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Oändlighet – Wikipedia
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<div class="vector-sitenotice-container"> <div id="siteNotice"><!-- CentralNotice --></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Webbplats"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Innehåll" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Innehåll</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">dölj</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">Inledning</div> </a> </li> <li id="toc-Oändlighet_och_kardinalitet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Oändlighet_och_kardinalitet"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Oändlighet och kardinalitet</span> </div> </a> <ul id="toc-Oändlighet_och_kardinalitet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Olika_stora_oändligheter" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Olika_stora_oändligheter"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Olika stora oändligheter</span> </div> </a> <ul id="toc-Olika_stora_oändligheter-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Potentiell_oändlighet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Potentiell_oändlighet"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Potentiell oändlighet</span> </div> </a> <ul id="toc-Potentiell_oändlighet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Faktisk_oändlighet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Faktisk_oändlighet"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Faktisk oändlighet</span> </div> </a> <ul id="toc-Faktisk_oändlighet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Frågor_kring_oändlighet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Frågor_kring_oändlighet"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Frågor kring oändlighet</span> </div> </a> <ul id="toc-Frågor_kring_oändlighet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Matematiska_bevis" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Matematiska_bevis"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Matematiska bevis</span> </div> </a> <ul id="toc-Matematiska_bevis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Se_även" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_även"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Se även</span> </div> </a> <ul id="toc-Se_även-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referenser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referenser"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Referenser</span> </div> </a> <button aria-controls="toc-Referenser-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>Växla underavsnittet Referenser</span> </button> <ul id="toc-Referenser-sublist" class="vector-toc-list"> <li id="toc-Noter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Noter"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Noter</span> </div> </a> <ul id="toc-Noter-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="Innehåll" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Växla innehållsförteckningen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Växla innehållsförteckningen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Oändlighet</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="Gå till en artikel på ett annat språk. Tillgänglig på 112 språk" > <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 språk</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 – schweizertyska" lang="gsw" hreflang="gsw" data-title="Unendlichkeit" data-language-autonym="Alemannisch" data-language-local-name="schweizertyska" 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 – amhariska" lang="am" hreflang="am" data-title="አዕላፍ" data-language-autonym="አማርኛ" data-language-local-name="amhariska" 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 – arabiska" lang="ar" hreflang="ar" data-title="لانهاية" data-language-autonym="العربية" data-language-local-name="arabiska" 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 – aragonesiska" lang="an" hreflang="an" data-title="Infinito" data-language-autonym="Aragonés" data-language-local-name="aragonesiska" 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 – assamesiska" lang="as" hreflang="as" data-title="অসীম" data-language-autonym="অসমীয়া" data-language-local-name="assamesiska" 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 – asturiska" lang="ast" hreflang="ast" data-title="Infinitu" data-language-autonym="Asturianu" data-language-local-name="asturiska" 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 – azerbajdzjanska" lang="az" hreflang="az" data-title="Sonsuzluq" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdzjanska" 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 – bengali" lang="bn" hreflang="bn" data-title="অসীম" data-language-autonym="বাংলা" data-language-local-name="bengali" 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 – banjariska" lang="bjn" hreflang="bjn" data-title="Infinity" data-language-autonym="Banjar" data-language-local-name="banjariska" 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 – min nan" lang="nan" hreflang="nan" data-title="Bû-hān" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan" 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 – basjkiriska" lang="ba" hreflang="ba" data-title="Сикһеҙлек" data-language-autonym="Башҡортса" data-language-local-name="basjkiriska" 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 – belarusiska" lang="be" hreflang="be" data-title="Бесканечнасць" data-language-autonym="Беларуская" data-language-local-name="belarusiska" 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 – belarusiska (tarasjkevitsa)" lang="be-tarask" hreflang="be-tarask" data-title="Бясконцасьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusiska (tarasjkevitsa)" 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 – bulgariska" lang="bg" hreflang="bg" data-title="Безкрайност" data-language-autonym="Български" data-language-local-name="bulgariska" 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 – bosniska" lang="bs" hreflang="bs" data-title="Beskonačnost" data-language-autonym="Bosanski" data-language-local-name="bosniska" 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 – katalanska" lang="ca" hreflang="ca" data-title="Infinit" data-language-autonym="Català" data-language-local-name="katalanska" 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 – tjuvasjiska" lang="cv" hreflang="cv" data-title="Вĕçсĕрлĕх" data-language-autonym="Чӑвашла" data-language-local-name="tjuvasjiska" 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 – tjeckiska" lang="cs" hreflang="cs" data-title="Nekonečno" data-language-autonym="Čeština" data-language-local-name="tjeckiska" 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 – korsikanska" lang="co" hreflang="co" data-title="Infinitu" data-language-autonym="Corsu" data-language-local-name="korsikanska" 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 – walesiska" lang="cy" hreflang="cy" data-title="Anfeidredd" data-language-autonym="Cymraeg" data-language-local-name="walesiska" 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 – danska" lang="da" hreflang="da" data-title="Uendelighed" data-language-autonym="Dansk" data-language-local-name="danska" 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 – marockansk arabiska" lang="ary" hreflang="ary" data-title="لامسالية" data-language-autonym="الدارجة" data-language-local-name="marockansk arabiska" 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) – tyska" lang="de" hreflang="de" data-title="Unendlich (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="tyska" 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 – estniska" lang="et" hreflang="et" data-title="Lõpmatus" data-language-autonym="Eesti" data-language-local-name="estniska" 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 – grekiska" lang="el" hreflang="el" data-title="Άπειρο" data-language-autonym="Ελληνικά" data-language-local-name="grekiska" 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 – engelska" lang="en" hreflang="en" data-title="Infinity" data-language-autonym="English" data-language-local-name="engelska" 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 – spanska" lang="es" hreflang="es" data-title="Infinito" data-language-autonym="Español" data-language-local-name="spanska" 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 – baskiska" lang="eu" hreflang="eu" data-title="Infinitu" data-language-autonym="Euskara" data-language-local-name="baskiska" 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 – persiska" lang="fa" hreflang="fa" data-title="بینهایت" data-language-autonym="فارسی" data-language-local-name="persiska" 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 – franska" lang="fr" hreflang="fr" data-title="Infini" data-language-autonym="Français" data-language-local-name="franska" 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 – iriska" lang="ga" hreflang="ga" data-title="Éigríoch" data-language-autonym="Gaeilge" data-language-local-name="iriska" 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 – galiciska" lang="gl" hreflang="gl" data-title="Infinito" data-language-autonym="Galego" data-language-local-name="galiciska" 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 – koreanska" lang="ko" hreflang="ko" data-title="무한" data-language-autonym="한국어" data-language-local-name="koreanska" 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) – armeniska" lang="hy" hreflang="hy" data-title="Անվերջություն (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="armeniska" 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 – kroatiska" lang="hr" hreflang="hr" data-title="Beskonačnost" data-language-autonym="Hrvatski" data-language-local-name="kroatiska" 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 – indonesiska" lang="id" hreflang="id" data-title="Takhingga" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiska" 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 – isländska" lang="is" hreflang="is" data-title="Óendanleiki" data-language-autonym="Íslenska" data-language-local-name="isländska" 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) – italienska" lang="it" hreflang="it" data-title="Infinito (matematica)" data-language-autonym="Italiano" data-language-local-name="italienska" 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 – hebreiska" lang="he" hreflang="he" data-title="אינסוף" data-language-autonym="עברית" data-language-local-name="hebreiska" 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 – georgiska" lang="ka" hreflang="ka" data-title="უსასრულობა" data-language-autonym="ქართული" data-language-local-name="georgiska" 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 – kazakiska" lang="kk" hreflang="kk" data-title="Шексіздік" data-language-autonym="Қазақша" data-language-local-name="kazakiska" 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 – korniska" lang="kw" hreflang="kw" data-title="Didhiwedhter" data-language-autonym="Kernowek" data-language-local-name="korniska" 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 – kurdiska" lang="ku" hreflang="ku" data-title="Bêdawî" data-language-autonym="Kurdî" data-language-local-name="kurdiska" 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 – kirgiziska" lang="ky" hreflang="ky" data-title="Чексиздик" data-language-autonym="Кыргызча" data-language-local-name="kirgiziska" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="utmärkt artikel"><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 – lettiska" lang="lv" hreflang="lv" data-title="Bezgalība" data-language-autonym="Latviešu" data-language-local-name="lettiska" 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 – litauiska" lang="lt" hreflang="lt" data-title="Begalybė" data-language-autonym="Lietuvių" data-language-local-name="litauiska" 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 – ungerska" lang="hu" hreflang="hu" data-title="Végtelen" data-language-autonym="Magyar" data-language-local-name="ungerska" 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 – makedonska" lang="mk" hreflang="mk" data-title="Бесконечност" data-language-autonym="Македонски" data-language-local-name="makedonska" 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 – malagassiska" lang="mg" hreflang="mg" data-title="Tsiefa" data-language-autonym="Malagasy" data-language-local-name="malagassiska" 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 – egyptisk arabiska" lang="arz" hreflang="arz" data-title="ملهاش نهايه" data-language-autonym="مصرى" data-language-local-name="egyptisk arabiska" 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 – malajiska" lang="ms" hreflang="ms" data-title="Ketakterhinggaan" data-language-autonym="Bahasa Melayu" data-language-local-name="malajiska" 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 – mongoliska" lang="mn" hreflang="mn" data-title="Хязгааргүй" data-language-autonym="Монгол" data-language-local-name="mongoliska" 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 – burmesiska" lang="my" hreflang="my" data-title="အနန္တ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmesiska" 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 – nederländska" lang="nl" hreflang="nl" data-title="Oneindigheid" data-language-autonym="Nederlands" data-language-local-name="nederländska" 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 – japanska" lang="ja" hreflang="ja" data-title="無限" data-language-autonym="日本語" data-language-local-name="japanska" 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 – nordfrisiska" lang="frr" hreflang="frr" data-title="Ünentelkhaid" data-language-autonym="Nordfriisk" data-language-local-name="nordfrisiska" 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 – norskt bokmål" lang="nb" hreflang="nb" data-title="Uendelig" data-language-autonym="Norsk bokmål" data-language-local-name="norskt 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 – nynorska" lang="nn" hreflang="nn" data-title="Uendeleg" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorska" 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 – occitanska" lang="oc" hreflang="oc" data-title="Infinit" data-language-autonym="Occitan" data-language-local-name="occitanska" 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 – uzbekiska" lang="uz" hreflang="uz" data-title="Cheksizlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekiska" 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 – jamaikansk engelsk kreol" lang="jam" hreflang="jam" data-title="Infiniti" data-language-autonym="Patois" data-language-local-name="jamaikansk engelsk kreol" 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 – lågtyska" lang="nds" hreflang="nds" data-title="Unendlichkeid" data-language-autonym="Plattdüütsch" data-language-local-name="lågtyska" 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 – polska" lang="pl" hreflang="pl" data-title="Nieskończoność" data-language-autonym="Polski" data-language-local-name="polska" 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 – portugisiska" lang="pt" hreflang="pt" data-title="Infinito" data-language-autonym="Português" data-language-local-name="portugisiska" 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 – rumänska" lang="ro" hreflang="ro" data-title="Infinit" data-language-autonym="Română" data-language-local-name="rumänska" 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 – ryska" lang="ru" hreflang="ru" data-title="Бесконечность" data-language-autonym="Русский" data-language-local-name="ryska" 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 – skotska" lang="sco" hreflang="sco" data-title="Infinity" data-language-autonym="Scots" data-language-local-name="skotska" 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 – albanska" lang="sq" hreflang="sq" data-title="Pafundësia" data-language-autonym="Shqip" data-language-local-name="albanska" 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) – sicilianska" lang="scn" hreflang="scn" data-title="Nfinitu (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="sicilianska" 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 – singalesiska" lang="si" hreflang="si" data-title="අනන්තය" data-language-autonym="සිංහල" data-language-local-name="singalesiska" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Infinity" title="Infinity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Infinity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Nekone%C4%8Dno" title="Nekonečno – slovakiska" lang="sk" hreflang="sk" data-title="Nekonečno" data-language-autonym="Slovenčina" data-language-local-name="slovakiska" 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 – slovenska" lang="sl" hreflang="sl" data-title="Neskončnost" data-language-autonym="Slovenščina" data-language-local-name="slovenska" 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 – centralkurdiska" lang="ckb" hreflang="ckb" data-title="بێکۆتایی" data-language-autonym="کوردی" data-language-local-name="centralkurdiska" 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 – serbiska" lang="sr" hreflang="sr" data-title="Бесконачност" data-language-autonym="Српски / srpski" data-language-local-name="serbiska" 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) – serbokroatiska" lang="sh" hreflang="sh" data-title="Beskonačnost (matematika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatiska" 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 – finska" lang="fi" hreflang="fi" data-title="Äärettömyys" data-language-autonym="Suomi" data-language-local-name="finska" class="interlanguage-link-target"><span>Suomi</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 – tatariska" lang="tt" hreflang="tt" data-title="Чиксезлек" data-language-autonym="Татарча / tatarça" data-language-local-name="tatariska" 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 – thailändska" lang="th" hreflang="th" data-title="อนันต์" data-language-autonym="ไทย" data-language-local-name="thailändska" 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 – tadzjikiska" lang="tg" hreflang="tg" data-title="Беинтиҳоӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="tadzjikiska" 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 – turkiska" lang="tr" hreflang="tr" data-title="Sonsuz" data-language-autonym="Türkçe" data-language-local-name="turkiska" 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 – ukrainska" lang="uk" hreflang="uk" data-title="Нескінченність" data-language-autonym="Українська" data-language-local-name="ukrainska" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%AA%D9%86%D8%A7%DB%81%DB%8C_%D8%A7%D9%88%D8%B1_%D9%84%D8%A7%D9%85%D8%AA%D9%86%D8%A7%DB%81%DB%8C" title="متناہی اور لامتناہی – urdu" lang="ur" hreflang="ur" data-title="متناہی اور لامتناہی" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Lopm%C3%A4tomuz" title="Lopmätomuz – veps" lang="vep" hreflang="vep" data-title="Lopmätomuz" data-language-autonym="Vepsän kel’" data-language-local-name="veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%C3%B4_t%E1%BA%ADn" title="Vô tận – vietnamesiska" lang="vi" hreflang="vi" data-title="Vô tận" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesiska" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%84%A1%E9%99%90" title="無限 – litterär kineiska" lang="lzh" hreflang="lzh" data-title="無限" data-language-autonym="文言" data-language-local-name="litterär kineiska" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Infinidad" title="Infinidad – waray" lang="war" hreflang="war" data-title="Infinidad" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%97%A0%E7%A9%B7" title="无穷 – wu" lang="wuu" hreflang="wuu" data-title="无穷" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%95%D7%9E%D7%A2%D7%A0%D7%93%D7%9C%D7%A2%D7%9B%D7%A7%D7%99%D7%99%D7%98" title="אומענדלעכקייט – jiddisch" lang="yi" hreflang="yi" data-title="אומענדלעכקייט" data-language-autonym="ייִדיש" data-language-local-name="jiddisch" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%84%A1%E7%AA%AE%E7%9B%A1" title="無窮盡 – kantonesiska" lang="yue" hreflang="yue" data-title="無窮盡" data-language-autonym="粵語" data-language-local-name="kantonesiska" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Begal%C4%ABb%C4%97" title="Begalībė – samogitiska" lang="sgs" hreflang="sgs" data-title="Begalībė" data-language-autonym="Žemaitėška" data-language-local-name="samogitiska" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%97%A0%E7%A9%B7" title="无穷 – kinesiska" lang="zh" hreflang="zh" data-title="无穷" data-language-autonym="中文" data-language-local-name="kinesiska" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q205#sitelinks-wikipedia" title="Redigera interwikilänkar" class="wbc-editpage">Redigera länkar</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namnrymder"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/O%C3%A4ndlighet" title="Visa innehållssidan [c]" accesskey="c"><span>Artikel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskussion:O%C3%A4ndlighet" rel="discussion" title="Diskussion om innehållssidan [t]" accesskey="t"><span>Diskussion</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Ändra språkvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">svenska</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Visningar"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/O%C3%A4ndlighet"><span>Läs</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit" title="Redigera denna sida [v]" accesskey="v"><span>Redigera</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit" title="Redigera wikitexten för den här sidan [e]" accesskey="e"><span>Redigera wikitext</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=O%C3%A4ndlighet&action=history" title="Tidigare versioner av sidan [h]" accesskey="h"><span>Visa historik</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sidverktyg"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" 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vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit" title="Redigera wikitexten för den här sidan [e]" accesskey="e"><span>Redigera wikitext</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=O%C3%A4ndlighet&action=history"><span>Visa historik</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Allmänt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:L%C3%A4nkar_hit/O%C3%A4ndlighet" title="Lista över alla wikisidor som länkar hit [j]" accesskey="j"><span>Sidor som länkar hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:Senaste_relaterade_%C3%A4ndringar/O%C3%A4ndlighet" rel="nofollow" title="Visa senaste ändringarna av sidor som den här sidan länkar till 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href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fsv.wikipedia.org%2Fwiki%2FO%25C3%25A4ndlighet"><span>Hämta