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data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Beginning</div> </a> </li> <li id="toc-Infinity_in_Mathematics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Infinity_in_Mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Infinity in Mathematics</span> </div> </a> <button aria-controls="toc-Infinity_in_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 Infinity in Mathematics subsection</span> </button> <ul id="toc-Infinity_in_Mathematics-sublist" class="vector-toc-list"> <li id="toc-Counting_infinity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Counting_infinity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Counting infinity</span> </div> </a> <ul id="toc-Counting_infinity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ordering_infinity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ordering_infinity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Ordering infinity</span> </div> </a> <ul id="toc-Ordering_infinity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_real_line_and_complex_plane" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_real_line_and_complex_plane"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>The real line and complex plane</span> </div> </a> <ul id="toc-The_real_line_and_complex_plane-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-The_arithmetic_of_infinity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#The_arithmetic_of_infinity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>The arithmetic of infinity</span> </div> </a> <button aria-controls="toc-The_arithmetic_of_infinity-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 The arithmetic of infinity subsection</span> </button> <ul id="toc-The_arithmetic_of_infinity-sublist" class="vector-toc-list"> <li id="toc-Addition,_multiplication,_exponentiation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Addition,_multiplication,_exponentiation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Addition, multiplication, exponentiation</span> </div> </a> <ul id="toc-Addition,_multiplication,_exponentiation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Subtraction,_division" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Subtraction,_division"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Subtraction, division</span> </div> </a> <ul id="toc-Subtraction,_division-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Related_pages" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_pages"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Related pages</span> </div> </a> <ul id="toc-Related_pages-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_websites" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_websites"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Other websites</span> </div> </a> <ul id="toc-Other_websites-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 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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Infinity</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 112 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-112" 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">112 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Oneindigheid" title="Oneindigheid – Afrikaans" lang="af" hreflang="af" data-title="Oneindigheid" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Unendlichkeit" title="Unendlichkeit – Alemannic" lang="gsw" hreflang="gsw" data-title="Unendlichkeit" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%8B%95%E1%88%8B%E1%8D%8D" title="አዕላፍ – Amharic" lang="am" hreflang="am" data-title="አዕላፍ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%84%D8%A7%D9%86%D9%87%D8%A7%D9%8A%D8%A9" title="لانهاية – Arabic" lang="ar" hreflang="ar" data-title="لانهاية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Infinito" title="Infinito – Aragonese" lang="an" hreflang="an" data-title="Infinito" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%85%E0%A6%B8%E0%A7%80%E0%A6%AE" title="অসীম – Assamese" lang="as" hreflang="as" data-title="অসীম" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Infinitu" title="Infinitu – Asturian" lang="ast" hreflang="ast" data-title="Infinitu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sonsuzluq" title="Sonsuzluq – Azerbaijani" lang="az" hreflang="az" data-title="Sonsuzluq" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B3%D9%88%D9%86%D8%B3%D9%88%D8%B2" title="سونسوز – South Azerbaijani" lang="azb" hreflang="azb" data-title="سونسوز" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%B8%E0%A7%80%E0%A6%AE" title="অসীম – Bangla" lang="bn" hreflang="bn" data-title="অসীম" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/Infinity" title="Infinity – Banjar" lang="bjn" hreflang="bjn" data-title="Infinity" data-language-autonym="Banjar" data-language-local-name="Banjar" class="interlanguage-link-target"><span>Banjar</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/B%C3%BB-h%C4%81n" title="Bû-hān – Minnan" lang="nan" hreflang="nan" data-title="Bû-hān" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D0%B8%D0%BA%D2%BB%D0%B5%D2%99%D0%BB%D0%B5%D0%BA" title="Сикһеҙлек – Bashkir" lang="ba" hreflang="ba" data-title="Сикһеҙлек" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%B0%D0%BD%D0%B5%D1%87%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Бесканечнасць – Belarusian" lang="be" hreflang="be" data-title="Бесканечнасць" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%91%D1%8F%D1%81%D0%BA%D0%BE%D0%BD%D1%86%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Бясконцасьць – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Бясконцасьць" 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%91%D0%B5%D0%B7%D0%BA%D1%80%D0%B0%D0%B9%D0%BD%D0%BE%D1%81%D1%82" title="Безкрайност – Bulgarian" lang="bg" hreflang="bg" data-title="Безкрайност" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Beskona%C4%8Dnost" title="Beskonačnost – Bosnian" lang="bs" hreflang="bs" data-title="Beskonačnost" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Infinit" title="Infinit – Catalan" lang="ca" hreflang="ca" data-title="Infinit" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%92%C4%95%C3%A7%D1%81%C4%95%D1%80%D0%BB%C4%95%D1%85" title="Вĕçсĕрлĕх – Chuvash" lang="cv" hreflang="cv" data-title="Вĕçсĕрлĕх" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Nekone%C4%8Dno" title="Nekonečno – Czech" lang="cs" hreflang="cs" data-title="Nekonečno" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Kusingaperi" title="Kusingaperi – Shona" lang="sn" hreflang="sn" data-title="Kusingaperi" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Infinitu" title="Infinitu – Corsican" lang="co" hreflang="co" data-title="Infinitu" data-language-autonym="Corsu" data-language-local-name="Corsican" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Anfeidredd" title="Anfeidredd – Welsh" lang="cy" hreflang="cy" data-title="Anfeidredd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Uendelighed" title="Uendelighed – Danish" lang="da" hreflang="da" data-title="Uendelighed" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%84%D8%A7%D9%85%D8%B3%D8%A7%D9%84%D9%8A%D8%A9" title="لامسالية – Moroccan Arabic" lang="ary" hreflang="ary" data-title="لامسالية" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Unendlich_(Mathematik)" title="Unendlich (Mathematik) – German" lang="de" hreflang="de" data-title="Unendlich (Mathematik)" 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/L%C3%B5pmatus" title="Lõpmatus – Estonian" lang="et" hreflang="et" data-title="Lõpmatus" 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%86%CF%80%CE%B5%CE%B9%CF%81%CE%BF" title="Άπειρο – Greek" lang="el" hreflang="el" data-title="Άπειρο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Infinity" title="Infinity – English" lang="en" hreflang="en" data-title="Infinity" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Infinito" title="Infinito – Spanish" lang="es" hreflang="es" data-title="Infinito" 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/Senfineco" title="Senfineco – Esperanto" lang="eo" hreflang="eo" data-title="Senfineco" 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/Infinitu" title="Infinitu – Basque" lang="eu" hreflang="eu" data-title="Infinitu" 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%A8%DB%8C%E2%80%8C%D9%86%D9%87%D8%A7%DB%8C%D8%AA" title="بی‌نهایت – Persian" lang="fa" hreflang="fa" data-title="بی‌نهایت" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Anant" title="Anant – Fiji Hindi" lang="hif" hreflang="hif" data-title="Anant" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Infini" title="Infini – French" lang="fr" hreflang="fr" data-title="Infini" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/%C3%89igr%C3%ADoch" title="Éigríoch – Irish" lang="ga" hreflang="ga" data-title="Éigríoch" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Infinito" title="Infinito – Galician" lang="gl" hreflang="gl" data-title="Infinito" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%84%A1%E9%99%90" title="無限 – Gan" lang="gan" hreflang="gan" data-title="無限" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%85%E0%AA%A8%E0%AA%82%E0%AA%A4" title="અનંત – Gujarati" lang="gu" hreflang="gu" data-title="અનંત" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AC%B4%ED%95%9C" title="무한 – Korean" lang="ko" hreflang="ko" data-title="무한" 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/%D4%B1%D5%B6%D5%BE%D5%A5%D6%80%D5%BB%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6_(%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1)" title="Անվերջություն (մաթեմատիկա) – Armenian" lang="hy" hreflang="hy" data-title="Անվերջություն (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A4%82%E0%A4%A4" title="अनंत – Hindi" lang="hi" hreflang="hi" data-title="अनंत" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Beskona%C4%8Dnost" title="Beskonačnost – Croatian" lang="hr" hreflang="hr" data-title="Beskonačnost" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Awan_inggana" title="Awan inggana – Iloko" lang="ilo" hreflang="ilo" data-title="Awan inggana" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Takhingga" title="Takhingga – Indonesian" lang="id" hreflang="id" data-title="Takhingga" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%93endanleiki" title="Óendanleiki – Icelandic" lang="is" hreflang="is" data-title="Óendanleiki" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Infinito_(matematica)" title="Infinito (matematica) – Italian" lang="it" hreflang="it" data-title="Infinito (matematica)" 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%90%D7%99%D7%A0%D7%A1%D7%95%D7%A3" title="אינסוף – Hebrew" lang="he" hreflang="he" data-title="אינסוף" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%A8%E0%B2%82%E0%B2%A4" title="ಅನಂತ – Kannada" lang="kn" hreflang="kn" data-title="ಅನಂತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A3%E1%83%A1%E1%83%90%E1%83%A1%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%9D%E1%83%91%E1%83%90" title="უსასრულობა – Georgian" lang="ka" hreflang="ka" data-title="უსასრულობა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A8%D0%B5%D0%BA%D1%81%D1%96%D0%B7%D0%B4%D1%96%D0%BA" title="Шексіздік – Kazakh" lang="kk" hreflang="kk" data-title="Шексіздік" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Didhiwedhter" title="Didhiwedhter – Cornish" lang="kw" hreflang="kw" data-title="Didhiwedhter" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Enfini" title="Enfini – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Enfini" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/B%C3%AAdaw%C3%AE" title="Bêdawî – Kurdish" lang="ku" hreflang="ku" data-title="Bêdawî" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A7%D0%B5%D0%BA%D1%81%D0%B8%D0%B7%D0%B4%D0%B8%D0%BA" title="Чексиздик – Kyrgyz" lang="ky" hreflang="ky" data-title="Чексиздик" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://la.wikipedia.org/wiki/Infinitas" title="Infinitas – Latin" lang="la" hreflang="la" data-title="Infinitas" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bezgal%C4%ABba" title="Bezgalība – Latvian" lang="lv" hreflang="lv" data-title="Bezgalība" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Begalyb%C4%97" title="Begalybė – Lithuanian" lang="lt" hreflang="lt" data-title="Begalybė" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/li_ci%27i" title="li ci'i – Lojban" lang="jbo" hreflang="jbo" data-title="li ci'i" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/V%C3%A9gtelen" title="Végtelen – Hungarian" lang="hu" hreflang="hu" data-title="Végtelen" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Бесконечност – Macedonian" lang="mk" hreflang="mk" data-title="Бесконечност" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tsiefa" title="Tsiefa – Malagasy" lang="mg" hreflang="mg" data-title="Tsiefa" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%A8%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%A4" title="അനന്തത – Malayalam" lang="ml" hreflang="ml" data-title="അനന്തത" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A4%82%E0%A4%A4" title="अनंत – Marathi" lang="mr" hreflang="mr" data-title="अनंत" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D9%84%D9%87%D8%A7%D8%B4_%D9%86%D9%87%D8%A7%D9%8A%D9%87" title="ملهاش نهايه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ملهاش نهايه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ketakterhinggaan" title="Ketakterhinggaan – Malay" lang="ms" hreflang="ms" data-title="Ketakterhinggaan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D1%8F%D0%B7%D0%B3%D0%B0%D0%B0%D1%80%D0%B3%D2%AF%D0%B9" title="Хязгааргүй – Mongolian" lang="mn" hreflang="mn" data-title="Хязгааргүй" 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%94%E1%80%94%E1%80%B9%E1%80%90" title="အနန္တ – Burmese" lang="my" hreflang="my" data-title="အနန္တ" 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/Oneindigheid" title="Oneindigheid – Dutch" lang="nl" hreflang="nl" data-title="Oneindigheid" 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/%E7%84%A1%E9%99%90" title="無限 – Japanese" lang="ja" hreflang="ja" data-title="無限" 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-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/%C3%9Cnentelkhaid" title="Ünentelkhaid – Northern Frisian" lang="frr" hreflang="frr" data-title="Ünentelkhaid" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Uendelig" title="Uendelig – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Uendelig" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Uendeleg" title="Uendeleg – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Uendeleg" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Infinit" title="Infinit – Occitan" lang="oc" hreflang="oc" data-title="Infinit" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Cheksizlik" title="Cheksizlik – Uzbek" lang="uz" hreflang="uz" data-title="Cheksizlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%A8%E0%A9%B0%E0%A8%A4" title="ਅਨੰਤ – Punjabi" lang="pa" hreflang="pa" data-title="ਅਨੰਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%86%D8%A7%D9%86%D8%AA%DB%8C" title="انانتی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انانتی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Infiniti" title="Infiniti – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Infiniti" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Unendlichkeid" title="Unendlichkeid – Low German" lang="nds" hreflang="nds" data-title="Unendlichkeid" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Niesko%C5%84czono%C5%9B%C4%87" title="Nieskończoność – Polish" lang="pl" hreflang="pl" data-title="Nieskończoność" 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/Infinito" title="Infinito – Portuguese" lang="pt" hreflang="pt" data-title="Infinito" 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/Infinit" title="Infinit – Romanian" lang="ro" hreflang="ro" data-title="Infinit" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Бесконечность – Rusyn" lang="rue" hreflang="rue" data-title="Бесконечность" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Бесконечность – Russian" lang="ru" hreflang="ru" data-title="Бесконечность" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Infinity" title="Infinity – Scots" lang="sco" hreflang="sco" data-title="Infinity" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Pafund%C3%ABsia" title="Pafundësia – Albanian" lang="sq" hreflang="sq" data-title="Pafundësia" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Nfinitu_(matim%C3%A0tica)" title="Nfinitu (matimàtica) – Sicilian" lang="scn" hreflang="scn" data-title="Nfinitu (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%85%E0%B6%B1%E0%B6%B1%E0%B7%8A%E0%B6%AD%E0%B6%BA" title="අනන්තය – Sinhala" lang="si" hreflang="si" data-title="අනන්තය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Nekone%C4%8Dno" title="Nekonečno – Slovak" lang="sk" hreflang="sk" data-title="Nekonečno" 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/Neskon%C4%8Dnost" title="Neskončnost – Slovenian" lang="sl" hreflang="sl" data-title="Neskončnost" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%8E%DA%A9%DB%86%D8%AA%D8%A7%DB%8C%DB%8C" title="بێکۆتایی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بێکۆتایی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B0%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Бесконачност – Serbian" lang="sr" hreflang="sr" data-title="Бесконачност" 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-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Beskona%C4%8Dnost_(matematika)" title="Beskonačnost (matematika) – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Beskonačnost (matematika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/%C3%84%C3%A4rett%C3%B6myys" title="Äärettömyys – Finnish" lang="fi" hreflang="fi" data-title="Äärettömyys" 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/O%C3%A4ndlighet" title="Oändlighet – Swedish" lang="sv" hreflang="sv" data-title="Oändlighet" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kawalang-hanggan" title="Kawalang-hanggan – Tagalog" lang="tl" hreflang="tl" data-title="Kawalang-hanggan" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AE%BF" title="முடிவிலி – Tamil" lang="ta" hreflang="ta" data-title="முடிவிலி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A7%D0%B8%D0%BA%D1%81%D0%B5%D0%B7%D0%BB%D0%B5%D0%BA" title="Чиксезлек – Tatar" lang="tt" hreflang="tt" data-title="Чиксезлек" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%99%E0%B8%B1%E0%B8%99%E0%B8%95%E0%B9%8C" title="อนันต์ – Thai" lang="th" hreflang="th" data-title="อนันต์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%91%D0%B5%D0%B8%D0%BD%D1%82%D0%B8%D2%B3%D0%BE%D3%A3" title="Беинтиҳоӣ – Tajik" lang="tg" hreflang="tg" data-title="Беинтиҳоӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sonsuz" title="Sonsuz – Turkish" lang="tr" hreflang="tr" data-title="Sonsuz" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9D%D0%B5%D1%81%D0%BA%D1%96%D0%BD%D1%87%D0%B5%D0%BD%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Нескінченність – Ukrainian" lang="uk" hreflang="uk" data-title="Нескінченність" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a 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data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Simple English Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Infinite.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Infinite.svg/200px-Infinite.svg.png" decoding="async" width="200" height="133" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Infinite.svg/300px-Infinite.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Infinite.svg/400px-Infinite.svg.png 2x" data-file-width="330" data-file-height="220" /></a><figcaption>The infinity symbol</figcaption></figure> <p><b>Infinity</b> (<span class="mwe-math-element"><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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span>) is a <a href="/w/index.php?title=Mathematical_concept&action=edit&redlink=1" class="new" title="Mathematical concept (not yet started)">mathematical concept</a> which is about things that never end. It is written in a single digit. Infinity means many different things, depending on when it is used. The word is from <a href="/wiki/Latin" title="Latin">Latin</a> origin, meaning "without end". Infinity goes on forever, so sometimes space, numbers, and other things are said to be 'infinite', because they never come to a stop. </p><p>Infinity is usually not an actual number, but it is sometimes used as one. Infinity often says how <i>many</i> there is of something, instead of how <i>big</i> something is. For example, there are infinitely many <a href="/wiki/Whole_number" class="mw-redirect" title="Whole number">whole numbers</a> (called <a href="/wiki/Integer" title="Integer">integers</a>), but there is no integer which is infinitely big. But different kinds of math have different kinds of infinity. So its meaning often changes. </p><p>There are two kinds of infinity: <a href="/wiki/Potential" class="mw-disambig" title="Potential">potential</a> infinity and <a href="https://simple.wiktionary.org/wiki/actual" class="extiw" title="wikt:actual">actual</a> infinity. Potential infinity is a process that never stops. For example, adding 10 to a number. No <a href="/wiki/Matter" title="Matter">matter</a> how many times 10 is added, 10 more can still be added. Actual infinity, on the other hand, refers to objects that are accepted as infinite entities (such as <a href="/wiki/Transfinite_number" title="Transfinite number">transfinite numbers</a>).