b>Example number Infobox</b> </caption> <tbody><tr style="height:1em; border-collapse: collapse"> <td colspan="2" align="center" style="font-size:130%">←<span class="nowrap"> </span><b>N − 1</b><span class="nowrap"> </span><span style="font-size:120%"><b>N</b></span><span class="nowrap"> </span><b>N + 1</b><span class="nowrap"> </span>→ </td></tr> <tr style="height:1em;"> <td colspan="2" align="center">←<span class="nowrap"> </span><i>x</i><sub>0</sub><span class="nowrap"> </span><i>x</i><sub>1</sub><span class="nowrap"> </span><i>x</i><sub>2</sub><span class="nowrap"> </span><i>x</i><sub>3</sub><span class="nowrap"> </span><i>x</i><sub>4</sub><span class="nowrap"> </span><b>N</b><span class="nowrap"> </span><i>x</i><sub>6</sub><span class="nowrap"> </span><i>x</i><sub>7</sub><span class="nowrap"> </span><i>x</i><sub>8</sub><span class="nowrap"> </span><i>x</i><sub>9</sub><span class="nowrap"> </span>→ </td></tr> <tr style="height:1em; border-collapse: collapse"> <td colspan="2" align="center"><a href="/wiki/List_of_numbers" title="List of numbers">List of numbers</a> <span style="font-size:120%">‧</span> <a href="/wiki/Integers" class="mw-redirect" title="Integers">Integers</a> </td></tr> <tr style="height:1em; border-collapse: collapse"> <td colspan="2" align="center">←<span class="nowrap"> </span><i>y</i><span class="nowrap"> </span>2<i>y</i><span class="nowrap"> </span>3<i>y</i><span class="nowrap"> </span>4<i>y</i><span class="nowrap"> </span>5<i>y</i><span class="nowrap"> </span>6<i>y</i><span class="nowrap"> </span>7<i>y</i><span class="nowrap"> </span>8<i>y</i><span class="nowrap"> </span>9<i>y</i><span class="nowrap"> </span>10<i>y</i><span class="nowrap"> </span>→ </td></tr> <tr style="height:1em"> <td> <a href="/wiki/Cardinal_number" title="Cardinal number">Cardinal</a> </td> <td><a href="/wiki/N" title="N">en</a> </td></tr> <tr style="height:1em"> <td> <a href="/wiki/Ordinal_number" title="Ordinal number">Ordinal</a> </td> <td>Nth </td></tr> <tr style="height:1em"> <td> <a href="/wiki/Factorization" title="Factorization">Factorization</a> </td> <td>1 × N (<a href="/wiki/Prime_number" title="Prime number">prime</a>) or <i>p</i><sub><i>a</i></sub> × <i>p</i><sub><i>b</i></sub> × ...<span class="nowrap"> </span> </td></tr> <tr style="height:1em"> <td> <a href="/wiki/Divisors" class="mw-redirect" title="Divisors">Divisors</a> </td> <td>1, <i>p</i><sub><i>a</i></sub>, <i>p</i><sub><i>b</i></sub>, <i>p</i><sub><i>c</i></sub>, ..., <i>p</i><sub><i>a</i></sub> × <i>p</i><sub><i>b</i></sub>, ..., N </td></tr> <tr style="height:1em"> <td> <a href="/wiki/Roman_numeral" class="mw-redirect" title="Roman numeral">Roman numeral</a> </td> <td>"N" </td></tr> <tr style="height:1em"> <td> <a href="/wiki/Binary_numeral_system" class="mw-redirect" title="Binary numeral system">Binary</a> </td> <td>"N<sub>2</sub>" </td></tr> <tr style="height:1em"> <td> ...</td> <td>... </td></tr> <tr style="height:1em"> <td> <a href="/wiki/Hexadecimal" title="Hexadecimal">Hexadecimal</a> </td> <td>"N<sub>16</sub>" </td></tr></tbody></table> <p>The Infobox — added at the top of the page using the template <span class="nowrap">{{</span><a href="/wiki/Template:Infobox_number" title="Template:Infobox number">Infobox number</a><span class="nowrap">}}</span> — should include the symbol of the number in <a href="/wiki/List_of_numeral_systems" title="List of numeral systems">all known numeral systems</a> for which <a href="/wiki/Unicode_character" class="mw-redirect" title="Unicode character">Unicode characters</a> exist, as long as it fits within a reasonable amount of space (examples include Egyptian, Roman, Tamil, Cyrillic, and Burmese; refer to the Infobox at <a href="/wiki/1" title="1">the article for 1</a> for an example with relevant <a href="/wiki/Help:Wikitext" title="Help:Wikitext">Wiki markup</a>). Divisors should be listed in the Infobox if they fit in a reasonable amount of space, as they should generally be omitted from the article prose. </p><p>These are exceptions to the usual practice of only summarizing body text in the Infobox (see <a href="/wiki/MOS:INFOBOXEXCEPTIONS" class="mw-redirect" title="MOS:INFOBOXEXCEPTIONS">MOS:INFOBOXEXCEPTIONS</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Symbolic_and_linguistic_representations" data-mw-thread-id="h-Symbolic_and_linguistic_representations-General_guidelines"><span