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class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=ko.wikipedia.org&uselang=ko" class=""><span>기부</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EC%A7%91%ED%95%A9%EB%A1%A0" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다" class=""><span>계정 만들기</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EC%A7%91%ED%95%A9%EB%A1%A0" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o" class=""><span>로그인</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="더 많은 옵션" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="개인 도구" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">개인 도구</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="사용자 메뉴" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=ko.wikipedia.org&uselang=ko"><span>기부</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EC%A7%91%ED%95%A9%EB%A1%A0" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>계정 만들기</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EC%A7%91%ED%95%A9%EB%A1%A0" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>로그인</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 로그아웃한 편집자를 위한 문서 <a href="/wiki/%EB%8F%84%EC%9B%80%EB%A7%90:%EC%86%8C%EA%B0%9C" aria-label="편집에 관해 더 알아보기"><span>더 알아보기</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EA%B8%B0%EC%97%AC" title="이 IP 주소의 편집 목록 [y]" accesskey="y"><span>기여</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EC%82%AC%EC%9A%A9%EC%9E%90%ED%86%A0%EB%A1%A0" title="현재 사용하는 IP 주소에 대한 토론 문서 [n]" accesskey="n"><span>토론</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></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="사이트"> <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="목차" 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">목차</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">숨기기</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">처음 위치</div> </a> </li> <li id="toc-공리적_집합론" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#공리적_집합론"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>공리적 집합론</span> </div> </a> <button aria-controls="toc-공리적_집합론-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>공리적 집합론 하위섹션 토글하기</span> </button> <ul id="toc-공리적_집합론-sublist" class="vector-toc-list"> <li id="toc-일차_술어논리를_사용한_공리적_집합론" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#일차_술어논리를_사용한_공리적_집합론"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>일차 술어논리를 사용한 공리적 집합론</span> </div> </a> <ul id="toc-일차_술어논리를_사용한_공리적_집합론-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-같이_보기" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#같이_보기"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>같이 보기</span> </div> </a> <ul id="toc-같이_보기-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-참고_문헌" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#참고_문헌"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>참고 문헌</span> </div> </a> <ul id="toc-참고_문헌-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-외부_링크" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#외부_링크"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>외부 링크</span> </div> </a> <ul id="toc-외부_링크-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="목차" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="목차" > <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="목차 토글" > <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">목차 토글</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">집합론</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="다른 언어로 문서를 방문합니다. 119개 언어로 읽을 수 있습니다" > <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-119" 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">119개 언어</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/Stelteorie" title="Stelteorie – 아프리칸스어" lang="af" hreflang="af" data-title="Stelteorie" data-language-autonym="Afrikaans" data-language-local-name="아프리칸스어" 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/Mengenlehre" title="Mengenlehre – 독일어(스위스)" lang="gsw" hreflang="gsw" data-title="Mengenlehre" data-language-autonym="Alemannisch" data-language-local-name="독일어(스위스)" 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%88%A5%E1%8A%90_%E1%88%B5%E1%89%A5%E1%88%B5%E1%89%A5" title="ሥነ ስብስብ – 암하라어" lang="am" hreflang="am" data-title="ሥነ ስብስብ" data-language-autonym="አማርኛ" data-language-local-name="암하라어" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Teor%C3%ADa_de_conchuntos" title="Teoría de conchuntos – 아라곤어" lang="an" hreflang="an" data-title="Teoría de conchuntos" data-language-autonym="Aragonés" data-language-local-name="아라곤어" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%B8%E0%A4%AE%E0%A5%81%E0%A4%9A%E0%A5%8D%E0%A4%9A%E0%A4%AF_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4" title="समुच्चय सिद्धान्त – 앙가어" lang="anp" hreflang="anp" data-title="समुच्चय सिद्धान्त" data-language-autonym="अंगिका" data-language-local-name="앙가어" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D9%85%D8%AC%D9%85%D9%88%D8%B9%D8%A7%D8%AA" title="نظرية المجموعات – 아랍어" lang="ar" hreflang="ar" data-title="نظرية المجموعات" data-language-autonym="العربية" data-language-local-name="아랍어" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%B9%E0%A6%A4%E0%A6%BF_%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="সংহতি তত্ত্ব – 아삼어" lang="as" hreflang="as" data-title="সংহতি তত্ত্ব" data-language-autonym="অসমীয়া" data-language-local-name="아삼어" 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/Teor%C3%ADa_de_conxuntos" title="Teoría de conxuntos – 아스투리아어" lang="ast" hreflang="ast" data-title="Teoría de conxuntos" data-language-autonym="Asturianu" data-language-local-name="아스투리아어" 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/%C3%87oxluqlar_n%C9%99z%C9%99riyy%C9%99si" title="Çoxluqlar nəzəriyyəsi – 아제르바이잔어" lang="az" hreflang="az" data-title="Çoxluqlar nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="아제르바이잔어" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9A%D2%AF%D0%BC%D3%99%D0%BA%D0%BB%D0%B5%D0%BA%D1%82%D3%99%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Күмәклектәр теорияһы – 바슈키르어" lang="ba" hreflang="ba" data-title="Күмәклектәр теорияһы" data-language-autonym="Башҡортса" data-language-local-name="바슈키르어" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Aibiu_teuor%C4%97j%C4%97" title="Aibiu teuorėjė – Samogitian" lang="sgs" hreflang="sgs" data-title="Aibiu teuorėjė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Teorya_nin_set" title="Teorya nin set – Central Bikol" lang="bcl" hreflang="bcl" data-title="Teorya nin set" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0%D1%9E" title="Тэорыя мностваў – 벨라루스어" lang="be" hreflang="be" data-title="Тэорыя мностваў" data-language-autonym="Беларуская" data-language-local-name="벨라루스어" 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%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0%D1%9E" title="Тэорыя мностваў – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Тэорыя мностваў" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%B0%D1%82%D0%B0" title="Теория на множествата – 불가리아어" lang="bg" hreflang="bg" data-title="Теория на множествата" data-language-autonym="Български" data-language-local-name="불가리아어" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%87%E0%A6%9F_%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="সেট তত্ত্ব – 벵골어" lang="bn" hreflang="bn" data-title="সেট তত্ত্ব" data-language-autonym="বাংলা" data-language-local-name="벵골어" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Teorienn_an_teskado%C3%B9" title="Teorienn an teskadoù – 브르타뉴어" lang="br" hreflang="br" data-title="Teorienn an teskadoù" data-language-autonym="Brezhoneg" data-language-local-name="브르타뉴어" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Teorija_skupova" title="Teorija skupova – 보스니아어" lang="bs" hreflang="bs" data-title="Teorija skupova" data-language-autonym="Bosanski" data-language-local-name="보스니아어" 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/Teoria_de_conjunts" title="Teoria de conjunts – 카탈로니아어" lang="ca" hreflang="ca" data-title="Teoria de conjunts" data-language-autonym="Català" data-language-local-name="카탈로니아어" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%8C%DB%86%D8%B1%DB%8C%DB%8C_%DA%A9%DB%86%D9%85%DB%95%DA%B5%DB%95" title="تیۆریی کۆمەڵە – 소라니 쿠르드어" lang="ckb" hreflang="ckb" data-title="تیۆریی کۆمەڵە" data-language-autonym="کوردی" data-language-local-name="소라니 쿠르드어" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Teorie_mno%C5%BEin" title="Teorie množin – 체코어" lang="cs" hreflang="cs" data-title="Teorie množin" data-language-autonym="Čeština" data-language-local-name="체코어" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%99%D1%8B%D1%88%D1%81%D0%B5%D0%BD_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B9%C4%95" title="Йышсен теорийĕ – 추바시어" lang="cv" hreflang="cv" data-title="Йышсен теорийĕ" data-language-autonym="Чӑвашла" data-language-local-name="추바시어" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Damcaniaeth_setiau" title="Damcaniaeth setiau – 웨일스어" lang="cy" hreflang="cy" data-title="Damcaniaeth setiau" data-language-autonym="Cymraeg" data-language-local-name="웨일스어" 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/M%C3%A6ngdel%C3%A6re" title="Mængdelære – 덴마크어" lang="da" hreflang="da" data-title="Mængdelære" data-language-autonym="Dansk" data-language-local-name="덴마크어" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Mengenlehre" title="Mengenlehre – 독일어" lang="de" hreflang="de" data-title="Mengenlehre" data-language-autonym="Deutsch" data-language-local-name="독일어" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%98%CE%B5%CF%89%CF%81%CE%AF%CE%B1_%CF%83%CF%85%CE%BD%CF%8C%CE%BB%CF%89%CE%BD" title="Θεωρία συνόλων – 그리스어" lang="el" hreflang="el" data-title="Θεωρία συνόλων" data-language-autonym="Ελληνικά" data-language-local-name="그리스어" 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/Set_theory" title="Set theory – 영어" lang="en" hreflang="en" data-title="Set