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Tillgänglig på 31 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-31" 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">31 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%81%D8%A7%D8%B1%D9%82%D8%A9_%D8%A8%D8%A7%D9%86%D8%A7%D8%AE_%D8%AA%D8%A7%D8%B1%D8%B3%D9%83%D9%8A" title="مفارقة باناخ تارسكي – arabiska" lang="ar" hreflang="ar" data-title="مفارقة باناخ تارسكي" data-language-autonym="العربية" data-language-local-name="arabiska" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B4%D0%BE%D0%BA%D1%81_%D0%BD%D0%B0_%D0%91%D0%B0%D0%BD%D0%B0%D1%85-%D0%A2%D0%B0%D1%80%D1%81%D0%BA%D0%B8" title="Парадокс на Банах-Тарски – bulgariska" lang="bg" hreflang="bg" data-title="Парадокс на Банах-Тарски" data-language-autonym="Български" data-language-local-name="bulgariska" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Paradoxa_de_Banach-Tarski" title="Paradoxa de Banach-Tarski – katalanska" lang="ca" hreflang="ca" data-title="Paradoxa de Banach-Tarski" data-language-autonym="Català" data-language-local-name="katalanska" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Banach%C5%AFv%E2%80%93Tarsk%C3%A9ho_paradox" title="Banachův–Tarského paradox – tjeckiska" lang="cs" hreflang="cs" data-title="Banachův–Tarského paradox" data-language-autonym="Čeština" data-language-local-name="tjeckiska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Banach-Tarski-Paradoxon" title="Banach-Tarski-Paradoxon – tyska" lang="de" hreflang="de" data-title="Banach-Tarski-Paradoxon" 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/Banachi-Tarski_paradoks" title="Banachi-Tarski paradoks – estniska" lang="et" hreflang="et" data-title="Banachi-Tarski paradoks" data-language-autonym="Eesti" data-language-local-name="estniska" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox" title="Banach–Tarski paradox – engelska" lang="en" hreflang="en" data-title="Banach–Tarski paradox" 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/Paradoja_de_Banach-Tarski" title="Paradoja de Banach-Tarski – spanska" lang="es" hreflang="es" data-title="Paradoja de Banach-Tarski" data-language-autonym="Español" data-language-local-name="spanska" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D8%A7%D8%B1%D8%A7%D8%AF%D9%88%DA%A9%D8%B3_%D8%A8%D8%A7%D9%86%D8%A7%D8%AE%E2%80%93%D8%AA%D8%A7%D8%B1%D8%B3%DA%A9%DB%8C" title="پارادوکس باناخ–تارسکی – persiska" lang="fa" hreflang="fa" data-title="پارادوکس باناخ–تارسکی" data-language-autonym="فارسی" data-language-local-name="persiska" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Paradoxe_de_Banach-Tarski" title="Paradoxe de Banach-Tarski – franska" lang="fr" hreflang="fr" data-title="Paradoxe de Banach-Tarski" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%94%EB%82%98%ED%9D%90-%ED%83%80%EB%A5%B4%EC%8A%A4%ED%82%A4_%EC%97%AD%EC%84%A4" title="바나흐-타르스키 역설 – koreanska" lang="ko" hreflang="ko" data-title="바나흐-타르스키 역설" data-language-autonym="한국어" data-language-local-name="koreanska" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Paradoks_Banacha_i_Tarskoga" title="Paradoks Banacha i Tarskoga – kroatiska" lang="hr" hreflang="hr" data-title="Paradoks Banacha i Tarskoga" data-language-autonym="Hrvatski" data-language-local-name="kroatiska" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Paradoks_Banach%E2%80%93Tarski" title="Paradoks Banach–Tarski – indonesiska" lang="id" hreflang="id" data-title="Paradoks Banach–Tarski" 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/Banach%E2%80%93Tarski_%C3%BEvers%C3%B6gnin" title="Banach–Tarski þversögnin – isländska" lang="is" hreflang="is" data-title="Banach–Tarski