data-mw-comment-start="" id="h-Symbolic_and_linguistic_representations-General_guidelines"></span>Symbolic and linguistic representations<span data-mw-comment-end="h-Symbolic_and_linguistic_representations-General_guidelines"></span></h3></div> <ul><li>For numbers which are also individual characters, information about <a href="/wiki/Etymology" title="Etymology">etymology</a>, history, and appearance (etc.) should remain in the articles about the specific <a href="/wiki/Numeral_system" title="Numeral system">numeral systems</a> (e.g. <a href="/wiki/Roman_numeral" class="mw-redirect" title="Roman numeral">Roman numerals</a>, <a href="/wiki/Tamil_numerals" title="Tamil numerals">Tamil numerals</a>), which should be linked from their symbols in the Infobox. An exception is made for the <a href="/wiki/English_numerals" title="English numerals">English numerals</a>, where their etymology and history of symbolic representation should be written in <a href="/wiki/Wikipedia:SUMMARY" class="mw-redirect" title="Wikipedia:SUMMARY">summary style</a> with a <span class="nowrap">{{</span><a href="/wiki/Template:Main" title="Template:Main">main</a><span class="nowrap">}}</span> template at the start of the section, e.g.: <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system" title="History of the Hindu–Arabic numeral system">History of the Hindu–Arabic numeral system</a></div></li> <li>Translations (of which there are a huge number) should be defered to Wiktionary. Check that there is a link (produced with <code><span class="nowrap">{{</span><a href="/wiki/Template:Wiktionary" title="Template:Wiktionary">wiktionary</a><span class="nowrap">}}</span></code>) in the "See also" section or lower (for numbers where a Wiktionary entry exists; numeral preferred - e.g. <a href="https://en.wiktionary.org/wiki/1" class="extiw" title="wikt:1">wikt:1</a> - but word or words if needed - e.g. <a href="https://en.wiktionary.org/wiki/one_million" class="extiw" title="wikt:one million">wikt:one million</a>).</li> <li>Explanation about how to construct number names in words to the articles <a href="/wiki/Cardinal_numeral" title="Cardinal numeral">Cardinal numeral</a> and <a href="/wiki/Ordinal_numeral" title="Ordinal numeral">Ordinal numeral</a> should not be specified either; these are automatically linked from the Infobox. (These cover all languages, so language-specific details are further deferred to articles like <a href="/wiki/English_numerals" title="English numerals">English numerals</a>.)</li></ul> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Assessing_mathematical_number_facts" data-mw-thread-id="h-Assessing_mathematical_number_facts"><span data-mw-comment-start="" id="h-Assessing_mathematical_number_facts"></span>Assessing mathematical number facts<span data-mw-comment-end="h-Assessing_mathematical_number_facts"></span></h2></div> <p>The purpose of number articles is to provide a broad overview of a number's history, mathematical, scientific, or cultural properties and uses, without going into excessive detail (see <a href="/wiki/Wikipedia:Summary" class="mw-redirect" title="Wikipedia:Summary">WP:Summary</a>). While there is an endless array of true mathematical facts about a given number, not all of them are appropriate for inclusion. This section provides several criteria for assessing the suitability of a mathematical number fact. </p> <div class="mw-heading mw-heading3"><h3 id="Simple_facts" data-mw-thread-id="h-Simple_facts-Assessing_mathematical_number_facts"><span data-mw-comment-start="" id="h-Simple_facts-Assessing_mathematical_number_facts"></span>Simple facts<span data-mw-comment-end="h-Simple_facts-Assessing_mathematical_number_facts"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/SIMPLE"></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:NUM/SIMPLE&redirect=no">WP:NUM/SIMPLE</a></span></li></ul></div></div> <p>Simple facts are helpful, easily understood details about a number. They do not have to be sourced and should be included in a number article, although they are usually not sufficient reason to justify the existence of an article on their own. This criterion should be applied sparingly. A good <a href="/wiki/Rule_of_thumb" title="Rule of thumb">rule of thumb</a> is: "Would someone with no background in mathematics be expected to know this?". </p><p><b>Examples of <i>simple facts</i>:</b> </p> <ul><li>On <a href="/wiki/1729_(number)" title="1729 (number)">1729</a>: 1729 is the natural number following 1728 and preceding 1730.