theory" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Aro-teorio" title="Aro-teorio – 에스페란토어" lang="eo" hreflang="eo" data-title="Aro-teorio" data-language-autonym="Esperanto" data-language-local-name="에스페란토어" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_de_conjuntos" title="Teoría de conjuntos – 스페인어" lang="es" hreflang="es" data-title="Teoría de conjuntos" data-language-autonym="Español" data-language-local-name="스페인어" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Hulgateooria" title="Hulgateooria – 에스토니아어" lang="et" hreflang="et" data-title="Hulgateooria" data-language-autonym="Eesti" data-language-local-name="에스토니아어" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Multzo-teoria" title="Multzo-teoria – 바스크어" lang="eu" hreflang="eu" data-title="Multzo-teoria" data-language-autonym="Euskara" data-language-local-name="바스크어" 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/%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87%E2%80%8C%D9%87%D8%A7" title="نظریه مجموعه‌ها – 페르시아어" lang="fa" hreflang="fa" data-title="نظریه مجموعه‌ها" data-language-autonym="فارسی" data-language-local-name="페르시아어" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Joukko-oppi" title="Joukko-oppi – 핀란드어" lang="fi" hreflang="fi" data-title="Joukko-oppi" data-language-autonym="Suomi" data-language-local-name="핀란드어" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Hulgateooria" title="Hulgateooria – Võro" lang="vro" hreflang="vro" data-title="Hulgateooria" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Mongdarl%C3%A6ra" title="Mongdarlæra – 페로어" lang="fo" hreflang="fo" data-title="Mongdarlæra" data-language-autonym="Føroyskt" data-language-local-name="페로어" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9orie_des_ensembles" title="Théorie des ensembles – 프랑스어" lang="fr" hreflang="fr" data-title="Théorie des ensembles" data-language-autonym="Français" data-language-local-name="프랑스어" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Mengdeliar" title="Mengdeliar – 북부 프리지아어" lang="frr" hreflang="frr" data-title="Mengdeliar" data-language-autonym="Nordfriisk" data-language-local-name="북부 프리지아어" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Teorie_dai_insiemis" title="Teorie dai insiemis – 프리울리어" lang="fur" hreflang="fur" data-title="Teorie dai insiemis" data-language-autonym="Furlan" data-language-local-name="프리울리어" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Tacartheoiric" title="Tacartheoiric – 아일랜드어" lang="ga" hreflang="ga" data-title="Tacartheoiric" data-language-autonym="Gaeilge" data-language-local-name="아일랜드어" 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/Teor%C3%ADa_de_conxuntos" title="Teoría de conxuntos – 갈리시아어" lang="gl" hreflang="gl" data-title="Teoría de conxuntos" data-language-autonym="Galego" data-language-local-name="갈리시아어" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%A7%D7%91%D7%95%D7%A6%D7%95%D7%AA" title="תורת הקבוצות – 히브리어" lang="he" hreflang="he" data-title="תורת הקבוצות" data-language-autonym="עברית" data-language-local-name="히브리어" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%AE%E0%A5%81%E0%A4%9A%E0%A5%8D%E0%A4%9A%E0%A4%AF_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4" title="समुच्चय सिद्धान्त – 힌디어" lang="hi" hreflang="hi" data-title="समुच्चय सिद्धान्त" data-language-autonym="हिन्दी" data-language-local-name="힌디어" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Set_theory" title="Set theory – 피지 힌디어" lang="hif" hreflang="hif" data-title="Set theory" data-language-autonym="Fiji Hindi" data-language-local-name="피지 힌디어" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Teorija_skupova" title="Teorija skupova – 크로아티아어" lang="hr" hreflang="hr" data-title="Teorija skupova" data-language-autonym="Hrvatski" data-language-local-name="크로아티아어" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Halmazelm%C3%A9let" title="Halmazelmélet – 헝가리어" lang="hu" hreflang="hu" data-title="Halmazelmélet" data-language-autonym="Magyar" data-language-local-name="헝가리어" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%A1%D5%A6%D5%B4%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6%D5%B6%D5%A5%D6%80%D5%AB_%D5%BF%D5%A5%D5%BD%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Բազմությունների տեսություն – 아르메니아어" lang="hy" hreflang="hy" data-title="Բազմությունների տեսություն" data-language-autonym="Հայերեն" data-language-local-name="아르메니아어" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Theoria_de_insimules" title="Theoria de insimules – 인터링구아" lang="ia" hreflang="ia" data-title="Theoria de insimules" data-language-autonym="Interlingua" data-language-local-name="인터링구아" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Teori_himpunan" title="Teori himpunan – 인도네시아어" lang="id" hreflang="id" data-title="Teori himpunan" data-language-autonym="Bahasa Indonesia" data-language-local-name="인도네시아어" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Ensemblo-teorio" title="Ensemblo-teorio – 이도어" lang="io" hreflang="io" data-title="Ensemblo-teorio" data-language-autonym="Ido" data-language-local-name="이도어" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Mengjafr%C3%A6%C3%B0i" title="Mengjafræði – 아이슬란드어" lang="is" hreflang="is" data-title="Mengjafræði" data-language-autonym="Íslenska" data-language-local-name="아이슬란드어" 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/Teoria_degli_insiemi" title="Teoria degli insiemi – 이탈리아어" lang="it" hreflang="it" data-title="Teoria degli insiemi" data-language-autonym="Italiano" data-language-local-name="이탈리아어" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%9B%86%E5%90%88%E8%AB%96" title="集合論 – 일본어" lang="ja" hreflang="ja" data-title="集合論" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/T%C3%A9ori_impunan" title="Téori impunan – 자바어" lang="jv" hreflang="jv" data-title="Téori impunan" data-language-autonym="Jawa" data-language-local-name="자바어" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%9B%E1%83%A0%E1%83%90%E1%83%95%E1%83%9A%E1%83%94%E1%83%97%E1%83%90_%E1%83%97%E1%83%94%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90" title="სიმრავლეთა თეორია – 조지아어" lang="ka" hreflang="ka" data-title="სიმრავლეთა თეორია" data-language-autonym="ქართული" data-language-local-name="조지아어" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Kegbe%C9%A3lasi_l%C9%A9ma%C9%A3z%C9%A9y%C9%9B" title="Kegbeɣlasi lɩmaɣzɩyɛ – Kabiye" lang="kbp" hreflang="kbp" data-title="Kegbeɣlasi lɩmaɣzɩyɛ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/Thiori_ya_Seti" title="Thiori ya Seti – 키쿠유어" lang="ki" hreflang="ki" data-title="Thiori ya Seti" data-language-autonym="Gĩkũyũ" data-language-local-name="키쿠유어" class="interlanguage-link-target"><span>Gĩkũyũ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D0%B8%D1%8B%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Жиындар теориясы – 카자흐어" lang="kk" hreflang="kk" data-title="Жиындар теориясы" data-language-autonym="Қазақша" data-language-local-name="카자흐어" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B2%A3_%E0%B2%B8%E0%B2%BF%E0%B2%A6%E0%B3%8D%E0%B2%A7%E0%B2%BE%E0%B2%82%E0%B2%A4" title="ಗಣ ಸಿದ್ಧಾಂತ – 칸나다어" lang="kn" hreflang="kn" data-title="ಗಣ ಸಿದ್ಧಾಂತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="칸나다어" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D3%A9%D0%BF%D1%82%D2%AF%D0%BA%D1%82%D3%A9%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Көптүктөр теориясы – 키르기스어" lang="ky" hreflang="ky" data-title="Көптүктөр теориясы" data-language-autonym="Кыргызча" data-language-local-name="키르기스어" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="알찬 글"><a href="https://la.wikipedia.org/wiki/Theoria_copiarum" title="Theoria copiarum – 라틴어" lang="la" hreflang="la" data-title="Theoria copiarum" data-language-autonym="Latina" data-language-local-name="라틴어" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Teur%C3%ADa_di_cungjuunt" title="Teuría di cungjuunt – 롬바르드어" lang="lmo" hreflang="lmo" data-title="Teuría di cungjuunt" data-language-autonym="Lombard" data-language-local-name="롬바르드어" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Aibi%C5%B3_teorija" title="Aibių teorija – 리투아니아어" lang="lt" hreflang="lt" data-title="Aibių teorija" data-language-autonym="Lietuvių" data-language-local-name="리투아니아어" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kopu_teorija" title="Kopu teorija – 라트비아어" lang="lv" hreflang="lv" data-title="Kopu teorija" data-language-autonym="Latviešu" data-language-local-name="라트비아어" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%BD%D0%B0_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%B0%D1%82%D0%B0" title="Теорија на множествата – 마케도니아어" lang="mk" hreflang="mk" data-title="Теорија на множествата" data-language-autonym="Македонски" data-language-local-name="마케도니아어" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B4%A3%E0%B4%B8%E0%B4%BF%E0%B4%A6%E0%B5%8D%E0%B4%A7%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%82" title="ഗണസിദ്ധാന്തം – 말라얄람어" lang="ml" hreflang="ml" data-title="ഗണസിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="말라얄람어" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9E%D0%BB%D0%BE%D0%BD%D0%BB%D0%BE%D0%B3%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB" title="Олонлогийн онол – 몽골어" lang="mn" hreflang="mn" data-title="Олонлогийн онол" data-language-autonym="Монгол" data-language-local-name="몽골어" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%9A%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%B5%E0%A4%BE%E0%A4%A6" title="संचप्रवाद – 마라티어" lang="mr" hreflang="mr" data-title="संचप्रवाद" data-language-autonym="मराठी" data-language-local-name="마라티어" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Teori_set" title="Teori set – 말레이어" lang="ms" hreflang="ms" data-title="Teori set" data-language-autonym="Bahasa Melayu" data-language-local-name="말레이어" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%85%E1%80%AF%E1%80%9E%E1%80%AE%E1%80%A1%E1%80%AD%E1%80%AF%E1%80%9B%E1%80%AE" title="အစုသီအိုရီ – 