þversögnin" 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/Paradosso_di_Banach-Tarski" title="Paradosso di Banach-Tarski – italienska" lang="it" hreflang="it" data-title="Paradosso di Banach-Tarski" 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%94%D7%A4%D7%A8%D7%93%D7%95%D7%A7%D7%A1_%D7%A9%D7%9C_%D7%91%D7%A0%D7%9A-%D7%98%D7%A8%D7%A1%D7%A7%D7%99" title="הפרדוקס של בנך-טרסקי – hebreiska" lang="he" hreflang="he" data-title="הפרדוקס של בנך-טרסקי" 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%AC%E0%B2%BE%E0%B2%A8%E0%B2%BE%E0%B2%95%E0%B3%8D_%E0%B2%9F%E0%B2%BE%E0%B2%B0%E0%B3%8D%E0%B2%B8%E0%B3%8D%E0%B2%95%E0%B2%BF_%E0%B2%B5%E0%B2%BF%E0%B2%B0%E0%B3%8B%E0%B2%A7%E0%B2%BE%E0%B2%AD%E0%B2%BE%E0%B2%B8" title="ಬಾನಾಕ್ ಟಾರ್ಸ್ಕಿ ವಿರೋಧಾಭಾಸ – kannada" lang="kn" hreflang="kn" data-title="ಬಾನಾಕ್ ಟಾರ್ಸ್ಕಿ ವಿರೋಧಾಭಾಸ" 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%91%E1%83%90%E1%83%9C%E1%83%90%E1%83%AE%E1%83%98%E1%83%A1-%E1%83%A2%E1%83%90%E1%83%A0%E1%83%A1%E1%83%99%E1%83%98%E1%83%A1_%E1%83%9E%E1%83%90%E1%83%A0%E1%83%90%E1%83%93%E1%83%9D%E1%83%A5%E1%83%A1%E1%83%98" title="ბანახის-ტარსკის პარადოქსი – georgiska" lang="ka" hreflang="ka" data-title="ბანახის-ტარსკის პარადოქსი" data-language-autonym="ქართული" data-language-local-name="georgiska" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Paradoss_da_Banach-Tarski" title="Paradoss da Banach-Tarski – lombardiska" lang="lmo" hreflang="lmo" data-title="Paradoss da Banach-Tarski" data-language-autonym="Lombard" data-language-local-name="lombardiska" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Banach%E2%80%93Tarski-paradoxon" title="Banach–Tarski-paradoxon – ungerska" lang="hu" hreflang="hu" data-title="Banach–Tarski-paradoxon" data-language-autonym="Magyar" data-language-local-name="ungerska" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Banach-tarskiparadox" title="Banach-tarskiparadox – nederländska" lang="nl" hreflang="nl" data-title="Banach-tarskiparadox" 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/%E3%83%90%E3%83%8A%E3%83%83%E3%83%8F%EF%BC%9D%E3%82%BF%E3%83%AB%E3%82%B9%E3%82%AD%E3%83%BC%E3%81%AE%E3%83%91%E3%83%A9%E3%83%89%E3%83%83%E3%82%AF%E3%82%B9" title="バナッハ＝タルスキーのパラドックス – japanska" lang="ja" hreflang="ja" data-title="バナッハ＝タルスキーのパラドックス" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Paradoks_Banacha-Tarskiego" title="Paradoks Banacha-Tarskiego – polska" lang="pl" hreflang="pl" data-title="Paradoks Banacha-Tarskiego" 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/Paradoxo_de_Banach%E2%80%93Tarski" title="Paradoxo de Banach–Tarski – portugisiska" lang="pt" hreflang="pt" data-title="Paradoxo de Banach–Tarski" data-language-autonym="Português" data-language-local-name="portugisiska" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B4%D0%BE%D0%BA%D1%81_%D0%91%D0%B0%D0%BD%D0%B0%D1%85%D0%B0_%E2%80%94_%D0%A2%D0%B0%D1%80%D1%81%D0%BA%D0%BE%D0%B3%D0%BE" title="Парадокс Банаха — Тарского – ryska" lang="ru" hreflang="ru" data-title="Парадокс Банаха — Тарского" data-language-autonym="Русский" data-language-local-name="ryska" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox" title="Banach–Tarski paradox – Simple English" lang="en-simple" hreflang="en-simple" data-title="Banach–Tarski paradox" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B0%D0%BD%D0%B0%D1%85-%D0%A2%D0%B0%D1%80%D1%81%D0%BA%D0%B8_%D0%BF%D0%B0%D1%80%D0%B0%D0%B4%D0%BE%D0%BA%D1%81" title="Банах-Тарски парадокс – serbiska" lang="sr" hreflang="sr" data-title="Банах-Тарски парадокс" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Banachin%E2%80%93Tarskin_paradoksi" title="Banachin–Tarskin paradoksi – finska" lang="fi" hreflang="fi" data-title="Banachin–Tarskin paradoksi" data-language-autonym="Suomi" data-language-local-name="finska" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B4%D0%BE%D0%BA%D1%81_%D0%91%D0%B0%D0%BD%D0%B0%D1%85%D0%B0_%E2%80%94_%D0%A2%D0%B0%D1%80%D1%81%D1%8C%D0%BA%D0%BE%D0%B3%D0%BE" title="Парадокс Банаха — Тарського – ukrainska" lang="uk" hreflang="uk" data-title="Парадокс Банаха — Тарського" data-language-autonym="Українська" data-language-local-name="ukrainska" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ngh%E1%BB%8Bch_l%C3%BD_Banach%E2%80%93Tarski" title="Nghịch lý Banach–Tarski – vietnamesiska" lang="vi" hreflang="vi" data-title="Nghịch lý Banach–Tarski" data-language-autonym="Tiếng Việt" 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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"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sv" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fil:Banach-Tarski_Paradox.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Banach-Tarski_Paradox.svg/350px-Banach-Tarski_Paradox.svg.png" decoding="async" width="350" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Banach-Tarski_Paradox.svg/525px-Banach-Tarski_Paradox.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/74/Banach-Tarski_Paradox.svg/700px-Banach-Tarski_Paradox.svg.png 2x" data-file-width="445" data-file-height="100" /></a><figcaption>Kan ett klot delas i ett ändligt antal delar och sedan sättas ihop till två nya klot som är identiska med originalet?</figcaption></figure> <p><b>Banach–Tarskis paradox</b> är ett <a href="/wiki/Teorem" title="Teorem">teorem</a> i <a href="/wiki/M%C3%A4ngdteori" title="Mängdteori">mängdteorin</a> inom <a href="/wiki/Geometrin" class="mw-redirect" title="Geometrin">geometrin</a> som påstår följande: Ett givet <a href="/wiki/Klot" title="Klot">klot</a> i en tredimensionell rymd, kan sönderdelas i ett ändligt antal delmängder och sedan sättas ihop igen på ett nytt sätt, så att två identiska kopior av originalet erhålls. </p><p>Det var i en artikel publicerad 1924 som <a href="/wiki/Stefan_Banach" title="Stefan Banach">Stefan Banach</a> och <a href="/wiki/Alfred_Tarski" title="Alfred Tarski">Alfred Tarski</a> påvisade följande resultat, av många betraktat som mycket förvånande:<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> <table style="margin:1em auto;border-collapse:collapse;" class="cquote"> <tbody><tr> <td style="color:#b2b7f2; font-size:3em; line-height:0; font-family:serif; padding:.35em; vertical-align:top;"><b>”</b> </td> <td style="padding:.3em;">För alla par av tredimensionella <a href="/wiki/M%C3%A4ngd" title="Mängd">föremål</a> <i>A</i> och <i>B</i> går det att dela upp <i>A</i> i ett visst antal (<i>n</i> stycken) bitar och genom att rotera och <a href="/wiki/Translation_(matematik)" title="Translation (matematik)">flytta</a> dessa bitar bilda <i>B</i> (utan hål). </td> <td style="color:#b2b7f2; font-size:3em; line-height:0; font-family:serif; padding:.35em; vertical-align:bottom;"><b>„</b> </td></tr></tbody></table> <p>Satsen säger till exempel att en ärta kan delas i ändligt många bitar och sedan pusslas ihop till ett (solitt) jordklot. Teoremet har till och med uttrycks så här: </p> <table style="margin:1em auto;border-collapse:collapse;" class="cquote"> <tbody><tr> <td style="color:#b2b7f2; font-size:3em; line-height:0; font-family:serif; padding:.35em; vertical-align:top;"><b>”</b> </td> <td style="padding:.3em;">a pea can be chopped up and reassembled into the Sun </td> <td style="color:#b2b7f2; font-size:3em; line-height:0; font-family:serif; padding:.35em; vertical-align:bottom;"><b>„</b> </td></tr></tbody></table><p> och