</li> <li>On <a href="/wiki/1729_(number)" title="1729 (number)">1729</a>: 1729 is a composite number with factors 1, 7, 13, 19, 91, 133, 247, and 1729.</li></ul> <p><b>Examples that <i>are not</i> simple facts:</b> </p> <ul><li>On <a href="/wiki/9" title="9">9</a>: "The <a href="/wiki/Aliquot_sum" title="Aliquot sum">aliquot sum</a> of 9 is 4".</li> <li>On <a href="/wiki/11_(number)" title="11 (number)">11</a>: The rows of Pascal's triangle can be seen as representations of the powers of 11.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Formulaic_facts" data-mw-thread-id="h-Formulaic_facts-Assessing_mathematical_number_facts"><span data-mw-comment-start="" id="h-Formulaic_facts-Assessing_mathematical_number_facts"></span>Formulaic facts<span data-mw-comment-end="h-Formulaic_facts-Assessing_mathematical_number_facts"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/FORMULA"></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:NUM/FORMULA&redirect=no">WP:NUM/FORMULA</a></span></li></ul></div></div> <p>Facts for <a href="/wiki/Integer" title="Integer">integers</a> upon a slight modification of a <a href="/wiki/Expression_(mathematics)#Formal_definition" title="Expression (mathematics)">mathematical expression</a> are <a href="/wiki/Formula" title="Formula">formulaic</a> in nature. Their suitability in an article depends on the complexity and usefulness of the <a href="/wiki/Expression_(mathematics)#Formal_definition" title="Expression (mathematics)">mathematical expressions</a> of the facts derived from formulae, as well as the meaningful consequences generated by said relationships vis-à-vis the numbers (either as <a href="/wiki/Equality_(mathematics)" title="Equality (mathematics)">equalities</a>, or in proportion there-of, which attribute special <a href="/wiki/Property_(mathematics)" title="Property (mathematics)">properties</a>). These expressions include <a href="/wiki/Algebraic_formula" class="mw-redirect" title="Algebraic formula">algebraic formulae</a>, or expressions using <a href="/wiki/Recursion" title="Recursion">recursive methods</a>, as well as expressions that involve <a href="/wiki/Modular_arithmetic" title="Modular arithmetic">modular arithmetic</a>. Significance of the defining mathematical expressions that generate these facts need to have been covered separately by primary and secondary sources, to be of interest. </p><p>The first few non-trivial elements of an integer sequence generated from formulaic mathematical expressions should be included and, for finite sequences, the last element should be included as well. Integer entries from a large sequence that are not the of the first few or the last entries should generally not be included unless the specific number it is covered in depth by the mathematical literature. Ideally, the specific integer entry being referenced should have applications in an <a href="/wiki/List_of_unsolved_problems_in_mathematics" title="List of unsolved problems in mathematics">unsolved</a> or important solved problem in mathematics. </p><p><b>Examples that are formulaic:</b> </p> <ul><li>On <a href="/wiki/5" title="5">5</a>: "5 is the third <a href="/wiki/Odd_number" class="mw-redirect" title="Odd number">odd number</a>."</li> <li>On <a href="/wiki/5" title="5">5</a>: "5 is the first <a href="/wiki/Pentagonal_number" title="Pentagonal number">pentagonal number</a> after 1."</li> <li>On <a href="/wiki/1729_(number)" title="1729 (number)">1729</a>: "It is the tenth <a href="/wiki/Centered_cube_number" title="Centered cube number">centered cube number</a>, the nineteenth <a href="/wiki/Dodecagonal_number" title="Dodecagonal number">dodecagonal number</a>, the thirteenth 24-<a href="/wiki/Polygonal_number" title="Polygonal number">gonal</a> and the seventh 84-gonal number."</li> <li>On <a href="/wiki/744_(number)" title="744 (number)">744</a>: "The number partitions of the square of seven (49) into prime parts is 744."</li></ul> <p><b>Examples that are non-formulaic:</b> </p> <ul><li>On <a href="/wiki/3" title="3">3</a>: "3 is the first odd <a href="/wiki/Prime" class="mw-redirect" title="Prime">prime</a>".