버마어" lang="my" hreflang="my" data-title="အစုသီအိုရီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="버마어" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Mengdenleer" title="Mengdenleer – 저지 독일어" lang="nds" hreflang="nds" data-title="Mengdenleer" data-language-autonym="Plattdüütsch" data-language-local-name="저지 독일어" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B8%E0%A5%87%E0%A4%9F_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4" title="सेट सिद्धान्त – 네와르어" lang="new" hreflang="new" data-title="सेट सिद्धान्त" data-language-autonym="नेपाल भाषा" data-language-local-name="네와르어" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Verzamelingenleer" title="Verzamelingenleer – 네덜란드어" lang="nl" hreflang="nl" data-title="Verzamelingenleer" data-language-autonym="Nederlands" data-language-local-name="네덜란드어" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Mengdel%C3%A6re" title="Mengdelære – 노르웨이어(니노르스크)" lang="nn" hreflang="nn" data-title="Mengdelære" data-language-autonym="Norsk nynorsk" data-language-local-name="노르웨이어(니노르스크)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Mengdel%C3%A6re" title="Mengdelære – 노르웨이어(보크말)" lang="nb" hreflang="nb" data-title="Mengdelære" data-language-autonym="Norsk bokmål" data-language-local-name="노르웨이어(보크말)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Ensemble-teorie" title="Ensemble-teorie – Novial" lang="nov" hreflang="nov" data-title="Ensemble-teorie" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Teoria_deis_ensembles" title="Teoria deis ensembles – 오크어" lang="oc" hreflang="oc" data-title="Teoria deis ensembles" data-language-autonym="Occitan" data-language-local-name="오크어" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%B8%E0%AD%87%E0%AC%9F_%E0%AC%A4%E0%AC%A4%E0%AD%8D%E0%AC%A4%E0%AD%8D%E0%AD%B1" title="ସେଟ ତତ୍ତ୍ୱ – 오리야어" lang="or" hreflang="or" data-title="ସେଟ ତତ୍ତ୍ୱ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="오리야어" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A9%88%E0%A8%9F_%E0%A8%B8%E0%A8%BF%E0%A8%A7%E0%A8%BE%E0%A8%82%E0%A8%A4" title="ਸੈਟ ਸਿਧਾਂਤ – 펀잡어" lang="pa" hreflang="pa" data-title="ਸੈਟ ਸਿਧਾਂਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="펀잡어" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pfl mw-list-item"><a href="https://pfl.wikipedia.org/wiki/Mengenlehre" title="Mengenlehre – Palatine German" lang="pfl" hreflang="pfl" data-title="Mengenlehre" data-language-autonym="Pälzisch" data-language-local-name="Palatine German" class="interlanguage-link-target"><span>Pälzisch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Teoria_mnogo%C5%9Bci" title="Teoria mnogości – 폴란드어" lang="pl" hreflang="pl" data-title="Teoria mnogości" data-language-autonym="Polski" data-language-local-name="폴란드어" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Teor%C3%ACa_dj%27ansem" title="Teorìa dj'ansem – Piedmontese" lang="pms" hreflang="pms" data-title="Teorìa dj'ansem" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B3%DB%8C%D9%B9_%D8%AA%DA%BE%DB%8C%D9%88%D8%B1%DB%8C" title="سیٹ تھیوری – Western Punjabi" lang="pnb" hreflang="pnb" data-title="سیٹ تھیوری" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF_%D8%B3%D9%8A%D9%BC_%D9%86%D8%B8%D8%B1%D9%8A%D9%87" title="د سيټ نظريه – 파슈토어" lang="ps" hreflang="ps" data-title="د سيټ نظريه" data-language-autonym="پښتو" data-language-local-name="파슈토어" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teoria_dos_conjuntos" title="Teoria dos conjuntos – 포르투갈어" lang="pt" hreflang="pt" data-title="Teoria dos conjuntos" data-language-autonym="Português" data-language-local-name="포르투갈어" 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/Teoria_mul%C8%9Bimilor" title="Teoria mulțimilor – 루마니아어" lang="ro" hreflang="ro" data-title="Teoria mulțimilor" data-language-autonym="Română" data-language-local-name="루마니아어" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2" title="Теория множеств – 러시아어" lang="ru" hreflang="ru" data-title="Теория множеств" data-language-autonym="Русский" data-language-local-name="러시아어" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD" title="Теорія множин – 루신어" lang="rue" hreflang="rue" data-title="Теорія множин" data-language-autonym="Русиньскый" data-language-local-name="루신어" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2" title="Теория множеств – 야쿠트어" lang="sah" hreflang="sah" data-title="Теория множеств" data-language-autonym="Саха тыла" data-language-local-name="야쿠트어" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Set_theory" title="Set theory – 스코틀랜드어" lang="sco" hreflang="sco" data-title="Set theory" data-language-autonym="Scots" data-language-local-name="스코틀랜드어" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Teorija_skupova" title="Teorija skupova – 세르비아-크로아티아어" lang="sh" hreflang="sh" data-title="Teorija skupova" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="세르비아-크로아티아어" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B7%94%E0%B6%BD%E0%B6%9A_%E0%B7%80%E0%B7%8F%E0%B6%AF%E0%B6%BA" title="කුලක වාදය – 싱할라어" lang="si" hreflang="si" data-title="කුලක වාදය" data-language-autonym="සිංහල" data-language-local-name="싱할라어" 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/Set_theory" title="Set theory – Simple English" lang="en-simple" hreflang="en-simple" data-title="Set theory" 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/Te%C3%B3ria_mno%C5%BE%C3%ADn" title="Teória množín – 슬로바키아어" lang="sk" hreflang="sk" data-title="Teória množín" data-language-autonym="Slovenčina" data-language-local-name="슬로바키아어" 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/Teorija_mno%C5%BEic" title="Teorija množic – 슬로베니아어" lang="sl" hreflang="sl" data-title="Teorija množic" data-language-autonym="Slovenščina" data-language-local-name="슬로베니아어" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Teoria_e_vendosur" title="Teoria e vendosur – 알바니아어" lang="sq" hreflang="sq" data-title="Teoria e vendosur" data-language-autonym="Shqip" data-language-local-name="알바니아어" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D1%81%D0%BA%D1%83%D0%BF%D0%BE%D0%B2%D0%B0" title="Теорија скупова – 세르비아어" lang="sr" hreflang="sr" data-title="Теорија скупова" data-language-autonym="Српски / srpski" data-language-local-name="세르비아어" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/M%C3%A4ngdteori" title="Mängdteori – 스웨덴어" lang="sv" hreflang="sv" data-title="Mängdteori" data-language-autonym="Svenska" data-language-local-name="스웨덴어" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Nadharia_seti" title="Nadharia seti – 스와힐리어" lang="sw" hreflang="sw" data-title="Nadharia seti" data-language-autonym="Kiswahili" data-language-local-name="스와힐리어" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%A3%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81" title="கணக் கோட்பாடு – 타밀어" lang="ta" hreflang="ta" data-title="கணக் கோட்பாடு" data-language-autonym="தமிழ்" data-language-local-name="타밀어" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B9%80%E0%B8%8B%E0%B8%95" title="ทฤษฎีเซต – 태국어" lang="th" hreflang="th" data-title="ทฤษฎีเซต" data-language-autonym="ไทย" data-language-local-name="태국어" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/K%C3%B6pl%C3%BCkler_we_san_k%C3%B6pl%C3%BCkleri" title="Köplükler we san köplükleri – 투르크멘어" lang="tk" hreflang="tk" data-title="Köplükler we san köplükleri" data-language-autonym="Türkmençe" data-language-local-name="투르크멘어" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Teorya_ng_pangkat" title="Teorya ng pangkat – 타갈로그어" lang="tl" hreflang="tl" data-title="Teorya ng pangkat" data-language-autonym="Tagalog" data-language-local-name="타갈로그어" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/K%C3%BCmeler_teorisi" title="Kümeler teorisi – 튀르키예어" lang="tr" hreflang="tr" data-title="Kümeler teorisi" data-language-autonym="Türkçe" data-language-local-name="튀르키예어" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D2%AF%D0%BF%D0%BB%D0%B5%D0%BA_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D0%B5" title="Күплек теориясе – 타타르어" lang="tt" hreflang="tt" data-title="Күплек теориясе" data-language-autonym="Татарча / tatarça" data-language-local-name="타타르어" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD" title="Теорія множин – 우크라이나어" lang="uk" hreflang="uk" data-title="Теорія множин" data-language-autonym="Українська" data-language-local-name="우크라이나어" 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%86%D8%B8%D8%B1%DB%8C%DB%82_%D8%B7%D8%A7%D9%82%D9%85" title="نظریۂ طاقم – 우르두어" lang="ur" hreflang="ur" data-title="نظریۂ طاقم" data-language-autonym="اردو" data-language-local-name="우르두어" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/To%CA%BBplamlar_nazariyasi" title="Toʻplamlar nazariyasi – 우즈베크어" lang="uz" hreflang="uz" data-title="Toʻplamlar nazariyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="우즈베크어" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/%C3%84j%C3%BCziden_teorii" title="Äjüziden teorii – Veps" lang="vep" hreflang="vep" data-title="Äjüziden teorii" 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/L%C3%BD_thuy%E1%BA%BFt_t%E1%BA%ADp_h%E1%BB%A3p" title="Lý thuyết tập hợp – 베트남어" lang="vi" hreflang="vi" data-title="Lý thuyết tập hợp" data-language-autonym="Tiếng Việt" data-language-local-name="베트남어" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Verzoameliengeleer" title="Verzoameliengeleer – West Flemish" lang="vls" hreflang="vls" data-title="Verzoameliengeleer" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Konletateor" title="Konletateor – 볼라퓌크어" lang="vo" hreflang="vo" data-title="Konletateor" data-language-autonym="Volapük" data-language-local-name="볼라퓌크어" class="interlanguage-link-target"><span>Volapük</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Teyorya_set" title="Teyorya set – 와라이어" lang="war" hreflang="war" data-title="Teyorya set" data-language-autonym="Winaray" data-language-local-name="와라이어" 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/%E9%9B%86%E5%90%88%E8%AE%BA" title="集合论 – 우어" lang="wuu" hreflang="wuu" data-title="集合论" data-language-autonym="吴语" data-language-local-name="우어" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a 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decoding="async" width="220" height="157" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/330px-Venn_A_intersect_B.