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Infinity_in_Mathematics">Infinity in Mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=1" title="Change section: Infinity in Mathematics" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=1" title="Edit section's source code: Infinity in Mathematics"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Mathematician" title="Mathematician">Mathematicians</a> have different sizes of infinity and three different kinds of infinity.<sup id="cite_ref-ax_2-0" class="reference"><a href="#cite_note-ax-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Counting_infinity">Counting infinity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=2" title="Change section: Counting infinity" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=2" title="Edit section's source code: Counting infinity"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The number of things, beginning with 0, 1, 2, 3, ..., to include infinite cardinal numbers. There are many different <a href="/wiki/Cardinal_numbers" class="mw-redirect" title="Cardinal numbers">cardinal numbers</a>. Infinity can be defined in one of two ways: Infinity is a number so big that a part of it can be of the same size; Infinity is larger than all of the <a href="/wiki/Natural_numbers" class="mw-redirect" title="Natural numbers">natural numbers</a>. There is a smallest infinite number, <i>countable infinity</i>. It is the counting number for all of the whole numbers. It is also the counting number of the <a href="/wiki/Rational_numbers" class="mw-redirect" title="Rational numbers">rational numbers</a>. The <a href="/wiki/Mathematical_notation" title="Mathematical notation">mathematical notation</a> is the Hebrew letter <a href="/wiki/Aleph" title="Aleph">aleph</a> with a subscript zero; <span class="mwe-math-element"><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 _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721cd7f8c15a2e72ad162bdfa5baea8eef98aab1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.475ex; height:2.509ex;" alt="{\displaystyle \aleph _{0}}"></span>. It is spoken "<a href="/wiki/Aleph_null" title="Aleph null">aleph naught</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> </p><p>It was a surprise to learn that there are larger infinite numbers.<sup id="cite_ref-ax_2-1" class="reference"><a href="#cite_note-ax-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The number of <a href="/wiki/Real_numbers" class="mw-redirect" title="Real numbers">real numbers</a>, that is, all numbers with decimals, is larger than the number of <a href="/wiki/Rational_numbers" class="mw-redirect" title="Rational numbers">rational numbers</a>, the number of fractions. This shows that there are real numbers which are not fractions. The smallest infinite number greater than <span class="mwe-math-element"><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 _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721cd7f8c15a2e72ad162bdfa5baea8eef98aab1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.475ex; height:2.509ex;" alt="{\displaystyle \aleph _{0}}"></span> is <span class="mwe-math-element"><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 _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78c211ce8badf4ffbf9417ecceb0ef7ab0a8caed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.475ex; height:2.509ex;" alt="{\displaystyle \aleph _{1}}"></span> (<a href="/wiki/Aleph_one" title="Aleph one">aleph one</a>). The number of mathematical <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">functions</a> is the next infinite cardinal 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 \aleph _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/765bb468708b2eec66bf2dc6505a4c92959d697d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.475ex; height:2.509ex;" alt="{\displaystyle \aleph _{2}}"></span>. And these numbers, called aleph numbers,<sup id="cite_ref-:0_4-0" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> go on without end. </p> <div class="mw-heading mw-heading3"><h3 id="Ordering_infinity">Ordering infinity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=3" title="Change section: Ordering infinity" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=3" title="Edit section's source code: Ordering infinity"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A different <i>type</i> of infinity are the <a href="/wiki/Ordinal_numbers" class="mw-redirect" title="Ordinal numbers">ordinal numbers</a>, beginning "first, second, third, ...". The order "first, second, third, ..." and so on to infinity is <i>different</i> from the order <i>ending</i> "..., third, second, first". The difference is important for <a href="/wiki/Mathematical_induction" title="Mathematical induction">mathematical induction</a>. The simple <i>first, second, third, ... </i> has the mathematical name: the Greek letter omega with subscript zero: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a713d16c489051d4f515e12b1f86061c6be799b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.5ex; height:2.009ex;" alt="{\displaystyle \omega _{0}}"></span>.