</li> <li>On <a href="/wiki/19_(number)" title="19 (number)">19</a>: "19 forms a <a href="/wiki/Twin_prime" title="Twin prime">twin prime</a> with 17, a <a href="/wiki/Cousin_prime" title="Cousin prime">cousin prime</a> with 23, and a <a href="/wiki/Sexy_prime" title="Sexy prime">sexy prime</a> with 13".</li> <li>On <a href="/wiki/11_(number)" title="11 (number)">11</a>: "11 is the first prime exponent that does not yield a <a href="/wiki/Mersenne_prime" title="Mersenne prime">Mersenne prime</a>, where <span class="mwe-math-element"><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^{11}-1=2047}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo>=</mo> <mn>2047</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{11}-1=2047}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d33f462833ff6b8d2b868071d286a28ed6fb0fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:14.79ex; height:2.843ex;" alt="{\displaystyle 2^{11}-1=2047}"/></span>, which is composite."</li> <li>On <a href="/wiki/42_(number)" title="42 (number)">42</a>: The 1806th <a href="/wiki/Bernoulli_number" title="Bernoulli number">Bernoulli number</a> is the only Bernoulli number whose <a href="/wiki/Denominator" class="mw-redirect" title="Denominator">denominator</a> is the same as its index (1806) in the sequence of Bernoulli numbers.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Off-topic_facts" data-mw-thread-id="h-Off-topic_facts-Assessing_mathematical_number_facts"><span data-mw-comment-start="" id="h-Off-topic_facts-Assessing_mathematical_number_facts"></span>Off-topic facts<span data-mw-comment-end="h-Off-topic_facts-Assessing_mathematical_number_facts"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/OFFTOPIC"></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:NUM/OFFTOPIC&redirect=no">WP:NUM/OFFTOPIC</a></span></li></ul></div></div> <p>Off-topic facts are details which do not have a direct or substantial connection to the number <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"/></span> itself. Content on a page for number <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"/></span> should focus primarily on that specific number and not about another number or topic, even if they are related 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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"/></span>. Including such facts dilutes the focus of the content and can be confusing for readers. </p><p><b>Examples of Off-topic facts:</b> </p> <ul><li>On <a href="/wiki/5" title="5">5</a>: "The factorial of five, 5! = 120, which is multiply perfect".</li> <li>On <a href="/wiki/5" title="5">5</a>: "A magic constant of 505 is generated by a 10 × 10 normal magic square". (The only connection here being that 505 contains two 5s.)</li> <li>On <a href="/wiki/744_(number)" title="744 (number)">744</a>: "The twentieth prime number is 71, where 31 is the eleventh; in turn, 20 is the eleventh composite number that is also the sixth self-convolution of Fibonacci numbers before 38, which is the prime index of 163."</li></ul> <p><b>Examples of On-topic facts:</b> </p> <ul><li>On <a href="/wiki/5" title="5">5</a>: "5 is the first of the three known <a href="/wiki/Wilson_primes" class="mw-redirect" title="Wilson primes">Wilson primes</a> 5, 13, 563".</li> <li>On <a href="/wiki/9" title="9">9</a>: "The <a href="/wiki/Aliquot_sum" title="Aliquot sum">aliquot sum</a> of 9 is 4".</li> <li>On <a href="/wiki/19_(number)" title="19 (number)">19</a>: "19 forms a <a href="/wiki/Twin_prime" title="Twin prime">twin prime</a> with 17, a <a href="/wiki/Cousin_prime" title="Cousin prime">cousin prime</a> with 23, and a <a href="/wiki/Sexy_prime" title="Sexy prime">sexy prime</a> with 13".</li> <li>On <a href="/wiki/11_(number)" title="11 (number)">11</a>: The rows of Pascal's triangle can be seen as representation of the powers of 11.</li></ul> <p>Note that even if a fact is on-topic, it may still not be interesting enough, too routine, or lack sufficient verification from reliable sources for inclusion in the article. </p> <div class="mw-heading mw-heading3"><h3 id="Connection" data-mw-thread-id="h-Connection-Assessing_mathematical_number_facts"><span data-mw-comment-start="" id="h-Connection-Assessing_mathematical_number_facts"></span>Connection<span data-mw-comment-end="h-Connection-Assessing_mathematical_number_facts"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/CONNECTION"></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:NUM/CONNECTION&redirect=no">WP:NUM/CONNECTION</a></span></li></ul></div></div> <p>The existence of a connection between a number and an important or prominent object is usually acceptable. </p><p>Examples that are a connection to an important object: </p> <ul><li>On <a href="/wiki/5" title="5">5</a>: "In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: <span class="texhtml"><i>K</i><sub>5</sub></span>, the complete graph with five vertices, where every pair of distinct vertices in a pentagon is joined by unique edges belonging to a pentagram."