förkortad url</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fsv.wikipedia.org%2Fwiki%2FO%25C3%25A4ndlighet"><span>Ladda ner QR-kod</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Skriv ut/exportera </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Special:Bok&bookcmd=book_creator&referer=O%C3%A4ndlighet"><span>Skapa en bok</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=O%C3%A4ndlighet&action=show-download-screen"><span>Ladda ned som PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=O%C3%A4ndlighet&printable=yes" title="Utskriftsvänlig version av den här sidan [p]" accesskey="p"><span>Utskriftsvänlig version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> På andra projekt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Infinity" hreflang="en"><span>Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q205" title="Länk till anslutet databasobjekt [g]" accesskey="g"><span>Wikidata-objekt</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Sidverktyg"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">dölj</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">Från Wikipedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Omdirigerad från <a href="/w/index.php?title=O%C3%A4ndlig&redirect=no" class="mw-redirect" title="Oändlig">Oändlig</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sv" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r51224235">.mw-parser-output table.ambox{margin:0 10%;border-collapse:collapse;background:#fbfbfb;border:1px solid #aaa;border-left:10px solid #608ec2}.mw-parser-output table.ambox th.ambox-text,.mw-parser-output table.ambox td.ambox-text{padding:.25em .5em;width:100%}.mw-parser-output table.ambox td.ambox-image{padding:2px 0 2px .5em;text-align:center;vertical-align:middle}.mw-parser-output table.ambox td.ambox-imageright{padding:2px 4px 2px 0;text-align:center;vertical-align:middle}.mw-parser-output table.ambox-notice{border-left:10px solid #608ec2}.mw-parser-output table.ambox-delete,.mw-parser-output table.ambox-serious{border-left:10px solid #b22222}.mw-parser-output table.ambox-content{border-left:10px solid #f28500}.mw-parser-output table.ambox-style{border-left:10px solid #f4c430}.mw-parser-output table.ambox-merge{border-left:10px solid #9932cc}.mw-parser-output table.ambox-protection{border-left:10px solid #bba}.mw-parser-output .ambox+link+.ambox{border-top-width:0}.mw-parser-output .messagebox{border:1px solid #aaaaaa;background-color:#f8f9fa;width:80%;margin:0 auto 1em auto;padding:.2em}.mw-parser-output .messagebox.merge{border:1px solid #c0b8cc;background-color:#f0e5ff;text-align:center}.mw-parser-output .messagebox.cleanup{border:1px solid #9f9fff;background-color:#efefff;text-align:center}.mw-parser-output .messagebox.standard-talk{border:1px solid #c0c090;background-color:#f8eaba}.mw-parser-output .messagebox.nested-talk{border:1px solid #c0c090;background-color:#f8eaba;width:100%;margin:2px 4px}</style><table class="metadata ambox ambox-content" style=""> <tbody><tr> <td class="ambox-image"> <div style="width:52px;"><span typeof="mw:File"><a href="/wiki/Fil:Question_book-4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/40px-Question_book-4.svg.png" decoding="async" width="40" height="31" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/60px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/80px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></a></span></div></td> <td class="ambox-text">Den här artikeln <b>behöver <a href="/wiki/Wikipedia:K%C3%A4llh%C3%A4nvisningar" title="Wikipedia:Källhänvisningar">källhänvisningar</a> för att kunna <a href="/wiki/Wikipedia:Verifierbarhet" title="Wikipedia:Verifierbarhet">verifieras</a>.</b> <small>(2014-01)</small> <br /><small>Åtgärda genom att lägga till pålitliga källor (<a href="/wiki/Wikipedia:Introduktion_till_k%C3%A4llh%C3%A4nvisningar" title="Wikipedia:Introduktion till källhänvisningar">gärna som fotnoter</a>). Uppgifter utan källhänvisning kan <a href="/wiki/Mall:K%C3%A4lla_beh%C3%B6vs" title="Mall:Källa behövs">ifrågasättas</a> och tas bort utan att det behöver diskuteras på <a href="/wiki/Diskussion:O%C3%A4ndlighet" title="Diskussion:Oändlighet">diskussionssidan</a>.</small></td> </tr> </tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Eternal_clock.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Eternal_clock.jpg/250px-Eternal_clock.jpg" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Eternal_clock.jpg/375px-Eternal_clock.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Eternal_clock.jpg/500px-Eternal_clock.jpg 2x" data-file-width="1975" data-file-height="1978" /></a><figcaption>Oändlig tid.</figcaption></figure> <p><b>Oändlighet</b> är ett begrepp för obegränsning och obundenhet i storlek, antal eller utsträckning. Dess motsats är <a href="/w/index.php?title=%C3%84ndlighet&action=edit&redlink=1" class="new" title="Ändlighet [inte skriven än]">ändlighet</a>. Man skiljer mellan <i>potentiell oändlighet</i> och <i>faktisk oändlighet</i>. Den matematiska symbolen är en <a href="/wiki/Lemniskata" title="Lemniskata">lemniskata</a> (∞). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Oändlighet_och_kardinalitet"><span id="O.C3.A4ndlighet_och_kardinalitet"></span>Oändlighet och kardinalitet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=1" title="Redigera avsnitt: Oändlighet och kardinalitet" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=1" title="Redigera avsnitts källkod: Oändlighet och kardinalitet"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mycket av problemet med att förstå oändligheter ligger i vad man menar med ordet oändligt, och även antal. En möjlig definition för oändlighet (men inte den enda) ges med hjälp av <a href="/wiki/Kardinalitet" title="Kardinalitet">kardinalitet</a> – där man säger att två <a href="/wiki/M%C3%A4ngd" title="Mängd">mängder</a> är lika stora om man kan para ihop <i>varje</i> element i den ena mängden med ett (och endast ett) element i den andra mängden, och vice versa. Har du tre tärningar och tre femtioöringar är de lika många, eftersom de kan paras ihop ett och ett. </p><p>Matematikern <a href="/wiki/Richard_Dedekind" title="Richard Dedekind">Richard Dedekind</a> gav en definition av oändlighet som bygger på att en mängd är oändlig om man kan ta bort minst ett element från mängden, och den fortfarande är lika stor (det vill säga har samma kardinalitet). Det kan matematiskt uttryckas på följande vis: <i>En mängd A är oändlig om det finns en mängd </i><b>B</b> ⊂ <b>A</b><i> sådan att </i><b>A</b><i> och </i><b>B</b><i> har samma kardinalitet.</i> Ett exempel på detta är de naturliga talen <span style="white-space:nowrap">ℕ = {0, 1, 2, 3, …</span>} och de jämna (icke-negativa) talen <span style="white-space:nowrap"><b>B</b> = {0, 2, 4, 6, 8, …</span>}. Eftersom man kan para ihop <i>varje</i> element i <b>B</b> med ett naturligt tal (exempelvis genom att dela med två) har de samma kardinalitet som ℕ själv – de är lika många (enligt detta sätt att mäta). </p><p>Ett exempel på detta är paradoxen <a href="/wiki/Hilberts_hotell" title="Hilberts hotell">Hilberts hotell</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Olika_stora_oändligheter"><span id="Olika_stora_o.C3.A4ndligheter"></span>Olika stora oändligheter</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=2" title="Redigera avsnitt: Olika stora oändligheter" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=2" title="Redigera avsnitts källkod: Olika stora oändligheter"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Radionella_tal.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Radionella_tal.png/250px-Radionella_tal.png" decoding="async" width="250" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Radionella_tal.png/375px-Radionella_tal.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Radionella_tal.png/500px-Radionella_tal.png 2x" data-file-width="799" data-file-height="638" /></a><figcaption>En av flera möjliga sätt att räkna upp de <a href="/wiki/Rationella_tal" title="Rationella tal">rationella talen</a>.</figcaption></figure> <p><a href="/wiki/Naturliga_tal" title="Naturliga tal">De naturliga talen</a>, och alla mängder som är lika stora som dessa kallas för <a href="/wiki/Uppr%C3%A4knelig" class="mw-redirect" title="Uppräknelig"><i>uppräkneliga</i></a> – det går att börja att räkna vid ett element (exempelvis 0) och om man räknar på ett bra vis kommer man förr eller senare fram till vilket element som helst i mängden (exempelvis 10<sup>1000</sup>+1). Räknar man däremot på ett dåligt vis – exempelvis bara alla jämna tal – kan man räkna oändligt länge utan att få med ens 1. Något överraskande är det att även de rationella talen – alla möjliga bråktal – är uppräkneliga. Trots att de till skillnad från de naturliga talen är en <a href="/wiki/T%C3%A4t_m%C3%A4ngd" title="Tät mängd">tät mängd</a> – varje intervall på tallinjen innehåller oändligt många rationella tal – är de alltså inte fler än de betydligt glesare naturliga talen. Detta kan uppfattas som icke-intuitivt, men det man måste fråga sig är <i>hur man bedömer oändligheter</i>. Om man använder kardinalitet är frågan om även de rationella talen går att räkna upp i en ordning, vilket faktiskt går (se bild). </p><p>Däremot visar sig de <a href="/wiki/Reella_tal" title="Reella tal">reella talen</a> <i>inte</i> vara uppräkneliga. De är alltså i denna mening <i>fler</i> än de naturliga talen, och slutsatsen blir alltså att det finns större och mindre oändligheter. </p> <div class="mw-heading mw-heading2"><h2 id="Potentiell_oändlighet"><span id="Potentiell_o.C3.A4ndlighet"></span>Potentiell oändlighet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=3" title="Redigera avsnitt: Potentiell oändlighet" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=3" title="Redigera avsnitts källkod: Potentiell oändlighet"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Potentiell oändlighet</i> används för att hänvisa till processer som i princip kan fortsätta för evigt, eller till objekt som i princip kan förstoras för alltid. Exempelvis sekvensen <span style="white-space:nowrap">2, 4, 6, 8, 10, 12, …</span> är potentiellt oändlig: det är tydligt hur man förlänger den bortom alla gränser. Om en <a href="/wiki/Matematisk" class="mw-redirect" title="Matematisk">matematisk</a> <a href="/wiki/Funktion" title="Funktion">funktion</a> växer bortom alla gränser när argumentet närmar sig ett visst värde, då säger man (egentligen felaktigt) att <a href="/wiki/Gr%C3%A4nsv%C3%A4rde" title="Gränsvärde">gränsvärdet</a> är oändlighet (skrivs som ∞); detta är även ett exempel på potentiell oändlighet. Konceptet av potentiell oändlighet är allmänt accepterat och ställer inte till med några problem. </p> <div class="mw-heading mw-heading2"><h2 id="Faktisk_oändlighet"><span id="Faktisk_o.C3.A4ndlighet"></span>Faktisk oändlighet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=4" title="Redigera avsnitt: Faktisk oändlighet" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=4" title="Redigera avsnitts källkod: Faktisk oändlighet"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Faktisk oändlighet</i> betecknas som en komplett och existerande enhet med oändlig storlek. Möjligheten till detta har varit föremål för mycket debatt. I <a href="/wiki/Matematik" title="Matematik">matematiken</a> dröjde det till 1863 innan oändliga mängder systematiskt studerades. <a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a> som