<sup id="cite_ref-:0_4-1" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> (Or simply omega <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span>.) The infinite series ending "... third, second, first" is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{*}\omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{*}\omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0621c6aad98a84351d9ca1668f9051eca25d36c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.5ex; height:2.343ex;" alt="{\displaystyle ^{*}\omega }"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="The_real_line_and_complex_plane">The real line and complex plane</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=4" title="Change section: The real line and complex plane" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=4" title="Edit section's source code: The real line and complex plane"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The third <i>type</i> of infinity has the symbol <span class="mwe-math-element"><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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span>. This is treated as addition to the <a href="/wiki/Real_numbers" class="mw-redirect" title="Real numbers">real numbers</a> or the <a href="/wiki/Complex_numbers" class="mw-redirect" title="Complex numbers">complex numbers</a>. It is the result of <a href="/wiki/Division_by_zero" title="Division by zero">division by zero</a>, or to indicate that a <a href="/wiki/Series" title="Series">series</a> is increasing (or decreasing) without bound. The series 1, 2, 3, ... increases without upper bound. This is written: the limit is <span class="mwe-math-element"><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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span>. In <a href="/wiki/Calculus" title="Calculus">calculus</a>, the <a href="/wiki/Integral" title="Integral">integral</a> over all real numbers is written: <span class="mwe-math-element"><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 _{-\infty }^{+\infty }f(x)\,dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{-\infty }^{+\infty }f(x)\,dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74f7b7a8dc036650173774d3b6f7f80bb7df04d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:13.355ex; height:6.176ex;" alt="{\displaystyle \int _{-\infty }^{+\infty }f(x)\,dx}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="The_arithmetic_of_infinity">The arithmetic of infinity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=5" title="Change section: The arithmetic of infinity" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=5" title="Edit section's source code: The arithmetic of infinity"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Each kind of infinity has different rules. </p> <div class="mw-heading mw-heading3"><h3 id="Addition,_multiplication,_exponentiation"><span id="Addition.2C_multiplication.2C_exponentiation"></span>Addition, multiplication, exponentiation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=6" title="Change section: Addition, multiplication, exponentiation" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=6" title="Edit section's source code: Addition, multiplication, exponentiation"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <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 \aleph _{0}+1=1+\aleph _{0}=\aleph _{0}+\aleph _{0}=\aleph _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mo>=</mo> <mn>1</mn> <mo>+</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph _{0}+1=1+\aleph _{0}=\aleph _{0}+\aleph _{0}=\aleph _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51c3a345a05e65a6691dc60ab0628a2ce637bd43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:32.514ex; height:2.509ex;" alt="{\displaystyle \aleph _{0}+1=1+\aleph _{0}=\aleph _{0}+\aleph _{0}=\aleph _{0}}"></span> Addition with "alephs" is <a href="/wiki/Commutative" class="mw-redirect" title="Commutative">commutative</a>. </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 2\times \aleph _{0}=\aleph _{0}\times 2=\aleph _{0}\times \aleph _{0}=\aleph _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>×</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>×</mo> <mn>2</mn> <mo>=</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>×</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\times \aleph _{0}=\aleph _{0}\times 2=\aleph _{0}\times \aleph _{0}=\aleph _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/688e476cac43d85dba635b5deb0951eebe651644" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:32.514ex; height:2.509ex;" alt="{\displaystyle 2\times \aleph _{0}=\aleph _{0}\times 2=\aleph _{0}\times \aleph _{0}=\aleph _{0}}"></span> Multiplication with "alephs" is commutative. </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 \aleph _{0}+\aleph _{1}=\aleph _{1}\times \aleph _{0}=\aleph _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph _{0}+\aleph _{1}=\aleph _{1}\times \aleph _{0}=\aleph _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a424286f767594f82b5cad549621fa749359ab03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.25ex; height:2.509ex;" alt="{\displaystyle \aleph _{0}+\aleph _{1}=\aleph _{1}\times \aleph _{0}=\aleph _{1}}"></span> </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 {\aleph _{0}}^{\aleph _{0}}>3^{\aleph _{0}}>2^{\aleph _{0}}=\aleph _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> <mo>></mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> <mo>></mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> <mo>=</mo> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\aleph _{0}}^{\aleph _{0}}>3^{\aleph _{0}}>2^{\aleph _{0}}=\aleph _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4259ebd969ee7e79822a4d14d7918ea8a50f5fca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.774ex; height:3.009ex;" alt="{\displaystyle {\aleph _{0}}^{\aleph _{0}}>3^{\aleph _{0}}>2^{\aleph _{0}}=\aleph _{1}}"></span>.