</li> <li>On <a href="/wiki/9" title="9">9</a>: "A polygon with nine sides is called a <a href="/wiki/Nonagon" title="Nonagon">nonagon</a>".</li></ul> <div class="mw-heading mw-heading3"><h3 id="No_Wikipedia_page" data-mw-thread-id="h-No_Wikipedia_page-Assessing_mathematical_number_facts"><span data-mw-comment-start="" id="h-No_Wikipedia_page-Assessing_mathematical_number_facts"></span>No Wikipedia page<span data-mw-comment-end="h-No_Wikipedia_page-Assessing_mathematical_number_facts"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/NOPAGE"></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:NUM/NOPAGE&redirect=no">WP:NUM/NOPAGE</a></span></li></ul></div></div> <p>If a property is not important enough to have a Wikipedia page, it probably isn't important that the number in question satisfies it. This does not necessarily mean that if a property does have a Wikipedia page, it should automatically be included. </p> <div class="mw-heading mw-heading3"><h3 id="OEIS" data-mw-thread-id="h-OEIS-Assessing_mathematical_number_facts"><span data-mw-comment-start="" id="h-OEIS-Assessing_mathematical_number_facts"></span>OEIS<span data-mw-comment-end="h-OEIS-Assessing_mathematical_number_facts"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/OEIS"></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:NUM/OEIS&redirect=no">WP:NUM/OEIS</a></span></li></ul></div></div> <p><a href="/wiki/OEIS" class="mw-redirect" title="OEIS">OEIS</a> is considered a reliable source. However, a mathematical fact appearing in <a href="/wiki/OEIS" class="mw-redirect" title="OEIS">OEIS</a> is not <i>by itself</i> a good reason to include it in a Wikipedia article. OEIS has hundreds of thousands of sequences, most of which do not belong on Wikipedia. If an OEIS sequence has almost no mentions outside of OEIS, the number <span class="texhtml"><i>N</i></span> being part of that sequence shouldn't be on the page for <span class="texhtml"><i>N</i></span>. If <span class="texhtml"><i>N</i></span> is a member of an OEIS sequence that is discussed in sources other than OEIS, this rule does not disqualify <span class="texhtml"><i>N</i></span> being a member of that sequence from inclusion on the page for <span class="texhtml"><i>N</i></span>. </p> <div class="mw-heading mw-heading3"><h3 id="No_original_research_and_no_synthesis" data-mw-thread-id="h-No_original_research_and_no_synthesis-Assessing_mathematical_number_facts"><span data-mw-comment-start="" id="h-No_original_research_and_no_synthesis-Assessing_mathematical_number_facts"></span>No original research and no synthesis<span data-mw-comment-end="h-No_original_research_and_no_synthesis-Assessing_mathematical_number_facts"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/ORSYNTH"></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:NUM/ORSYNTH&redirect=no">WP:NUM/ORSYNTH</a></span></li></ul></div></div> <p>Violations of <a href="/wiki/Wikipedia:OR" class="mw-redirect" title="Wikipedia:OR">WP:OR</a> and <a href="/wiki/Wikipedia:SYNTH" class="mw-redirect" title="Wikipedia:SYNTH">WP:SYNTH</a> should be removed even if they pass all of the previous tests. Most facts need to be stated in a <a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">reliable source</a>, external to Wikipedia, prior to inclusion. </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Assessing_content_outside_of_pure_mathematics" data-mw-thread-id="h-Assessing_content_outside_of_pure_mathematics"><span data-mw-comment-start="" id="h-Assessing_content_outside_of_pure_mathematics"></span>Assessing content outside of pure mathematics<span data-mw-comment-end="h-Assessing_content_outside_of_pure_mathematics"></span></h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/OTHER"></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:NUM/OTHER&redirect=no">WP:NUM/OTHER</a></span></li></ul></div></div> <p>It