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/440px-Venn_A_intersect_B.svg.png 2x" data-file-width="350" data-file-height="250" /></a><figcaption></figcaption></figure> <p><b>집합론</b>(集合論, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">set theory</span>)은 추상적 대상들의 모임인 <a href="/wiki/%EC%A7%91%ED%95%A9" title="집합">집합</a>을 연구하는 <a href="/wiki/%EC%88%98%ED%95%99" title="수학">수학</a> 이론이다. 집합론은 <a href="/wiki/%EC%88%A0%EC%96%B4%EB%85%BC%EB%A6%AC%ED%95%99" class="mw-redirect" title="술어논리학">술어논리학</a>과 함께 대부분의 <a href="/wiki/%EC%88%98%ED%95%99%EA%B8%B0%EC%B4%88%EB%A1%A0" title="수학기초론">수학기초론</a> 체계의 근본으로, 현대 수학을 논리적으로 지탱하는 밑바탕이 된다. </p><p><a href="/wiki/%EC%86%8C%EB%B0%95%ED%95%9C_%EC%A7%91%ED%95%A9%EB%A1%A0" title="소박한 집합론">소박한 집합론</a>에서는 집합을 단순히 대상들을 모아서 만들어지는 자명한 개념으로 이해한다. 중학교 및 고등학교 등의 교육과정에서 다루는 집합의 개념은 이에 해당한다. </p><p>소박한 집합론의 모순을 해결하기 위해 등장한 <a href="/wiki/%EA%B3%B5%EB%A6%AC%EC%A0%81_%EC%A7%91%ED%95%A9%EB%A1%A0" class="mw-redirect" title="공리적 집합론">공리적 집합론</a>은 집합들과 그 포함관계가 만족하는 <a href="/wiki/%EA%B3%B5%EB%A6%AC" title="공리">공리</a>들을 규정하는 방법으로 집합을 간접적으로 정의한다. 여기에서 집합과 그 포함관계는 <a href="/wiki/%EC%9C%A0%ED%81%B4%EB%A6%AC%EB%93%9C_%EA%B8%B0%ED%95%98" class="mw-redirect" title="유클리드 기하">유클리드 기하</a>에서의 <a href="/wiki/%EC%A0%90_(%EC%88%98%ED%95%99)" class="mw-redirect" title="점 (수학)">점</a>이나 <a href="/wiki/%EC%A7%81%EC%84%A0" title="직선">선</a>과 같은 <a href="/wiki/%EB%AC%B4%EC%A0%95%EC%9D%98_%EC%9A%A9%EC%96%B4" title="무정의 용어">무정의 용어</a>로 볼 수 있다. 공리적 집합론은 대부분의 경우 대학에서 수학을 전공하지 않는 이상 배우지 않는다. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="공리적_집합론"><span id=".EA.B3.B5.EB.A6.AC.EC.A0.81_.EC.A7.91.ED.95.A9.EB.A1.A0"></span>공리적 집합론</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%A7%91%ED%95%A9%EB%A1%A0&action=edit&section=1" title="부분 편집: 공리적 집합론"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>공리적 집합론</b>은 술어논리를 이용하여 기술한 체계를 가지고 집합의 성질을 규명하는 수학의 한 분야이다. </p> <div class="mw-heading mw-heading3"><h3 id="일차_술어논리를_사용한_공리적_집합론"><span id=".EC.9D.BC.EC.B0.A8_.EC.88.A0.EC.96.B4.EB.85.BC.EB.A6.AC.EB.A5.BC_.EC.82.AC.EC.9A.A9.ED.95.9C_.EA.B3.B5.EB.A6.AC.EC.A0.81_.EC.A7.91.ED.95.A9.EB.A1.A0"></span>일차 술어논리를 사용한 공리적 집합론</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%A7%91%ED%95%A9%EB%A1%A0&action=edit&section=2" title="부분 편집: 일차 술어논리를 사용한 공리적 집합론"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>단항 술어기호 '<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Set} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">t</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Set} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/163fec9d2871a1092a0ec3a62f1c68ce5be123ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.23ex; height:2.176ex;" alt="{\displaystyle \mathrm {Set} }"></span>'과 양항 술어기호인 포함관계 기호 '<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \in }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∈</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \in }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fe4d5b0a594c1da89b5e78e7dfbeed90bdcc32f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:1.843ex;" alt="{\displaystyle \in }"></span>'모두를 포함하거나 오로지 포함관계 기호만을 포함한 일차 술어논리 언어를 가지고 집합론을 구성할 수 있다. 일반적으로 대상 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>가 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Set} (x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">t</mi> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Set} (x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b980ca975d3012d82d64bcc60ba1328675fbf852" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.369ex; height:2.843ex;" alt="{\displaystyle \mathrm {Set} (x)}"></span>를 만족하면 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>를 집합이라 한다. 이 술어기호가 없는 집합론에서는 모든 대상을 집합으로 간주한다. 집합이 없는 대상을 원자(아톰, atom)이라 한다. 만일 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\in X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>∈</mo> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\in X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e580967f68f36743e894aa7944f032dda6ea01d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.15ex; height:2.176ex;" alt="{\displaystyle x\in X}"></span>이면 '<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>가 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span>의 원소다' 혹은 '<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span>가 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>를 포함한다((원소로) 가진다)'고 한다. 이는 기호로 표현한 것을 설명한다기보다는 자연어로 옮기는 방법을 서술한 것에 가깝다. </p><p>어떤 공리적 집합론에서도 보통 확장 공리는 채택하는 편이다. 확장 공리는 `집합 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span>와 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span>가 가지는 원소가 서로 꼭 같다면 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X=Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>=</mo> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X=Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0b549c2e838e7da9dfd27fe4e1eac711331bdef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.852ex; height:2.176ex;" alt="{\displaystyle X=Y}"></span>이다.'를 말한다. 기호로 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall X\forall Y((\mathrm {Set} (X)\wedge \mathrm {Set} (Y))\rightarrow (\forall z(z\in X\leftrightarrow z\in Y)\rightarrow (X=Y))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>X</mi> <mi mathvariant="normal">∀</mi> <mi>Y</mi> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">t</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">t</mi> </mrow> <mo stretchy="false">(</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∀</mi> <mi>z</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo>∈</mo> <mi>X</mi> <mo stretchy="false">↔</mo> <mi>z</mi> <mo>∈</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>=</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall X\forall Y((\mathrm {Set} (X)\wedge \mathrm {Set} (Y))\rightarrow (\forall z(z\in X\leftrightarrow z\in Y)\rightarrow (X=Y))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4d35ae26f6a09cf5ea67ff36b1536531301dfc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:62.579ex; height:2.843ex;" alt="{\displaystyle \forall X\forall Y((\mathrm {Set} (X)\wedge \mathrm {Set} (Y))\rightarrow (\forall z(z\in X\leftrightarrow z\in Y)\rightarrow (X=Y))}"></span>로 쓸 수 있다. </p><p>이제 소박한 집합론에서 말하는 '분명히 구별되는 대상들의 모임이 집합'이라는 정의를 공리적 집합론으로 가져오면 다음과 같이 표현할 수 있다. '임의의 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (n+1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (n+1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b30a29cfd35628469f9dbffea4804f5b422f3037" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.207ex; height:2.843ex;" alt="{\displaystyle (n+1)}"></span>개 자유변수 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu ,\nu _{1},\nu _{2},\ldots ,\nu _{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> <mo>,</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu ,\nu _{1},\nu _{2},\ldots ,\nu _{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1085d906fd817aa8c93ba3d03a8151344d9cad30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.251ex; height:2.009ex;" alt="{\displaystyle \nu ,\nu _{1},\nu _{2},\ldots ,\nu _{n}}"></span>를 가지는 논리 공식 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span>에 대하여 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall \nu _{1}\forall \nu _{2}\cdots \nu _{n}\exists X(\forall \nu (\nu \in X\leftrightarrow \varphi (\nu ,\nu _{1},\ldots ,\nu _{n}))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi mathvariant="normal">∀</mi> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mi mathvariant="normal">∃</mi> <mi>X</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">∀</mi> <mi>ν</mi> <mo stretchy="false">(</mo> <mi>ν</mi> <mo>∈</mo> <mi>X</mi> <mo stretchy="false">↔</mo> <mi>φ</mi> <mo stretchy="false">(</mo> <mi>ν</mi> <mo>,</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall \nu _{1}\forall \nu _{2}\cdots \nu _{n}\exists X(\forall \nu (\nu \in X\leftrightarrow \varphi (\nu ,\nu _{1},\ldots ,\nu _{n}))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d501ee9805373c4ddfa23f7ba968fa3a18bf300f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:46.376ex; height:2.843ex;" alt="{\displaystyle \forall \nu _{1}\forall \nu _{2}\cdots \nu _{n}\exists X(\forall \nu (\nu \in X\leftrightarrow \varphi (\nu ,\nu _{1},\ldots ,\nu _{n}))}"></span>가 성립한다'로 표현할 수 있다. 여기서 변수자리에 쓴 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span>는 그것이 어느 변수라도 될 수 있음을 표현하고자 한 것이다. 물론 변수 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span>는 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span>들 중 어느 하나라도 같아서는 안 된다. 그런데 이 공리는 도입하는 즉시 <a href="/wiki/%EB%9F%AC%EC%85%80%EC%9D%98_%EC%97%AD%EC%84%A4" title="러셀의 역설">러셀의 역설</a>과 유사한 역설에 직면하게 된다. 이를 피하기 위해 여러 방법이 사용되는데, 크게 세 가지로 구분된다. 하나는 분리공리만을 허용하는 것이고, 또 하나는 변수의 타입을 집합과 유로 구분하는 것이고, 또 하나는 사용할 수 있는 논리 공식에 제한을 두는 것이다. <a href="/wiki/ZFC" class="mw-redirect" title="ZFC">ZFC</a>에서는 분리공리만을 허용하며, 변수 타입을 집합과 유로 구분하는 것은 <a href="/wiki/%ED%8F%B0_%EB%85%B8%EC%9D%B4%EB%A7%8C-%EB%B2%A0%EB%A5%B4%EB%82%98%EC%9D%B4%EC%8A%A4-%EA%B4%B4%EB%8D%B8_%EC%A7%91%ED%95%A9%EB%A1%A0" title="폰 노이만-베르나이스-괴델 집합론">NBG</a>, 논리 공식에 제한을 두는 것은 New foundation에서 볼 수 있다. </p> <div class="mw-heading mw-heading2"><h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%A7%91%ED%95%A9%EB%A1%A0&action=edit&section=3" title="부분 편집: 같이 보기"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r38501082">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box metadata side-box-right plainlinks"><style data-mw-deduplicate="TemplateStyles:r36480595">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist"><b><a href="/wiki/%EC%9C%84%ED%82%A4%EB%AF%B8%EB%94%94%EC%96%B4_%EA%B3%B5%EC%9A%A9" title="위키미디어 공용">위키미디어 공용</a></b>에 관련된<br />미디어 분류가 있습니다.