<sup id="cite_ref-ax_2-2" class="reference"><a href="#cite_note-ax-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </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 1+\omega =\omega \neq \omega +1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mi>ω</mi> <mo>=</mo> <mi>ω</mi> <mo>≠</mo> <mi>ω</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+\omega =\omega \neq \omega +1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9ae46fe16a559ba811eee5ad6f5bcf008f5b63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.54ex; height:2.676ex;" alt="{\displaystyle 1+\omega =\omega \neq \omega +1}"></span>. Addition with "omegas" is not commutative. </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 2\times \omega =\omega \neq \omega \times 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>×</mo> <mi>ω</mi> <mo>=</mo> <mi>ω</mi> <mo>≠</mo> <mi>ω</mi> <mo>×</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\times \omega =\omega \neq \omega \times 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf1fbe3e2c3e5536300e27bd45d5f59c5a3f8da3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.54ex; height:2.676ex;" alt="{\displaystyle 2\times \omega =\omega \neq \omega \times 2}"></span>. Multiplication with "omegas" is not commutative. </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 \omega +\omega =\omega \times 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>+</mo> <mi>ω</mi> <mo>=</mo> <mi>ω</mi> <mo>×</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega +\omega =\omega \times 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae02ea75182095982119ebfff51ba4fb3c8b2e26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:14.279ex; height:2.343ex;" alt="{\displaystyle \omega +\omega =\omega \times 2}"></span> </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 \omega ^{\omega }>3^{\omega }>2^{\omega }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msup> <mo>></mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msup> <mo>></mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega ^{\omega }>3^{\omega }>2^{\omega }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ded0e2de67d7c131d94150e295cbcc827c84c3cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.731ex; height:2.343ex;" alt="{\displaystyle \omega ^{\omega }>3^{\omega }>2^{\omega }}"></span> </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 x+\infty =\infty =\infty +\infty =\infty \times \infty =2^{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>+</mo> <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 mathvariant="normal">∞</mi> <mo>×</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x+\infty =\infty =\infty +\infty =\infty \times \infty =2^{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/314e29a02c227f6b25083e2d0d5efb4a0108587d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:39.225ex; height:2.509ex;" alt="{\displaystyle x+\infty =\infty =\infty +\infty =\infty \times \infty =2^{\infty }}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Subtraction,_division"><span id="Subtraction.2C_division"></span>Subtraction, division</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=7" title="Change section: Subtraction, division" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=7" title="Edit section's source code: Subtraction, division"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Division by infinity (for example, with omegas or alephs) is not meaningful. Subtraction with infinity is not meaningful. </p> <div class="mw-heading mw-heading2"><h2 id="Related_pages">Related pages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=8" title="Change section: Related pages" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=8" title="Edit section's source code: Related pages"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Countable_set" title="Countable set">Countable set</a></li> <li><a href="/wiki/Eternity" title="Eternity">Eternity</a></li> <li><a href="/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel" title="Hilbert's paradox of the Grand Hotel">Hilbert's paradox of the Grand Hotel</a></li> <li><a href="/wiki/Riemann_sphere" title="Riemann sphere">Riemann sphere</a>, complex plane with a point at infinity</li> <li><a href="/wiki/Uncountable_set" title="Uncountable set">Uncountable set</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=9" title="Change section: References" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=9" title="Edit section's source code: References"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r9724317">.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"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r9724332">.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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://mathvault.ca/math-glossary/#infinite">"The Definitive Glossary of Higher Mathematical Jargon: Infinite"</a>. <i>Math Vault</i>. 