i översättning: </p><table style="margin:1em auto;border-collapse:collapse;" class="cquote"> <tbody><tr> <td style="color:#b2b7f2; font-size:3em; line-height:0; font-family:serif; padding:.35em; vertical-align:top;"><b>”</b> </td> <td style="padding:.3em;">en ärta kan hackas i bitar och sedan sättas ihop till ett klot av solens storlek </td> <td style="color:#b2b7f2; font-size:3em; line-height:0; font-family:serif; padding:.35em; vertical-align:bottom;"><b>„</b> </td></tr></tbody></table> <p>Detta utgör paradoxen i Banach-Tarskis teorem. Lösningen ligger i att ”bitarna” är så komplicerade att det inte går att definiera deras volym på ett vettigt sätt. Bitarna har bland annat egenskapen att deras volym förändras när de roteras. </p><p>Till skillnad från flertalet teorem inom geometrin beror resultatet på vilket mängdteoretiskt axiom som väljs. Teoremet kan bara bevisas när <a href="/wiki/Urvalsaxiomet" title="Urvalsaxiomet">urvalsaxiomet</a> används. <sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-reference-link-bracket">[</span>2<span class="cite-reference-link-bracket">]</span></a></sup> </p> <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=Banach-Tarskis_paradox&veaction=edit&section=1" title="Redigera avsnitt: Referenser" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Banach-Tarskis_paradox&action=edit&section=1" title="Redigera avsnitts källkod: Referenser"><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"><cite style="font-style:normal" class="journal" id="CITEREFBanach_&_Tarski1924">Banach & Tarski (1924). ”"Sur la décomposition des ensembles de points en parties respectivement congruentes”. <i>Fundamenta Mathematicae</i> 6: sid. 244–277.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%22Sur+la+d%C3%A9composition+des+ensembles+de+points+en+parties+respectivement+congruentes&rft.jtitle=Fundamenta+Mathematicae&rft.aulast=Banach+%26+Tarski&rft.au=Banach+%26+Tarski&rft.date=1924&rft.volume=6&rft.pages=sid.%26nbsp%3B244%E2%80%93277&rfr_id=info:sid/en.wikipedia.org:Banach-Tarskis_paradox"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <span class="reference-text"><cite style="font-style:normal" class="book" id="CITEREFWagon1994">Wagon, Stan (1994). <i><span>The Banach–Tarski Paradox</span></i>. Cambridge: Cambridge University Press. <a href="/wiki/Special:Bokk%C3%A4llor/0-521-45704-1" title="Special:Bokkällor/0-521-45704-1">ISBN 0-521-45704-1</a></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Banach%E2%80%93Tarski+Paradox&rft.aulast=Wagon&rft.aufirst=Stan&rft.au=Wagon%2C+Stan&rft.date=1994&rft.pub=Cambridge%3A+Cambridge+University+Press&rft.isbn=0-521-45704-1&rfr_id=info:sid/en.wikipedia.org:Banach-Tarskis_paradox"><span style="display: none;"> </span></span></span> </li> </ol></div>    </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="">Hämtad från ”<a dir="ltr" href="https://sv.wikipedia.org/w/index.php?title=Banach-Tarskis_paradox&oldid=38564515">https://sv.wikipedia.org/w/index.php?title=Banach-Tarskis_paradox&oldid=38564515</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Wikipedia:Kategorier" title="Wikipedia:Kategorier">Kategori</a>: <ul><li><a href="/wiki/Kategori:M%C3%A4ngdteori" title="Kategori:Mängdteori">Mängdteori</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"> Sidan redigerades senast den 9 januari 2017 kl. 21.25.</li> <li id="footer-info-copyright">Wikipedias text är tillgänglig under licensen <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.sv">Creative Commons Erkännande-dela-lika 4.0 Unported</a>. 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