<div style="padding-left:1em;"><b><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Set_theory?uselang=ko">집합론</a></b></div></div></div> </div> <ul><li><a href="/wiki/%EA%B2%8C%EC%98%A4%EB%A5%B4%ED%81%AC_%EC%B9%B8%ED%86%A0%EC%96%B4" title="게오르크 칸토어">게오르크 칸토어</a> (<a href="/wiki/1845%EB%85%84" title="1845년">1845년</a>-<a href="/wiki/1918%EB%85%84" title="1918년">1918년</a>) - <a href="/wiki/%EB%8F%85%EC%9D%BC" title="독일">독일</a>의 <a href="/wiki/%EC%88%98%ED%95%99%EC%9E%90" title="수학자">수학자</a> 및 <a href="/wiki/%EC%B2%A0%ED%95%99%EC%9E%90" title="철학자">철학자</a>로, 집합론의 창시자로 잘 알려져 있다.</li> <li><a href="/wiki/%EC%A3%BC%EC%84%B8%ED%8E%98_%ED%8E%98%EC%95%84%EB%85%B8" title="주세페 페아노">주세페 페아노</a> (<a href="/wiki/1858%EB%85%84" title="1858년">1858년</a>-<a href="/wiki/1932%EB%85%84" title="1932년">1932년</a>) - <a href="/wiki/%EC%9D%B4%ED%83%88%EB%A6%AC%EC%95%84" title="이탈리아">이탈리아</a>의 수학자 및 철학자로, <a href="/wiki/%ED%95%A9%EC%A7%91%ED%95%A9" title="합집합">합집합</a>과 <a href="/wiki/%EA%B5%90%EC%A7%91%ED%95%A9" title="교집합">교집합</a> 기호를 발명했고 <a href="/wiki/%EC%82%B0%EC%88%A0" title="산술">산술</a>을 형식화했다.</li> <li><a href="/wiki/%EC%86%8C%EB%B0%95%ED%95%9C_%EC%A7%91%ED%95%A9%EB%A1%A0" title="소박한 집합론">소박한 집합론</a></li> <li><a href="/wiki/%EA%B3%B5%EB%A6%AC%EC%A0%81_%EC%A7%91%ED%95%A9%EB%A1%A0" class="mw-redirect" title="공리적 집합론">공리적 집합론</a></li> <li><a href="/wiki/%EC%A7%91%ED%95%A9" title="집합">집합</a></li> <li><a href="/wiki/%EC%B2%B4%EB%A5%B4%EB%A9%9C%EB%A1%9C_%EC%A7%91%ED%95%A9%EB%A1%A0" class="mw-redirect" title="체르멜로 집합론">체르멜로 집합론</a>은 독일의 수학자 <a href="/wiki/%EC%97%90%EB%A5%B8%EC%8A%A4%ED%8A%B8_%EC%B2%B4%EB%A5%B4%EB%A9%9C%EB%A1%9C" title="에른스트 체르멜로">에른스트 체르멜로</a>가 개발한 공리계이다.</li> <li><a href="/wiki/%EC%B2%B4%EB%A5%B4%EB%A9%9C%EB%A1%9C-%ED%94%84%EB%A0%9D%EC%BC%88_%EC%A7%91%ED%95%A9%EB%A1%A0" title="체르멜로-프렝켈 집합론">체르멜로-프렝켈 집합론</a>은 가장 널리 사용되는 집합론의 공리계이다.</li></ul> <div class="mw-heading mw-heading2"><h2 id="참고_문헌"><span id=".EC.B0.B8.EA.B3.A0_.EB.AC.B8.ED.97.8C"></span>참고 문헌</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%A7%91%ED%95%A9%EB%A1%A0&action=edit&section=4" title="부분 편집: 참고 문헌"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation book">최창선 (2006). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141129034347/http://kyungmoon.com/shop_product/shop_pdt_view.php?p_idx=4599">《수학, 철학, 전산학, 언어학도를 위한 집합론 입문》</a>. 경문사. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/89-7282-777-0" title="특수:책찾기/89-7282-777-0"><bdi>89-7282-777-0</bdi></a>. 2014년 11월 29일에 <a rel="nofollow" class="external text" href="http://kyungmoon.com/shop_product/shop_pdt_view.php?p_idx=4599">원본 문서</a>에서 보존된 문서<span class="reference-accessdate">. 2014년 11월 19일에 확인함</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%EC%88%98%ED%95%99%2C+%EC%B2%A0%ED%95%99%2C+%EC%A0%84%EC%82%B0%ED%95%99%2C+%EC%96%B8%EC%96%B4%ED%95%99%EB%8F%84%EB%A5%BC+%EC%9C%84%ED%95%9C+%EC%A7%91%ED%95%A9%EB%A1%A0+%EC%9E%85%EB%AC%B8&rft.pub=%EA%B2%BD%EB%AC%B8%EC%82%AC&rft.date=2006&rft.isbn=89-7282-777-0&rft.au=%EC%B5%9C%EC%B0%BD%EC%84%A0&rft_id=http%3A%2F%2Fkyungmoon.com%2Fshop_product%2Fshop_pdt_view.php%3Fp_idx%3D4599&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">이식 (2007). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141129034349/http://kyungmoon.com/shop_product/shop_pdt_view.php?p_idx=2966">《집합론》</a>. 경문사. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-89-6105-051-7" title="특수:책찾기/978-89-6105-051-7"><bdi>978-89-6105-051-7</bdi></a>. 2014년 11월 29일에 <a rel="nofollow" class="external text" href="http://kyungmoon.com/shop_product/shop_pdt_view.php?p_idx=2966">원본 문서</a>에서 보존된 문서<span class="reference-accessdate">. 2014년 11월 19일에 확인함</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%EC%A7%91%ED%95%A9%EB%A1%A0&rft.pub=%EA%B2%BD%EB%AC%B8%EC%82%AC&rft.date=2007&rft.isbn=978-89-6105-051-7&rft.au=%EC%9D%B4%EC%8B%9D&rft_id=http%3A%2F%2Fkyungmoon.com%2Fshop_product%2Fshop_pdt_view.php%3Fp_idx%3D2966&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">허걸 (2008). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141129034344/http://kyungmoon.com/shop_product/shop_pdt_view.php?p_idx=3547">《집합론》</a>. 경문사. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/89-7282-702-9" title="특수:책찾기/89-7282-702-9"><bdi>89-7282-702-9</bdi></a>. 2014년 11월 29일에 <a rel="nofollow" class="external text" href="http://kyungmoon.com/shop_product/shop_pdt_view.php?p_idx=3547">원본 문서</a>에서 보존된 문서<span class="reference-accessdate">. 2014년 11월 19일에 확인함</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%EC%A7%91%ED%95%A9%EB%A1%A0&rft.pub=%EA%B2%BD%EB%AC%B8%EC%82%AC&rft.date=2008&rft.isbn=89-7282-702-9&rft.au=%ED%97%88%EA%B1%B8&rft_id=http%3A%2F%2Fkyungmoon.com%2Fshop_product%2Fshop_pdt_view.php%3Fp_idx%3D3547&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">이병무 (2009). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141129034412/http://kyungmoon.com/shop_product/shop_pdt_view.php?p_idx=6569">《쉬운 설명 다양한 예제 집합론의 이해》</a>. 경문사. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-89-6105-234-4" title="특수:책찾기/978-89-6105-234-4"><bdi>978-89-6105-234-4</bdi></a>. 2014년 11월 29일에 <a rel="nofollow" class="external text" href="http://kyungmoon.com/shop_product/shop_pdt_view.php?p_idx=6569">원본 문서</a>에서 보존된 문서<span class="reference-accessdate">. 2014년 11월 19일에 확인함</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%EC%89%AC%EC%9A%B4+%EC%84%A4%EB%AA%85+%EB%8B%A4%EC%96%91%ED%95%9C+%EC%98%88%EC%A0%9C+%EC%A7%91%ED%95%A9%EB%A1%A0%EC%9D%98+%EC%9D%B4%ED%95%B4&rft.pub=%EA%B2%BD%EB%AC%B8%EC%82%AC&rft.date=2009&rft.isbn=978-89-6105-234-4&rft.au=%EC%9D%B4%EB%B3%91%EB%AC%B4&rft_id=http%3A%2F%2Fkyungmoon.com%2Fshop_product%2Fshop_pdt_view.php%3Fp_idx%3D6569&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Jech, Thomas (2003). <a rel="nofollow" class="external text" href="https://archive.org/details/settheory0000jech_f7i4">《Set theory》</a>. Springer Monographs in Mathematics (영어) 3판. Springer-Verlag. <a href="/wiki/%EB%94%94%EC%A7%80%ED%84%B8_%EA%B0%9D%EC%B2%B4_%EC%8B%9D%EB%B3%84%EC%9E%90" title="디지털 객체 식별자">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2F3-540-44761-X">10.1007/3-540-44761-X</a>. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-3-540-44085-7" title="특수:책찾기/978-3-540-44085-7"><bdi>978-3-540-44085-7</bdi></a>. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EC%9D%BC%EB%A0%A8_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 일련 번호">ISSN</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/1439-7382">1439-7382</a>. <a href="/wiki/%EC%B2%B8%ED%8A%B8%EB%9E%84%EB%B8%94%EB%9D%BC%ED%8A%B8_%EB%A7%88%ED%8A%B8" title="첸트랄블라트 마트">Zbl</a> <a rel="nofollow" class="external text" href="//zbmath.org/?format=complete&q=an:1007.03002">1007.03002</a>. <a href="/wiki/%EC%9D%B8%ED%84%B0%EB%84%B7_%EC%95%84%EC%B9%B4%EC%9D%B4%EB%B8%8C" title="인터넷 아카이브">IA</a> <a rel="nofollow" class="external text" href="https://archive.org/details/settheory0000jech_f7i4">settheory0000jech_f7i4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Set+theory&rft.series=Springer+Monographs+in+Mathematics&rft.edition=3&rft.pub=Springer-Verlag&rft.date=2003&rft_id=%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A1007.03002&rft.issn=1439-7382&rft_id=info%3Adoi%2F10.1007%2F3-540-44761-X&rft.isbn=978-3-540-44085-7&rft.aulast=Jech&rft.aufirst=Thomas&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsettheory0000jech_f7i4&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Roitman, Judith (2011). 《Introduction to modern set theory》 (영어) 2판. Virginia Commonwealth University Press. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-0-9824062-4-3" title="특수:책찾기/978-0-9824062-4-3"><bdi>978-0-9824062-4-3</bdi></a>. <a href="/wiki/%EC%B2%B8%ED%8A%B8%EB%9E%84%EB%B8%94%EB%9D%BC%ED%8A%B8_%EB%A7%88%ED%8A%B8" title="첸트랄블라트 마트">Zbl</a> <a rel="nofollow" class="external text" href="//zbmath.org/?format=complete&q=an:0689.0400">0689.0400</a> <span style="font-size:100%" class="error citation-comment"><code class="cs1-code">|zbl=</code> 값 확인 필요 (<a href="/wiki/%EC%9C%84%ED%82%A4%EB%B0%B1%EA%B3%BC:%EC%9D%B8%EC%9A%A9_%EC%98%A4%EB%A5%98_%EB%8F%84%EC%9B%80%EB%A7%90#bad_zbl" title="위키백과:인용 오류 도움말">도움말</a>)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+modern+set+theory&rft.edition=2%ED%8C%90&rft.pub=Virginia+Commonwealth+University+Press&rft.date=2011&rft_id=%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A0689.0400&rft.isbn=978-0-9824062-4-3&rft.aulast=Roitman&rft.aufirst=Judith&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33"> CS1 관리 - 추가 문구 (<a href="/wiki/%EB%B6%84%EB%A5%98:CS1_%EA%B4%80%EB%A6%AC_-_%EC%B6%94%EA%B0%80_%EB%AC%B8%EA%B5%AC" title="분류:CS1 관리 - 추가 문구">링크</a>)</span></li> <li><cite class="citation book"><a href="/wiki/%ED%97%90%EB%AA%A8%EC%8B%9C_%ED%8C%94" title="헐모시 팔">Halmos, Paul R.</a> (1974). <a rel="nofollow" class="external text" href="https://archive.org/details/naivesettheory0000halm_r6r4">《Naive set theory》</a>. Undergraduate Texts in Mathematics (영어). Springer-Verlag. <a href="/wiki/%EB%94%94%EC%A7%80%ED%84%B8_%EA%B0%9D%EC%B2%B4_%EC%8B%9D%EB%B3%84%EC%9E%90" title="디지털 객체 식별자">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2F978-1-4757-1645-0">10.1007/978-1-4757-1645-0</a>. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-0-387-90092-6" title="특수:책찾기/978-0-387-90092-6"><bdi>978-0-387-90092-6</bdi></a>. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EC%9D%BC%EB%A0%A8_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 일련 번호">ISSN</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0172-6056">0172-6056</a>. <a href="/wiki/%EC%88%98%ED%95%99_%EB%A6%AC%EB%B7%B0" title="수학 리뷰">MR</a> <a rel="nofollow" class="external text" href="//www.ams.org/mathscinet-getitem?mr=0453532">0453532</a>. <a href="/wiki/%EC%B2%B8%ED%8A%B8%EB%9E%84%EB%B8%94%EB%9D%BC%ED%8A%B8_%EB%A7%88%ED%8A%B8" title="첸트랄블라트 마트">Zbl</a> <a rel="nofollow" class="external text" href="//zbmath.org/?format=complete&q=an:0287.04001">0287.04001</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Naive+set+theory&rft.series=Undergraduate+Texts+in+Mathematics&rft.pub=Springer-Verlag&rft.date=1974&rft_id=%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A0287.04001&rft_id=%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D0453532&rft_id=info%3Adoi%2F10.1007%2F978-1-4757-1645-0&rft.issn=0172-6056&rft.isbn=978-0-387-90092-6&rft.aulast=Halmos&rft.aufirst=Paul+R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnaivesettheory0000halm_r6r4&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book"><a href="/wiki/%EC%BC%80%EB%84%A4%EC%8A%A4_%EC%BF%A0%EB%84%8C" title="케네스 쿠넌">Kunen, Kenneth</a> (1980). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160911102401/http://store.elsevier.com/Set-Theory-An-Introduction-To-Independence-Proofs/K_-Kunen/isbn-9780444868398/">《Set theory: an introduction to independence proofs》</a>. Studies in Logic and the Foundations of Mathematics (영어) <b>102</b>. North-Holland. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-0-444-86839-8" title="특수:책찾기/978-0-444-86839-8"><bdi>978-0-444-86839-8</bdi></a>. <a href="/wiki/%EC%88%98%ED%95%99_%EB%A6%AC%EB%B7%B0" title="수학 리뷰">MR</a> <a rel="nofollow" class="external text" href="//www.ams.org/mathscinet-getitem?mr=597342">597342</a>. <a href="/wiki/%EC%B2%B8%ED%8A%B8%EB%9E%84%EB%B8%94%EB%9D%BC%ED%8A%B8_%EB%A7%88%ED%8A%B8" title="첸트랄블라트 마트">Zbl</a> <a rel="nofollow" class="external text" href="//zbmath.org/?format=complete&q=an:0534.03026">0534.03026</a>. 2016년 9월 11일에 <a rel="nofollow" class="external text" href="http://store.elsevier.com/Set-Theory-An-Introduction-To-Independence-Proofs/K_-Kunen/isbn-9780444868398/">원본 문서</a>에서 보존된 문서<span class="reference-accessdate">. 2016년 8월 11일에 확인함</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Set+theory%3A+an+introduction+to+independence+proofs&rft.series=Studies+in+Logic+and+the+Foundations+of+Mathematics&rft.pub=North-Holland&rft.date=1980&rft_id=%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A0534.03026&rft_id=%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D597342&rft.isbn=978-0-444-86839-8&rft.aulast=Kunen&rft.aufirst=Kenneth&rft_id=http%3A%2F%2Fstore.elsevier.com%2FSet-Theory-An-Introduction-To-Independence-Proofs%2FK_-Kunen%2Fisbn-9780444868398%2F&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Schindler, Ralf (2014). 《Set theory: exploring independence and truth》. Universitext (영어). Springer-Verlag. <a href="/wiki/%EB%94%94%EC%A7%80%ED%84%B8_%EA%B0%9D%EC%B2%B4_%EC%8B%9D%EB%B3%84%EC%9E%90" title="디지털 객체 식별자">doi</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2F978-3-319-06725-4">10.1007/978-3-319-06725-4</a>. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-3-319-06724-7" title="특수:책찾기/978-3-319-06724-7"><bdi>978-3-319-06724-7</bdi></a>. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EC%9D%BC%EB%A0%A8_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 일련 번호">ISSN</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0172-5939">0172-5939</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Set+theory%3A+exploring+independence+and+truth&rft.series=Universitext&rft.pub=Springer-Verlag&rft.date=2014&rft.issn=0172-5939&rft_id=info%3Adoi%2F10.1007%2F978-3-319-06725-4&rft.isbn=978-3-319-06724-7&rft.aulast=Schindler&rft.aufirst=Ralf&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="외부_링크"><span id=".EC.99.B8.EB.B6.80_.EB.A7.81.ED.81.AC"></span>외부 링크</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%A7%91%ED%95%A9%EB%A1%A0&action=edit&section=5" title="부분 편집: 외부 링크"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web"><a rel="nofollow" class="external text" href="https://encyclopediaofmath.org/wiki/Set_theory">“Set theory”</a>. 《Encyclopedia of Mathematics》 (영어). 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Korea Open Courseware.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%EC%A7%91%ED%95%A9%EB%A1%A0+%EB%B0%8F+%EC%8B%A4%EC%8A%B5&rft.pub=Korea+Open+Courseware&rft.date=2011&rft.au=%EC%9D%B4%EC%84%9D%EC%A2%85&rft_id=http%3A%2F%2Fwww.kocw.net%2Fhome%2Fsearch%2FkemView.do%3FkemId%3D332498&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%A7%91%ED%95%A9%EB%A1%A0" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r36480591">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output 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title="수학">수학</a>의 주요 분야</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%88%98%EB%A1%A0" title="수론">수론</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EB%8C%80%EC%88%98%EC%A0%81_%EC%88%98%EB%A1%A0" title="대수적 수론">대수적 수론</a></li> <li><a href="/wiki/%ED%95%B4%EC%84%9D%EC%A0%81_%EC%88%98%EB%A1%A0" title="해석적 수론">해석적 수론</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EB%8C%80%EC%88%98%ED%95%99" title="대수학">대수학</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%84%A0%ED%98%95%EB%8C%80%EC%88%98%ED%95%99" title="선형대수학">선형대수학</a></li> <li><a href="/wiki/%EC%B6%94%EC%83%81%EB%8C%80%EC%88%98%ED%95%99" title="추상대수학">추상대수학</a></li> <li><a href="/wiki/%EA%B5%B0%EB%A1%A0" title="군론">군론</a></li> <li><a href="/wiki/%ED%99%98%EB%A1%A0" title="환론">환론</a></li> <li><a href="/wiki/%EA%B0%80%ED%99%98%EB%8C%80%EC%88%98%ED%95%99" title="가환대수학">가환대수학</a></li> <li><a href="/wiki/%ED%98%B8%EB%AA%B0%EB%A1%9C%EC%A7%80_%EB%8C%80%EC%88%98%ED%95%99" title="호몰로지 대수학">호몰로지 대수학</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%ED%95%B4%EC%84%9D%ED%95%99_(%EC%88%98%ED%95%99)" title="해석학 (수학)">해석학</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EB%AF%B8%EC%A0%81%EB%B6%84%ED%95%99" title="미적분학">미적분학</a></li> <li><a href="/wiki/%EC%8B%A4%ED%95%B4%EC%84%9D%ED%95%99" title="실해석학">실해석학</a></li> <li><a href="/wiki/%EB%B3%B5%EC%86%8C%ED%95%B4%EC%84%9D%ED%95%99" title="복소해석학">복소해석학</a></li> <li><a href="/wiki/%EC%88%98%EC%B9%98%ED%95%B4%EC%84%9D%ED%95%99" title="수치해석학">수치해석학</a></li> <li><a href="/wiki/%EC%B8%A1%EB%8F%84%EB%A1%A0" class="mw-redirect" title="측도론">측도론</a></li> <li><a href="/wiki/%ED%95%A8%EC%88%98%ED%95%B4%EC%84%9D%ED%95%99" title="함수해석학">함수해석학</a></li> <li><a href="/wiki/%EC%A1%B0%ED%99%94%ED%95%B4%EC%84%9D%ED%95%99" title="조화해석학">조화해석학</a></li> <li><a href="/wiki/%EB%B9%84%ED%91%9C%EC%A4%80_%ED%95%B4%EC%84%9D%ED%95%99" title="비표준 해석학">비표준 해석학</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EA%B8%B0%ED%95%98%ED%95%99" title="기하학">기하학</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EB%8C%80%EC%88%98%EA%B8%B0%ED%95%98%ED%95%99" title="대수기하학">대수기하학</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0%EA%B8%B0%ED%95%98%ED%95%99" title="계산기하학">계산기하학</a></li> <li><a href="/wiki/%ED%95%B4%EC%84%9D%EA%B8%B0%ED%95%98%ED%95%99" title="해석기하학">해석기하학</a></li> <li><a href="/wiki/%EB%AF%B8%EB%B6%84%EA%B8%B0%ED%95%98%ED%95%99" title="미분기하학">미분기하학</a></li> <li><a href="/wiki/%EB%A6%AC%EB%A7%8C_%EA%B8%B0%ED%95%98%ED%95%99" title="리만 기하학">리만 기하학</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%9C%84%EC%83%81%EC%88%98%ED%95%99" title="위상수학">위상수학</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%9D%BC%EB%B0%98%EC%9C%84%EC%83%81%EC%88%98%ED%95%99" title="일반위상수학">일반위상수학</a></li> <li><a href="/wiki/%EB%8C%80%EC%88%98%EC%A0%81_%EC%9C%84%EC%83%81%EC%88%98%ED%95%99" title="대수적 위상수학">대수적 위상수학</a></li> <li><a href="/wiki/%EB%AF%B8%EB%B6%84%EC%9C%84%EC%83%81%EC%88%98%ED%95%99" title="미분위상수학">미분위상수학</a></li> <li><a href="/wiki/%EB%A7%A4%EB%93%AD_%EC%9D%B4%EB%A1%A0" title="매듭 이론">매듭 이론</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%88%98%ED%95%99%EA%B8%B0%EC%B4%88%EB%A1%A0" title="수학기초론">수학기초론</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%88%98%EB%A6%AC%EB%85%BC%EB%A6%AC%ED%95%99" class="mw-redirect" title="수리논리학">수리논리학</a></li> <li><a href="/wiki/%EB%AA%A8%ED%98%95_%EC%9D%B4%EB%A1%A0" title="모형 이론">모형 이론</a></li> <li><a href="/wiki/%EC%A6%9D%EB%AA%85_%EC%9D%B4%EB%A1%A0" title="증명 이론">증명 이론</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0_%EA%B0%80%EB%8A%A5%EC%84%B1_%EC%9D%B4%EB%A1%A0" title="계산 가능성 이론">계산 가능성 이론</a></li> <li><a class="mw-selflink selflink">집합론</a></li> <li><a href="/wiki/%EB%B2%94%EC%A3%BC%EB%A1%A0" title="범주론">범주론</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%9D%B4%EC%82%B0%EC%88%98%ED%95%99" title="이산수학">이산수학</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EA%B3%84%EC%82%B0_%EC%9D%B4%EB%A1%A0" title="계산 이론">계산 이론</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0_%EB%B3%B5%EC%9E%A1%EB%8F%84_%EC%9D%B4%EB%A1%A0" title="계산 복잡도 이론">계산 복잡도 이론</a></li> <li><a href="/wiki/%EC%95%94%ED%98%B8%ED%95%99" title="암호학">암호학</a></li> <li><a href="/wiki/%EC%A1%B0%ED%95%A9%EB%A1%A0" title="조합론">조합론</a></li> <li><a href="/wiki/%EA%B7%B8%EB%9E%98%ED%94%84_%EC%9D%B4%EB%A1%A0" title="그래프 이론">그래프 이론</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">확률과 통계</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%ED%99%95%EB%A5%A0%EB%A1%A0" title="확률론">확률론</a></li> <li><a href="/wiki/%ED%86%B5%EA%B3%84%ED%95%99" title="통계학">통계학</a></li> <li><a href="/wiki/%ED%99%95%EB%A5%A0%EB%AF%B8%EC%A0%81%EB%B6%84%ED%95%99" title="확률미적분학">확률미적분학</a></li> <li><a href="/wiki/%EA%B2%8C%EC%9E%84_%EC%9D%B4%EB%A1%A0" title="게임 이론">게임 이론</a></li> <li><a href="/wiki/%EA%B2%B0%EC%A0%95%EC%9D%B4%EB%A1%A0" class="mw-redirect" title="결정이론">결정이론</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r38501015"></div><div role="navigation" class="navbox" aria-labelledby="집합론" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r38585741"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-보기"><a href="/wiki/%ED%8B%80:%EC%A7%91%ED%95%A9%EB%A1%A0" title="틀:집합론"><abbr title="이 틀을 보기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-토론"><a href="/wiki/%ED%8B%80%ED%86%A0%EB%A1%A0:%EC%A7%91%ED%95%A9%EB%A1%A0" title="틀토론:집합론"><abbr title="이 틀에 관해 토론하기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-편집"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%AC%B8%EC%84%9C%ED%8E%B8%EC%A7%91/%ED%8B%80:%EC%A7%91%ED%95%A9%EB%A1%A0" title="특수:문서편집/틀:집합론"><abbr