2019-08-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-09-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Math+Vault&rft.atitle=The+Definitive+Glossary+of+Higher+Mathematical+Jargon%3A+Infinite&rft.date=2019-08-01&rft_id=https%3A%2F%2Fmathvault.ca%2Fmath-glossary%2F%23infinite&rfr_id=info%3Asid%2Fsimple.wikipedia.org%3AInfinity" class="Z3988"></span></span> </li> <li id="cite_note-ax-2"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-ax_2-0">2.0</a></sup> <sup><a href="#cite_ref-ax_2-1">2.1</a></sup> <sup><a href="#cite_ref-ax_2-2">2.2</a></sup></span> <span class="reference-text">To simply, we will assume several axioms like the <a href="/wiki/Axiom_of_choice" title="Axiom of choice">Axiom of choice</a> and the <a href="/w/index.php?title=Generalized_continuum_hypothesis&action=edit&redlink=1" class="new" title="Generalized continuum hypothesis (not yet started)">Generalized continuum hypothesis</a>.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9724332"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/transfinite-number">"Transfinite number | mathematics"</a>. <i>Encyclopedia Britannica</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-09-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Encyclopedia+Britannica&rft.atitle=Transfinite+number+%7C+mathematics&rft_id=https%3A%2F%2Fwww.britannica.com%2Fscience%2Ftransfinite-number&rfr_id=info%3Asid%2Fsimple.wikipedia.org%3AInfinity" class="Z3988"></span></span> </li> <li id="cite_note-:0-4"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:0_4-0">4.0</a></sup> <sup><a href="#cite_ref-:0_4-1">4.1</a></sup></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9724332"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mathvault.ca/hub/higher-math/math-symbols/set-theory-symbols/">"Comprehensive List of Set Theory Symbols"</a>. <i>Math Vault</i>. 2020-04-11<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-09-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Math+Vault&rft.atitle=Comprehensive+List+of+Set+Theory+Symbols&rft.date=2020-04-11&rft_id=https%3A%2F%2Fmathvault.ca%2Fhub%2Fhigher-math%2Fmath-symbols%2Fset-theory-symbols%2F&rfr_id=info%3Asid%2Fsimple.wikipedia.org%3AInfinity" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Other_websites">Other websites</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinity&veaction=edit&section=10" title="Change section: Other websites" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinity&action=edit&section=10" title="Edit section's source code: Other websites"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i><a rel="nofollow" class="external text" href="http://www.earlham.edu/~peters/writing/infapp.htm">A Crash Course in the Mathematics of Infinite Sets</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100227033849/http://www.earlham.edu/~peters/writing/infapp.htm">Archived</a> 2010-02-27 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i>, by Peter Suber. From the St. John's Review, XLIV, 2 (1998) 1-59. The stand-alone appendix to <i>Infinite Reflections</i>, below. A concise introduction to Cantor's mathematics of infinite sets.</li> <li><i><a rel="nofollow" class="external text" href="http://www.earlham.edu/~peters/writing/infinity.htm">Infinite Reflections</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091105182928/http://www.earlham.edu/~peters/writing/infinity.htm">Archived</a> 2009-11-05 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i>, by Peter Suber. How Cantor's mathematics of the infinite solves a handful of ancient philosophical problems of the infinite. From the St. John's Review, XLIV, 2 (1998) 1-59.</li> <li><a rel="nofollow" class="external text" href="http://pespmc1.vub.ac.be/INFINITY.html"><i>Infinity</i>, Principia Cybernetica</a></li> <li><a rel="nofollow" class="external text" href="http://www.c3.lanl.gov/mega-math/workbk/infinity/infinity.html">Hotel Infinity</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20040910082530/http://www.c3.lanl.gov/mega-math/workbk/infinity/infinity.html">Archived</a> 2004-09-10 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://samvak.tripod.com/infinite.html">The concepts of finiteness and infinity in philosophy</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://simple.wikipedia.org/w/index.php?title=Infinity&oldid=9912426">https://simple.wikipedia.org/w/index.php?title=Infinity&oldid=9912426</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Categories</a>: <ul><li><a href="/wiki/Category:Numbers" title="Category:Numbers">Numbers</a></li><li><a href="/wiki/Category:Mathematics" title="Category:Mathematics">Mathematics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Pages_using_the_JsonConfig_extension" title="Category:Pages using the JsonConfig extension">Pages using the JsonConfig extension</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</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 changed on 29 November 2024, at 09:22.</li> <li id="footer-info-copyright">Text is available under the <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a> and the <a href="/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License" title="Wikipedia:Text of the GNU Free Documentation License">GFDL</a>; additional terms may apply. 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