is preferable to have a stub article than to pad an article with trivial or tenuously related information. Normal Wikipedia policies, and guidelines, should be considered when choosing which content to include. Specifically, this also applies to scientific and other associations in fields benefiting from <a href="/wiki/Applied_mathematics" title="Applied mathematics">applications of mathematical knowledge</a>, and as such they must also be <a href="/wiki/Wikipedia:V" class="mw-redirect" title="Wikipedia:V">verifiable</a>, and covered with <a href="/wiki/Wikipedia:WEIGHT" class="mw-redirect" title="Wikipedia:WEIGHT">due weight</a>. </p><p>Aside from WP:DUE and WP:UNDUE content as described in sections above for mathematics-specific content, metrics for information that is due and not strictly dealing in <a href="/wiki/Pure_mathematics" title="Pure mathematics">pure mathematics</a>, yet is either <a href="/wiki/Applied_mathematics" title="Applied mathematics">applied mathematics</a> or regarding specific associations that are philosophical, cultural, or from other specific traditional uses in <a href="/wiki/Society" title="Society">society</a>, can be outlined. </p> <div class="mw-heading mw-heading3"><h3 id="Applied_mathematics" data-mw-thread-id="h-Applied_mathematics-Assessing_content_outside_of_pure_mathematics"><span data-mw-comment-start="" id="h-Applied_mathematics-Assessing_content_outside_of_pure_mathematics"></span>Applied mathematics<span data-mw-comment-end="h-Applied_mathematics-Assessing_content_outside_of_pure_mathematics"></span></h3></div> <p>A scientific notion referenced in a number article depends on the mathematics of its properties and characteristics, and how substantial they are, as aforementioned. Examples include: </p> <ul><li>a statement such as, <i>there is theoretical and empirical evidence to suggest that brain computation is organized via power-of-two-based permutation logic</i>,</li> <li><i>three soap films meet along a <a href="/wiki/Plateau%27s_laws" title="Plateau's laws">Plateau border</a> at <a href="/wiki/120_(number)" title="120 (number)">120</a> degree angles</i>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Philosophy_and_symbolism" data-mw-thread-id="h-Philosophy_and_symbolism-Assessing_content_outside_of_pure_mathematics"><span data-mw-comment-start="" id="h-Philosophy_and_symbolism-Assessing_content_outside_of_pure_mathematics"></span>Philosophy and symbolism<span data-mw-comment-end="h-Philosophy_and_symbolism-Assessing_content_outside_of_pure_mathematics"></span></h3></div> <p><a href="/wiki/Symbology" class="mw-redirect" title="Symbology">Symbolism</a> in lucky or unlucky numbers (as a form of <a href="/wiki/Numerology" title="Numerology">numerology</a>) can be included, such as a direct reference to mathematical properties of the number, even if mystical (i.e. <a href="/wiki/Plotinus#The_One" title="Plotinus">The One</a> in the philosophy of <a href="/wiki/Neoplatonism" title="Neoplatonism">neoplatonism</a>), or by popular association (including associations with numerals only); for example, the number <a href="/wiki/666_(number)" title="666 (number)">666</a> as the <a href="/wiki/Number_of_the_beast" title="Number of the beast">number of the beast</a>. Per <a href="/wiki/Wikipedia:FRINGE" class="mw-redirect" title="Wikipedia:FRINGE">WP:FRINGE</a>, all such examples need reliable mainstream sourcing. </p> <div class="mw-heading mw-heading3"><h3 id="What_not_to_include" data-mw-thread-id="h-What_not_to_include-Assessing_content_outside_of_pure_mathematics"><span data-mw-comment-start="" id="h-What_not_to_include-Assessing_content_outside_of_pure_mathematics"></span>What not to include<span data-mw-comment-end="h-What_not_to_include-Assessing_content_outside_of_pure_mathematics"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/NOT"></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:NUM/NOT&redirect=no">WP:NUM/NOT</a></span></li></ul></div></div> <p><b>Do not include</b> content that relates to the article's title only as an <a href="/wiki/Identifier" title="Identifier">identifier</a>, or label, or simple enumeration, or measurement, or as a trivial mention. This includes: </p> <ul><li><a href="/wiki/Telephone_number" title="Telephone number">telephone number</a> calling codes,</li> <li><a href="/wiki/Route_number" title="Route