title="이 틀을 편집하기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="집합론" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">집합론</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%A7%91%ED%95%A9" title="집합">집합</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%9B%90%EC%86%8C_(%EC%88%98%ED%95%99)" title="원소 (수학)">원소</a></li> <li><a href="/wiki/%EA%B3%B5%EC%A7%91%ED%95%A9" title="공집합">공집합</a></li> <li><a href="/wiki/%ED%95%9C%EC%9B%90%EC%86%8C_%EC%A7%91%ED%95%A9" title="한원소 집합">한원소 집합</a></li> <li><a href="/wiki/%EB%B6%80%EB%B6%84%EC%A7%91%ED%95%A9" title="부분집합">부분집합</a></li> <li><a href="/wiki/%EA%B5%90%EC%A7%91%ED%95%A9" title="교집합">교집합</a></li> <li><a href="/wiki/%ED%95%A9%EC%A7%91%ED%95%A9" title="합집합">합집합</a></li> <li><a href="/wiki/%EC%97%AC%EC%A7%91%ED%95%A9" title="여집합">여집합</a></li> <li><a href="/wiki/%EB%8C%80%EC%B9%AD%EC%B0%A8" title="대칭차">대칭차</a></li> <li><a href="/wiki/%EB%A9%B1%EC%A7%91%ED%95%A9" title="멱집합">멱집합</a></li> <li><a href="/wiki/%EA%B3%B1%EC%A7%91%ED%95%A9" title="곱집합">곱집합</a> <ul><li><a href="/wiki/%EC%88%9C%EC%84%9C%EC%8C%8D" title="순서쌍">순서쌍</a></li></ul></li> <li><a href="/wiki/%EC%9C%A0%ED%95%9C_%EC%A7%91%ED%95%A9" title="유한 집합">유한 집합</a></li> <li><a href="/wiki/%EB%AC%B4%ED%95%9C_%EC%A7%91%ED%95%A9" title="무한 집합">무한 집합</a> <ul><li><a href="/wiki/%EB%AC%B4%ED%95%9C_%EA%B3%B5%EB%A6%AC" title="무한 공리">무한 공리</a></li></ul></li> <li><a href="/wiki/%EA%B0%80%EC%82%B0_%EC%A7%91%ED%95%A9" title="가산 집합">가산 집합</a></li> <li><a href="/wiki/%EB%93%9C_%EB%AA%A8%EB%A5%B4%EA%B0%84%EC%9D%98_%EB%B2%95%EC%B9%99" title="드 모르간의 법칙">드 모르간의 법칙</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%ED%95%A8%EC%88%98" title="함수">함수</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%A0%95%EC%9D%98%EC%97%AD" title="정의역">정의역</a></li> <li><a href="/wiki/%EA%B3%B5%EC%97%AD" title="공역">공역</a></li> <li><a href="/wiki/%EC%B9%98%EC%97%AD" title="치역">치역</a></li> <li><a href="/wiki/%EC%83%81_(%EC%88%98%ED%95%99)" title="상 (수학)">상</a></li> <li><a href="/wiki/%EC%A0%84%EC%82%AC_%ED%95%A8%EC%88%98" title="전사 함수">전사 함수</a></li> <li><a href="/wiki/%EB%8B%A8%EC%82%AC_%ED%95%A8%EC%88%98" title="단사 함수">단사 함수</a></li> <li><a href="/wiki/%EC%A0%84%EB%8B%A8%EC%82%AC_%ED%95%A8%EC%88%98" title="전단사 함수">전단사 함수</a></li> <li><a href="/wiki/%EB%8B%A4%EA%B0%80_%ED%95%A8%EC%88%98" title="다가 함수">다가 함수</a></li> <li><a href="/wiki/%EC%97%AD%ED%95%A8%EC%88%98" title="역함수">역함수</a></li> <li><a href="/wiki/%ED%95%AD%EB%93%B1_%ED%95%A8%EC%88%98" title="항등 함수">항등 함수</a></li> <li><a href="/wiki/%EC%83%81%EC%88%98_%ED%95%A8%EC%88%98" title="상수 함수">상수 함수</a></li> <li><a href="/wiki/%EC%A7%80%EC%8B%9C_%ED%95%A8%EC%88%98" title="지시 함수">지시 함수</a></li> <li><a href="/wiki/%ED%95%A8%EC%88%98%EC%9D%98_%ED%95%A9%EC%84%B1" title="함수의 합성">함수의 합성</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EA%B8%B0%EC%88%98_(%EC%88%98%ED%95%99)" title="기수 (수학)">기수</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%A7%91%ED%95%A9%EC%9D%98_%ED%81%AC%EA%B8%B0" title="집합의 크기">집합의 크기</a></li> <li><a href="/wiki/%EC%B9%B8%ED%86%A0%EC%96%B4%EC%9D%98_%EC%A0%95%EB%A6%AC" title="칸토어의 정리">칸토어의 정리</a> <ul><li><a href="/wiki/%EB%8C%80%EA%B0%81%EC%84%A0_%EB%85%BC%EB%B2%95" title="대각선 논법">대각선 논법</a></li></ul></li> <li><a href="/wiki/%EC%95%8C%EB%A0%88%ED%94%84_%EC%88%98" title="알레프 수">알레프 수</a></li> <li><a href="/wiki/%EB%B2%A0%ED%8A%B8_%EC%88%98" title="베트 수">베트 수</a></li> <li><a href="/wiki/%EA%B7%B9%ED%95%9C_%EA%B8%B0%EC%88%98" title="극한 기수">극한 기수</a></li> <li><a href="/wiki/%EA%B8%B0%EB%A9%9C_%ED%95%A8%EC%88%98" title="기멜 함수">기멜 함수</a></li> <li><a href="/wiki/%EA%B0%80%EB%8A%A5_%EA%B3%B5%EC%A2%85%EB%8F%84" title="가능 공종도">가능 공종도</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%88%9C%EC%84%9C%EC%88%98" title="순서수">순서수</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%A0%95%EB%A0%AC_%EC%88%9C%EC%84%9C" class="mw-redirect" title="정렬 순서">정렬 순서</a></li> <li><a href="/wiki/%EC%B4%88%ED%95%9C%EA%B7%80%EB%82%A9%EB%B2%95" class="mw-redirect" title="초한귀납법">초한귀납법</a></li> <li><a href="/wiki/%EA%B3%B5%EC%A2%85%EB%8F%84" title="공종도">공종도</a> <ul><li><a href="/wiki/%EC%BE%A8%EB%8B%88%EA%B7%B8%EC%9D%98_%EC%A0%95%EB%A6%AC_(%EC%A7%91%ED%95%A9%EB%A1%A0)" title="쾨니그의 정리 (집합론)">쾨니그의 정리</a></li></ul></li> <li><a href="/wiki/%ED%95%98%EB%A5%B4%ED%86%A1%EC%8A%A4_%EC%88%98" title="하르톡스 수">하르톡스 수</a></li> <li><a href="/wiki/%EC%A0%95%EA%B7%9C_%ED%95%A8%EC%88%98" title="정규 함수">정규 함수</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">역설의 해소</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%86%8C%EB%B0%95%ED%95%9C_%EC%A7%91%ED%95%A9%EB%A1%A0" title="소박한 집합론">소박한 집합론</a></li> <li><a href="/wiki/%EB%9F%AC%EC%85%80%EC%9D%98_%EC%97%AD%EC%84%A4" title="러셀의 역설">러셀의 역설</a></li> <li><a href="/wiki/%EC%B9%B8%ED%86%A0%EC%96%B4_%EC%97%AD%EC%84%A4" title="칸토어 역설">칸토어 역설</a></li> <li><a href="/wiki/%EB%B6%80%EB%9E%84%EB%A6%AC%ED%8F%AC%EB%A5%B4%ED%8B%B0_%EC%97%AD%EC%84%A4" title="부랄리포르티 역설">부랄리포르티 역설</a></li> <li><a href="/wiki/%EB%AA%A8%EC%9E%84_(%EC%A7%91%ED%95%A9%EB%A1%A0)" title="모임 (집합론)">모임</a></li> <li><a href="/wiki/%EC%9C%A0%ED%98%95_%EC%9D%B4%EB%A1%A0" title="유형 이론">유형 이론</a> <ul><li>《<a href="/wiki/%EC%88%98%ED%95%99_%EC%9B%90%EB%A6%AC" title="수학 원리">수학 원리</a>》</li></ul></li> <li><a href="/wiki/%EC%B2%B4%EB%A5%B4%EB%A9%9C%EB%A1%9C-%ED%94%84%EB%A0%9D%EC%BC%88_%EC%A7%91%ED%95%A9%EB%A1%A0" title="체르멜로-프렝켈 집합론">체르멜로-프렝켈 집합론</a></li> <li><a href="/wiki/%EC%83%88_%EA%B8%B0%EC%B4%88" title="새 기초">새 기초</a></li> <li><a href="/wiki/%ED%8F%B0_%EB%85%B8%EC%9D%B4%EB%A7%8C-%EB%B2%A0%EB%A5%B4%EB%82%98%EC%9D%B4%EC%8A%A4-%EA%B4%B4%EB%8D%B8_%EC%A7%91%ED%95%A9%EB%A1%A0" title="폰 노이만-베르나이스-괴델 집합론">폰 노이만-베르나이스-괴델 집합론</a></li> <li><a href="/w/index.php?title=%EB%AA%A8%EC%8A%A4-%EC%BC%88%EB%A6%AC_%EC%A7%91%ED%95%A9%EB%A1%A0&action=edit&redlink=1" class="new" title="모스-켈리 집합론 (없는 문서)">모스-켈리 집합론</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%84%A0%ED%83%9D_%EA%B3%B5%EB%A6%AC" title="선택 공리">선택 공리</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EA%B0%80%EC%82%B0_%EC%84%A0%ED%83%9D_%EA%B3%B5%EB%A6%AC" class="mw-redirect" title="가산 선택 공리">가산 선택 공리</a></li> <li><a href="/wiki/%EC%9D%98%EC%A1%B4%EC%A0%81_%EC%84%A0%ED%83%9D_%EA%B3%B5%EB%A6%AC" class="mw-redirect" title="의존적 선택 공리">의존적 선택 공리</a></li> <li><a href="/wiki/%EC%B4%88%EB%A5%B8_%EB%B3%B4%EC%A1%B0%EC%A0%95%EB%A6%AC" title="초른 보조정리">초른 보조정리</a></li> <li><a href="/wiki/%EC%8A%88%ED%95%84%EB%9D%BC%EC%9D%B8_%ED%99%95%EC%9E%A5%EC%A0%95%EB%A6%AC" title="슈필라인 확장정리">슈필라인 확장정리</a></li> <li><a href="/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">바나흐-타르스키 역설</a></li> <li><a href="/wiki/%ED%8B%B0%ED%98%B8%EB%85%B8%ED%94%84_%EC%A0%95%EB%A6%AC" title="티호노프 정리">티호노프 정리</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">집합론의 <a href="/wiki/%EB%AA%A8%ED%98%95_%EC%9D%B4%EB%A1%A0" title="모형 이론">모형</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EA%B5%AC%EC%84%B1_%EA%B0%80%EB%8A%A5_%EC%A0%84%EC%B2%B4" title="구성 가능 전체">구성 가능 전체</a></li> <li><a href="/wiki/%EC%B6%94%EC%9D%B4%EC%A0%81_%EC%A7%91%ED%95%A9" title="추이적 집합">추이적 집합</a></li> <li><a href="/wiki/%EC%B6%94%EC%9D%B4%EC%A0%81_%EB%AA%A8%ED%98%95" title="추이적 모형">추이적 모형</a></li> <li><a href="/wiki/%EC%88%9C%EC%84%9C%EC%88%98_%EC%A0%95%EC%9D%98_%EA%B0%80%EB%8A%A5_%EC%A7%91%ED%95%A9" title="순서수 정의 가능 집합">순서수 정의 가능 집합</a></li> <li><a href="/wiki/%EA%B0%95%EC%A0%9C%EB%B2%95" title="강제법">강제법</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%ED%81%B0_%EA%B8%B0%EC%88%98" title="큰 기수">큰 기수</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EB%8F%84%EB%8B%AC_%EB%B6%88%EA%B0%80%EB%8A%A5%ED%95%9C_%EA%B8%B0%EC%88%98" title="도달 불가능한 기수">도달 불가능한 기수</a></li> <li><a href="/wiki/%EA%B0%80%EC%B8%A1_%EA%B8%B0%EC%88%98" title="가측 기수">가측 기수</a></li> <li><a href="/wiki/%EC%95%BD%EC%BD%A4%ED%8C%A9%ED%8A%B8_%EA%B8%B0%EC%88%98" title="약콤팩트 기수">약콤팩트 기수</a></li> <li><a href="/wiki/%EA%B0%95%EC%BD%A4%ED%8C%A9%ED%8A%B8_%EA%B8%B0%EC%88%98" title="강콤팩트 기수">강콤팩트 기수</a></li> <li><a href="/wiki/%EC%B4%88%EC%BD%A4%ED%8C%A9%ED%8A%B8_%EA%B8%B0%EC%88%98" title="초콤팩트 기수">초콤팩트 기수</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%B2%B4%EB%A5%B4%EB%A9%9C%EB%A1%9C-%ED%94%84%EB%A0%9D%EC%BC%88_%EC%A7%91%ED%95%A9%EB%A1%A0" title="체르멜로-프렝켈 집합론">ZF</a>와 독립된 명제</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%97%B0%EC%86%8D%EC%B2%B4_%EA%B0%80%EC%84%A4" title="연속체 가설">연속체 가설</a></li> <li><a href="/wiki/%ED%8A%B9%EC%9D%B4_%EA%B8%B0%EC%88%98_%EA%B0%80%EC%84%A4" title="특이 기수 가설">특이 기수 가설</a></li> <li><a href="/wiki/%EC%88%98%EC%8A%AC%EB%A6%B0_%EA%B0%80%EC%84%A4" class="mw-redirect" title="수슬린 가설">수슬린 가설</a></li> <li><a href="/wiki/%ED%99%94%EC%9D%B4%ED%8A%B8%ED%97%A4%EB%93%9C_%EB%AC%B8%EC%A0%9C" title="화이트헤드 문제">화이트헤드 문제</a></li> <li><a href="/wiki/%EA%B2%B0%EC%A0%95_%EC%A7%91%ED%95%A9" title="결정 집합">결정 공리</a></li> <li><a href="/wiki/%EB%A7%88%ED%8B%B4_%EA%B3%B5%EB%A6%AC" title="마틴 공리">마틴 공리</a></li> <li><a href="/wiki/%EB%8B%A4%EC%9D%B4%EC%95%84%EB%AA%AC%EB%93%9C_%EC%9B%90%EB%A6%AC" class="mw-redirect" title="다이아몬드 원리">다이아몬드 원리</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r38501015"></div><div role="navigation" class="navbox" aria-labelledby="컴퓨터_과학의_주요_분야" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r38585741"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-보기"><a href="/wiki/%ED%8B%80:%EC%BB%B4%ED%93%A8%ED%84%B0_%EA%B3%BC%ED%95%99" title="틀:컴퓨터 과학"><abbr title="이 틀을 보기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-토론"><a href="/wiki/%ED%8B%80%ED%86%A0%EB%A1%A0:%EC%BB%B4%ED%93%A8%ED%84%B0_%EA%B3%BC%ED%95%99" title="틀토론:컴퓨터 과학"><abbr title="이 틀에 관해 토론하기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-편집"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%AC%B8%EC%84%9C%ED%8E%B8%EC%A7%91/%ED%8B%80:%EC%BB%B4%ED%93%A8%ED%84%B0_%EA%B3%BC%ED%95%99" title="특수:문서편집/틀:컴퓨터 과학"><abbr title="이 틀을 편집하기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="컴퓨터_과학의_주요_분야" style="font-size:114%;margin:0 4em"><a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%EA%B3%BC%ED%95%99" title="컴퓨터 