initierade studiet stötte på omfattande motstånd från omgivningen. Han fortsatte dock och insåg att oändliga mängder till och med kan ha olika storlekar, skiljde mellan <a href="/wiki/Uppr%C3%A4kneligt_o%C3%A4ndlig" class="mw-redirect" title="Uppräkneligt oändlig">uppräkneligt oändliga</a> och <a href="/wiki/Ouppr%C3%A4knelig" class="mw-redirect" title="Ouppräknelig">ouppräkneliga</a> mängder, och utvecklade sin teori om <a href="/wiki/Kardinaltal" title="Kardinaltal">kardinaltal</a> baserad på observationen. Hans uppfattning rönte så småningom framgång och modern matematik accepterar faktisk oändlighet. Vissa utökade <a href="/wiki/Tal" title="Tal">talsystem</a>, som till exempel <a href="/wiki/Surreella_tal" title="Surreella tal">surrealistiska tal</a>, omfattar de vanliga (ändliga) talen och oändliga tal av olika storlekar. </p> <div class="mw-heading mw-heading2"><h2 id="Frågor_kring_oändlighet"><span id="Fr.C3.A5gor_kring_o.C3.A4ndlighet"></span>Frågor kring oändlighet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=5" title="Redigera avsnitt: Frågor kring oändlighet" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=5" title="Redigera avsnitts källkod: Frågor kring oändlighet"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En fråga är huruvida faktisk oändlighet finns i vårt <a href="/wiki/Universum" title="Universum">universum</a>, om det finns oändligt många stjärnor, om universum har oändlig volym och utsträcker sig i det oändliga och så vidare. Detta är en viktig öppen fråga för <a href="/wiki/Kosmologi" title="Kosmologi">kosmologin</a>. Det bör noteras att frågan om att vara oändlig är logiskt skild från frågan om att vara begränsad. Den tvådimensionella jordytan är exempelvis ändlig, men har ändå ingen ände. Genom att färdas rakt långt nog, så återkommer man i princip till startpunkten. I princip kan universum vara sådant på motsvarande sätt; om man flyger med rymdskepp rakt fram tillräckligt länge, kanske man slutligen återkommer till startpunkten, dock visar alla nuvarande observationer på att universum är "platt" och inte "krökt" och att man därmed aldrig kommer att komma runt universum så att man hamnar på samma plats igen. Detta kan dock bero på att krökningen är så avskalad att man inte kan observera den ens med ljusårs avstånd. </p><p>En annan fråga är om det matematiska begreppet oändlighet har någon koppling till det religiösa begreppet <a href="/wiki/Gud" title="Gud">gud</a>. Denna fråga ställdes av både Cantor, med hans begrepp <a href="/w/index.php?title=Absolut_o%C3%A4ndlighet&action=edit&redlink=1" class="new" title="Absolut oändlighet [inte skriven än]">absolut oändlighet</a> som han jämställde med Gud, och <a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Kurt Gödel</a> med sitt "<a href="/w/index.php?title=G%C3%B6dels_ontologiska_bevis&action=edit&redlink=1" class="new" title="Gödels ontologiska bevis [inte skriven än]">ontologiska bevis</a>" om existensen av ett väsen som han satte i samband med Gud. </p> <div class="mw-heading mw-heading2"><h2 id="Matematiska_bevis">Matematiska bevis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=6" title="Redigera avsnitt: Matematiska bevis" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=6" title="Redigera avsnitts källkod: Matematiska bevis"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Att det finns oändligt många <a href="/wiki/Naturliga_tal" title="Naturliga tal">naturliga tal</a> kan <a href="/wiki/Matematiskt_bevis" title="Matematiskt bevis">bevisas</a> genom <a href="/wiki/Indirekt_bevis" title="Indirekt bevis">indirekt bevisföring</a>: </p><p>Antag att det finns ett största naturligt tal, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. Enligt <a href="/wiki/Element%C3%A4r_algebra" title="Elementär algebra">elementär algebra</a> existerar det ett tal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fcdae040c463e5b4fad95e0336723b43c3283c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.502ex; height:2.343ex;" alt="{\displaystyle S+1}"></span> som är större än <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. Alltså kan inte <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> vara det största naturliga talet, således finns det oändligt många naturliga tal.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-reference-link-bracket">[</span>1<span class="cite-reference-link-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Se_även"><span id="Se_.C3.A4ven"></span>Se även</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=7" title="Redigera avsnitt: Se även" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=7" title="Redigera avsnitts källkod: Se även"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Apeiron" title="Apeiron">Apeiron</a></li> <li><a href="/wiki/Ouroboros" title="Ouroboros">Ouroboros</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referenser">Referenser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=8" title="Redigera avsnitt: Referenser" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=8" title="Redigera avsnitts källkod: Referenser"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Noter">Noter</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=O%C3%A4ndlighet&veaction=edit&section=9" title="Redigera avsnitt: Noter" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=O%C3%A4ndlighet&action=edit&section=9" title="Redigera avsnitts källkod: Noter"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <span class="reference-text"><a 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width:3em;text-align:left;"><div class="noprint plainlinks" style="background-color:transparent; padding:0; white-space:nowrap; font-weight:normal; font-size:80%; border:none;; color: inherit;"><a href="/wiki/Mall:O%C3%A4ndlighet" title="Mall:Oändlighet"><span title="Visa denna mall" style="border:none;;">v</span></a> <span style="font-size:80%;">•</span> <a class="external text" href="https://sv.wikipedia.org/w/index.php?title=Mall:O%C3%A4ndlighet&action=edit"><span style="border:none;;" title="Redigera den här mallen">r</span></a></div></div><span style="font-size:110%;"><a class="mw-selflink selflink">Oändlighet</a> (<span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><a href="/wiki/Lemniskata" title="Lemniskata">∞</a></span>)</span></th></tr><tr style="height:2px;"><td></td></tr><tr><td class="navbox-group" style=";;">Historia</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/w/index.php?title=Kontroversen_om_Cantors_teori&action=edit&redlink=1" class="new" title="Kontroversen om Cantors teori [inte skriven än]">Kontroversen om Cantors teori</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Omfattande grenar</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Icke-standardanalys" title="Icke-standardanalys">Icke-standardanalys</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=Intern_m%C3%A4ngdteori&action=edit&redlink=1" class="new" title="Intern mängdteori [inte skriven än]">Intern mängdteori</a><span style="font-weight:bold;"> · </span> <a href="/wiki/M%C3%A4ngdteori" title="Mängdteori">Mängdteori</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=Syntetisk_differentialgeometri&action=edit&redlink=1" class="new" title="Syntetisk differentialgeometri [inte skriven än]">Syntetisk differentialgeometri</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Formaliseringar</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Kardinaltal" title="Kardinaltal">Kardinaltal</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Hyperreella_tal" title="Hyperreella tal">Hyperreella tal</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Infinitesimal" title="Infinitesimal">Infinitesimal</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=O%C3%A4ndlighet_%2B_1&action=edit&redlink=1" class="new" title="Oändlighet + 1 [inte skriven än]">Oändlighet + 1</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Ordinaltal" title="Ordinaltal">Ordinaltal</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Surreella_tal" title="Surreella tal">Surreella tal</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Transfinita_tal" title="Transfinita tal">Transfinita tal</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Forskare</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Gottfried_Wilhelm_von_Leibniz" class="mw-redirect" title="Gottfried Wilhelm von Leibniz">Gottfried Wilhelm von Leibniz</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Abraham_Robinson" title="Abraham Robinson">Abraham Robinson</a></div></td></tr></tbody></table></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" 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style=";;">Tidsskalor</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-odd"><div style="padding:0em 0.25em"><a href="/wiki/Decimaltid" title="Decimaltid">Decimaltid</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Efemerid" title="Efemerid">Efemeridtid</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Geologisk_tidsskala" title="Geologisk tidsskala">Geologisk tidsskala</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Greenwich_Mean_Time" title="Greenwich Mean Time">Greenwich Mean Time</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Internationell_atomtid" title="Internationell atomtid">Internationell atomtid</a> (TAI)<span style="font-weight:bold;"> · </span> <a href="/wiki/Koordinerad_universell_tid" title="Koordinerad universell tid">Koordinerad universell tid</a> (UTC)<span style="font-weight:bold;"> · </span> <a href="/wiki/Normaltid" title="Normaltid">Normaltid</a><span 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decoding="async" width="40" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Wooden_hourglass_3.jpg/60px-Wooden_hourglass_3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Wooden_hourglass_3.jpg/80px-Wooden_hourglass_3.jpg 2x" data-file-width="967" data-file-height="1959" /></a></span></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;"><a href="/wiki/Tidm%C3%A4tning" title="Tidmätning">Tidmätning</a></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-even"><div style="padding:0em 0.25em"><a href="/wiki/Tidm%C3%A4tningens_historia" title="Tidmätningens historia">Tidmätningens historia</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Ur" title="Ur">Ur</a>: <a href="/wiki/Armbandsur" title="Armbandsur">Armbandsur</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Atomur" title="Atomur">Atomur</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Fickur" title="Fickur">Fickur</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Kronometer" title="Kronometer">Kronometer</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Kvartsur" title="Kvartsur">Kvartsur</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Pendelur" title="Pendelur">Pendelur</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Solur" title="Solur">Solur</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Timglas" title="Timglas">Timglas</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Vattenur" title="Vattenur">Vattenur</a><span style="font-weight:bold;"> · </span> <a href="/wiki/V%C3%A4ckarur" class="mw-redirect" title="Väckarur">Väckarur</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;"><a href="/wiki/Datering" title="Datering">Dateringstekniker</a></td><td style="text-align:left;border-left:2px solid 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