number">route or road numbers</a>, <a href="/wiki/Bus_route" class="mw-redirect" title="Bus route">bus routes</a>,</li> <li><a href="/wiki/Firearm" title="Firearm">firearms</a> (i.e. <a href="/wiki/Glock" title="Glock">Glock 17</a>),</li> <li>military and transportation classes of <a href="/wiki/Vehicle" title="Vehicle">vehicles</a>, <a href="/wiki/Aircraft" title="Aircraft">aircraft</a>, or otherwise,</li> <li>album titles or song titles that include a numeral</li> <li>book titles (except for when they deal directly with mathematics),</li> <li><a href="/wiki/Jersey_(clothing)#In_sports" class="mw-redirect" title="Jersey (clothing)">sports jerseys</a> (identified with numbers, or letters and numbers), NASCAR car numbers, etc.,</li> <li><a href="/wiki/World_record" title="World record">world records</a> of any sort, aside from records that could be of cultural interest in mathematics, such as enumerating digits of <a href="/wiki/Pi" title="Pi">pi</a> by memory, etc.,</li> <li>marketed items, such as <a href="/wiki/Bubble_gum" title="Bubble gum">bubble gum</a> <i>5</i>,</li></ul> <p>or any other concept or item that is not directly related to the number itself (in this case, only its numeral is being referenced). If there is plausible ambiguity between the number and another use of the numeral, they should be mentioned on a <a href="/wiki/Wikipedia:Disambiguation" title="Wikipedia:Disambiguation">disambiguation page</a> for the number. If necessary, a <a href="/wiki/Wikipedia:Hatnote" title="Wikipedia:Hatnote">hatnote</a> can be added at the top of the article to link to another article for disambiguation. This enables the article to remain focused on content specifically related to the number. </p><p><b>Examples of items to not include</b>: </p> <ul><li><a href="/wiki/Route_66" class="mw-redirect" title="Route 66">Route 66</a> which does not have a significant relationship with the <i>number</i> 66 - rather, the "66" is an identification code.</li> <li><a href="/wiki/86_(novel_series)" title="86 (novel series)">86 (novel series)</a> is not about the <i>number</i> 86.</li> <li>The 35 in <a href="/wiki/35_mm_film" class="mw-redirect mw-disambig" title="35 mm film">35 mm film</a> is a measurement, not a property of, or reference to, the number 35.</li> <li>The 9 in <a href="/wiki/ISO_9" title="ISO 9">ISO 9</a> is a simple enumeration of a series of items, with no significant relationship with the number 9.</li> <li>The centre-forward in <a href="/wiki/Association_football" title="Association football">association football</a> wearing the number 9 shirt is a trivial mention of the number 9.</li></ul> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Editing_practice" data-mw-thread-id="h-Editing_practice"><span data-mw-comment-start="" id="h-Editing_practice"></span>Editing practice<span data-mw-comment-end="h-Editing_practice"></span></h2></div> <div class="mw-heading mw-heading3"><h3 id="Naming_compliance" data-mw-thread-id="h-Naming_compliance-Editing_practice"><span data-mw-comment-start="" id="h-Naming_compliance-Editing_practice"></span>Naming compliance<span data-mw-comment-end="h-Naming_compliance-Editing_practice"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/NAME"></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:NUM/NAME&redirect=no">WP:NUM/NAME</a></span></li></ul></div></div> <p>For most cases, articles should be named <b>N (number)</b>, with the literal spelling of the numbers redirected accordingly (e.g., <a href="/wiki/Four_hundred_and_ninety-six" class="mw-redirect" title="Four hundred and ninety-six">Four hundred and ninety-six</a> redirects to <a href="/wiki/496_(number)" title="496 (number)">496 (number)</a>). </p><p>Numbers deserving their own article that are greater than 999, should have the article title written in digits without any separators between the digits of the integer part. Writing the number with separators may of course be acknowledged in the body of the article. Thus, the article on the <a href="/wiki/Taxicab_number" title="Taxicab number">taxicab number</a> 1,729 should be <a href="/wiki/1729_(number)" title="1729 (number)">1729 (number)</a>, though the article can mention that the number may be written "1,729" or "1.729." </p><p>Besides <a href="/wiki/%E2%88%921" title="−1">−1</a>, there are <i>no articles on negative integers</i>. Adding information about a negative number therefore can fall under articles representative of numbers' positive, absolute values. <a href="/wiki/One_half" title="One half">One half</a> is the chosen article name for <b><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><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span></b>. </p> <div class="mw-heading mw-heading3"><h3 id="Referencing" data-mw-thread-id="h-Referencing-Editing_practice"><span data-mw-comment-start="" id="h-Referencing-Editing_practice"></span>Referencing<span data-mw-comment-end="h-Referencing-Editing_practice"></span></h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1252059228"><div class="module-shortcutanchordiv"><span id="WP:NUM/REF"></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:NUM/REF&redirect=no">WP:NUM/REF</a></span></li></ul></div></div> <p>Just as with any information in Wikipedia, articles on numbers need to cite sources. (See <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">Wikipedia:Citing sources</a> for general information on citing sources.) Some statements that are easily verified with a pocket calculator <a href="/wiki/Wikipedia:CALC" class="mw-redirect" title="Wikipedia:CALC">might not need citations</a> (e.g., the fact that 2×3 = 6), but anything slightly more difficult to verify does. It is acceptable for a number article to have few citations if the articles to which it links have primary and secondary sourcing. For example, to avoid footnote overkill, an article about a number <i>p</i> that is a certain type of prime does not need citations to background reading about that type of prime. </p><p>It is not the place of this project to prescribe a citation format. Until Wikipedia decides on a uniform citation format, number articles may use whatever citation format would be acceptable in a mathematics journal. <a href="/wiki/Wikipedia:CITEVAR" class="mw-redirect" title="Wikipedia:CITEVAR">Consistency within an article is generally preferred</a>. </p><p>Web versions of respected professional journals are reliable sources. On the other hand, preprints on the <a href="/wiki/ArXiv" title="ArXiv">arXiv</a> that have not been peer-reviewed are generally unsuitable for our purposes. The <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">On-Line Encyclopedia of Integer Sequences</a> should be used with care: it is curated by experts and generally accurate, but it is by design rather indiscriminate about what it includes. From the standpoint of serious mathematical literature, some OEIS entries are mere curiosities. Those that are more noteworthy will include references into the literature that include more substantial discussions; consider supplementing citations to the OEIS with direct pointers to the peer-reviewed papers that it cites. <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a> has a history of being less than reliable, for example by including neologisms that have not become accepted mathematical terminology. It should be avoided. </p> <div class="mw-heading mw-heading3"><h3 id="Edit_summaries" data-mw-thread-id="h-Edit_summaries-Editing_practice"><span data-mw-comment-start="" id="h-Edit_summaries-Editing_practice"></span>Edit summaries<span data-mw-comment-end="h-Edit_summaries-Editing_practice"></span></h3></div> <p>Every project member (indeed anyone who edits Wikipedia) is encouraged to write brief but complete edit summaries. Please refer to <a href="/wiki/Wikipedia:Edit_summary" class="mw-redirect" title="Wikipedia:Edit summary">Wikipedia:Edit summary</a> for a guide on writing good edit summaries. </p></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" 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=Wikipedia:WikiProject_Numbers/Guidelines&oldid=1240601872">https://en.wikipedia.org/w/index.php?title=Wikipedia:WikiProject_Numbers/Guidelines&oldid=1240601872</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">Category</a>: <ul><li><a href="/wiki/Category:WikiProject_content_advice" title="Category:WikiProject content advice">WikiProject content advice</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 16 August 2024, at 08:22<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright"><span class="nowraplinks">This version of the page has been <a href="/wiki/Help:Page_history" title="Help:Page history">revised</a>. 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