과학">컴퓨터 과학</a>의 주요 분야</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%88%98%ED%95%99" title="수학">수학적 기초</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%88%98%EB%A6%AC%EB%85%BC%EB%A6%AC%ED%95%99" class="mw-redirect" title="수리논리학">수리논리학</a></li> <li><a class="mw-selflink selflink">집합론</a></li> <li><a href="/wiki/%EC%A0%95%EC%88%98%EB%A1%A0" class="mw-redirect" title="정수론">정수론</a></li> <li><a href="/wiki/%EA%B7%B8%EB%9E%98%ED%94%84_%EC%9D%B4%EB%A1%A0" title="그래프 이론">그래프 이론</a></li> <li><a href="/wiki/%EC%9C%A0%ED%98%95_%EC%9D%B4%EB%A1%A0" title="유형 이론">유형 이론</a></li> <li><a href="/wiki/%EB%B2%94%EC%A3%BC%EB%A1%A0" title="범주론">범주론</a></li> <li><a href="/wiki/%EC%88%98%EC%B9%98%ED%95%B4%EC%84%9D%ED%95%99" title="수치해석학">수치해석학</a></li> <li><a href="/wiki/%EC%9D%B4%EC%82%B0%EC%88%98%ED%95%99" title="이산수학">이산수학</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EA%B3%84%EC%82%B0_%EC%9D%B4%EB%A1%A0" title="계산 이론">계산 이론</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%98%A4%ED%86%A0%EB%A7%88%ED%83%80_%EC%9D%B4%EB%A1%A0" title="오토마타 이론">오토마타 이론</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0_%EA%B0%80%EB%8A%A5%EC%84%B1_%EC%9D%B4%EB%A1%A0" title="계산 가능성 이론">계산 가능성 이론</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0_%EB%B3%B5%EC%9E%A1%EB%8F%84_%EC%9D%B4%EB%A1%A0" title="계산 복잡도 이론">계산 복잡도 이론</a></li> <li><a href="/wiki/%EC%96%91%EC%9E%90%EC%BB%B4%ED%93%A8%ED%84%B0" class="mw-redirect" title="양자컴퓨터">양자 계산 이론</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98" title="알고리즘">알고리즘</a> & <a href="/wiki/%EC%9E%90%EB%A3%8C_%EA%B5%AC%EC%A1%B0" title="자료 구조">자료 구조</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98" title="알고리즘">알고리즘</a></li> <li><a href="/wiki/%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98_%EC%84%A4%EA%B3%84" title="알고리즘 설계">알고리즘 설계</a></li> <li><a href="/wiki/%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98_%ED%95%B4%EC%84%9D" class="mw-redirect" title="알고리즘 해석">알고리즘 해석</a></li> <li><a href="/wiki/%EC%9E%90%EB%A3%8C_%EA%B5%AC%EC%A1%B0" title="자료 구조">자료 구조</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0%EA%B8%B0%ED%95%98%ED%95%99" title="계산기하학">계산기하학</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%ED%94%84%EB%A1%9C%EA%B7%B8%EB%9E%98%EB%B0%8D_%EC%96%B8%EC%96%B4" title="프로그래밍 언어">프로그래밍 언어</a> & <a href="/wiki/%EC%BB%B4%ED%8C%8C%EC%9D%BC%EB%9F%AC" title="컴파일러">컴파일러</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EA%B5%AC%EB%AC%B8_%EB%B6%84%EC%84%9D" title="구문 분석">구문 분석</a></li> <li><a href="/wiki/%EC%BB%B4%ED%8C%8C%EC%9D%BC%EB%9F%AC" title="컴파일러">컴파일러</a></li> <li><a href="/wiki/%EC%9D%B8%ED%84%B0%ED%94%84%EB%A6%AC%ED%84%B0" title="인터프리터">인터프리터</a></li> <li><a href="/wiki/%ED%94%84%EB%A1%9C%EA%B7%B8%EB%9E%98%EB%B0%8D_%EC%96%B8%EC%96%B4" title="프로그래밍 언어">프로그래밍 언어</a></li> <li><a href="/wiki/%EA%B5%AC%EC%A1%B0%EC%A0%81_%ED%94%84%EB%A1%9C%EA%B7%B8%EB%9E%98%EB%B0%8D" title="구조적 프로그래밍">구조적 프로그래밍</a></li> <li><a href="/wiki/%EA%B0%9D%EC%B2%B4_%EC%A7%80%ED%96%A5_%ED%94%84%EB%A1%9C%EA%B7%B8%EB%9E%98%EB%B0%8D" title="객체 지향 프로그래밍">객체 지향 프로그래밍</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EB%B3%91%EB%A0%AC_%EC%BB%B4%ED%93%A8%ED%8C%85" title="병렬 컴퓨팅">병렬</a> & <a href="/wiki/%EB%B6%84%EC%82%B0_%EC%BB%B4%ED%93%A8%ED%8C%85" title="분산 컴퓨팅">분산 시스템</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EB%B3%91%EB%A0%AC_%EC%BB%B4%ED%93%A8%ED%8C%85" title="병렬 컴퓨팅">병렬 컴퓨팅</a></li> <li><a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%ED%81%B4%EB%9F%AC%EC%8A%A4%ED%84%B0" title="컴퓨터 클러스터">컴퓨터 클러스터</a></li> <li><a href="/wiki/%EB%B6%84%EC%82%B0_%EC%BB%B4%ED%93%A8%ED%8C%85" title="분산 컴퓨팅">분산 컴퓨팅</a></li> <li><a href="/wiki/%EA%B7%B8%EB%A6%AC%EB%93%9C_%EC%BB%B4%ED%93%A8%ED%8C%85" title="그리드 컴퓨팅">그리드 컴퓨팅</a></li> <li><a href="/wiki/%ED%81%B4%EB%9D%BC%EC%9A%B0%EB%93%9C_%EC%BB%B4%ED%93%A8%ED%8C%85" title="클라우드 컴퓨팅">클라우드 컴퓨팅</a></li> <li><a href="/wiki/%EC%84%9C%EB%B9%84%EC%8A%A4%ED%98%95_%EC%9D%B8%ED%94%84%EB%9D%BC%EC%8A%A4%ED%8A%B8%EB%9F%AD%EC%B2%98" title="서비스형 인프라스트럭처">IaaS</a></li> <li><a href="/wiki/%EC%84%9C%EB%B9%84%EC%8A%A4%ED%98%95_%ED%94%8C%EB%9E%AB%ED%8F%BC" title="서비스형 플랫폼">PaaS</a></li> <li><a href="/wiki/%EC%84%9C%EB%B9%84%EC%8A%A4%ED%98%95_%EC%86%8C%ED%94%84%ED%8A%B8%EC%9B%A8%EC%96%B4" title="서비스형 소프트웨어">SaaS</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%86%8C%ED%94%84%ED%8A%B8%EC%9B%A8%EC%96%B4_%EA%B3%B5%ED%95%99" title="소프트웨어 공학">소프트웨어 공학</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%9A%94%EA%B5%AC%EC%82%AC%ED%95%AD_%EB%B6%84%EC%84%9D" title="요구사항 분석">요구 분석</a></li> <li><a href="/wiki/%EC%86%8C%ED%94%84%ED%8A%B8%EC%9B%A8%EC%96%B4_%EC%84%A4%EA%B3%84" title="소프트웨어 설계">소프트웨어 설계</a></li> <li><a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%ED%94%84%EB%A1%9C%EA%B7%B8%EB%9E%98%EB%B0%8D" title="컴퓨터 프로그래밍">컴퓨터 프로그래밍</a></li> <li><a href="/wiki/%EC%A0%95%ED%98%95_%EA%B8%B0%EB%B2%95" title="정형 기법">정형 기법</a></li> <li><a href="/wiki/%EC%86%8C%ED%94%84%ED%8A%B8%EC%9B%A8%EC%96%B4_%ED%85%8C%EC%8A%A4%ED%8A%B8" title="소프트웨어 테스트">소프트웨어 테스트</a></li> <li><a href="/wiki/%EC%86%8C%ED%94%84%ED%8A%B8%EC%9B%A8%EC%96%B4_%EA%B0%9C%EB%B0%9C" title="소프트웨어 개발">소프트웨어 개발</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%8B%9C%EC%8A%A4%ED%85%9C_%EC%95%84%ED%82%A4%ED%85%8D%EC%B2%98" title="시스템 아키텍처">시스템 아키텍처</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%EA%B5%AC%EC%A1%B0" title="컴퓨터 구조">컴퓨터 아키텍처</a></li> <li><a href="/wiki/%EB%A7%88%EC%9D%B4%ED%81%AC%EB%A1%9C%EC%95%84%ED%82%A4%ED%85%8D%EC%B2%98" title="마이크로아키텍처">마이크로아키텍처</a></li> <li><a href="/wiki/%EC%9A%B4%EC%98%81_%EC%B2%B4%EC%A0%9C" class="mw-redirect" title="운영 체제">운영 체제</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%ED%86%B5%EC%8B%A0" title="통신">통신</a> & <a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%EB%84%A4%ED%8A%B8%EC%9B%8C%ED%81%AC" class="mw-redirect" title="컴퓨터 네트워크">네트워크</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%EC%98%A4%EB%94%94%EC%98%A4" class="mw-disambig" title="컴퓨터 오디오">컴퓨터 오디오</a></li> <li><a href="/wiki/%EB%9D%BC%EC%9A%B0%ED%8C%85" title="라우팅">라우팅</a></li> <li><a href="/wiki/%EB%84%A4%ED%8A%B8%EC%9B%8C%ED%81%AC_%ED%86%A0%ED%8F%B4%EB%A1%9C%EC%A7%80" title="네트워크 토폴로지">네트워크 토폴로지</a></li> <li><a href="/wiki/%EC%95%94%ED%98%B8%ED%95%99" title="암호학">암호학</a></li> <li><a href="/wiki/%EC%B0%A8%EC%84%B8%EB%8C%80_%ED%86%B5%EC%8B%A0%EB%A7%9D" title="차세대 통신망">차세대 통신망</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EB%8D%B0%EC%9D%B4%ED%84%B0%EB%B2%A0%EC%9D%B4%EC%8A%A4" title="데이터베이스">데이터베이스</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EB%8D%B0%EC%9D%B4%ED%84%B0_%EB%A7%88%EC%9D%B4%EB%8B%9D" title="데이터 마이닝">데이터 마이닝</a></li> <li><a href="/wiki/%EA%B4%80%EA%B3%84%ED%98%95_%EB%8D%B0%EC%9D%B4%ED%84%B0%EB%B2%A0%EC%9D%B4%EC%8A%A4" title="관계형 데이터베이스">RDBMS</a></li> <li><a href="/wiki/SQL" title="SQL">SQL</a></li> <li><a href="/wiki/NoSQL" title="NoSQL">NoSQL</a></li> <li><a href="/wiki/%EC%98%A4%EB%9D%BC%ED%81%B4_%EB%8D%B0%EC%9D%B4%ED%84%B0%EB%B2%A0%EC%9D%B4%EC%8A%A4" title="오라클 데이터베이스">오라클 데이터베이스</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%9D%B8%EA%B3%B5%EC%A7%80%EB%8A%A5" title="인공지능">인공지능</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%9E%90%EB%8F%99%ED%99%94%EB%90%9C_%EC%B6%94%EB%A1%A0" title="자동화된 추론">자동화된 추론</a></li> <li><a href="/wiki/%EC%A0%84%EC%82%B0%EC%96%B8%EC%96%B4%ED%95%99" title="전산언어학">전산언어학</a></li> <li><a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%EB%B9%84%EC%A0%84" title="컴퓨터 비전">컴퓨터 비전</a></li> <li><a href="/wiki/%EC%A7%84%ED%99%94_%EC%97%B0%EC%82%B0" title="진화 연산">진화 연산</a></li> <li><a href="/wiki/%EA%B8%B0%EA%B3%84_%ED%95%99%EC%8A%B5" title="기계 학습">기계 학습</a></li> <li><a href="/wiki/%EC%9E%90%EC%97%B0_%EC%96%B8%EC%96%B4_%EC%B2%98%EB%A6%AC" class="mw-redirect" title="자연 언어 처리">자연 언어 처리</a></li> <li><a href="/wiki/%EB%A1%9C%EB%B4%87%EA%B3%B5%ED%95%99" title="로봇공학">로봇학</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%EA%B7%B8%EB%9E%98%ED%94%BD" class="mw-redirect" title="컴퓨터 그래픽">컴퓨터 그래픽</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%8B%9C%EA%B0%81%ED%99%94" class="mw-disambig" title="시각화">시각화</a></li> <li><a href="/wiki/%EC%98%81%EC%83%81_%EC%B2%98%EB%A6%AC" title="영상 처리">영상 처리</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%9D%B8%EA%B0%84%EA%B3%BC_%EC%BB%B4%ED%93%A8%ED%84%B0_%EC%83%81%ED%98%B8_%EC%9E%91%EC%9A%A9" class="mw-redirect" title="인간과 컴퓨터 상호 작용">인간과 컴퓨터 상호 작용</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%BB%B4%ED%93%A8%ED%84%B0_%EC%A0%91%EA%B7%BC%EC%84%B1" title="컴퓨터 접근성">컴퓨터 접근성</a></li> <li><a href="/wiki/%EC%82%AC%EC%9A%A9%EC%9E%90_%EC%9D%B8%ED%84%B0%ED%8E%98%EC%9D%B4%EC%8A%A4" title="사용자 인터페이스">사용자 인터페이스</a></li> <li><a href="/wiki/%EC%B0%A9%EC%9A%A9_%EC%BB%B4%ED%93%A8%ED%84%B0" title="착용 컴퓨터">착용 컴퓨터</a></li> <li><a href="/wiki/%EC%9C%A0%EB%B9%84%EC%BF%BC%ED%84%B0%EC%8A%A4_%EC%BB%B4%ED%93%A8%ED%8C%85" title="유비쿼터스 컴퓨팅">유비쿼터스 컴퓨팅</a></li> <li><a href="/wiki/%EA%B0%80%EC%83%81%ED%98%84%EC%8B%A4" class="mw-redirect" title="가상현실">가상현실</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EA%B3%84%EC%82%B0%EA%B3%BC%ED%95%99" title="계산과학">계산과학</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%9D%B8%EA%B3%B5%EC%83%9D%EB%AA%85" title="인공생명">인공생명</a></li> <li><a href="/wiki/%EC%83%9D%EB%AC%BC%EC%A0%95%EB%B3%B4%ED%95%99" title="생물정보학">생물정보학</a></li> <li><a href="/wiki/%EC%9D%B8%EC%A7%80%EA%B3%BC%ED%95%99" class="mw-redirect" title="인지과학">인지과학</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0%ED%99%94%ED%95%99" title="계산화학">계산화학</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0%EC%8B%A0%EA%B2%BD%EA%B3%BC%ED%95%99" title="계산신경과학">계산신경과학</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0%EB%AC%BC%EB%A6%AC%ED%95%99" title="계산물리학">계산물리학</a></li> <li><a href="/wiki/%EC%88%98%EC%B9%98%ED%95%B4%EC%84%9D%ED%95%99" title="수치해석학">수치해석학</a></li> <li><a href="/wiki/%EA%B8%B0%ED%98%B8%EA%B3%84%EC%82%B0" title="기호계산">기호계산</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%EC%A0%95%EB%B3%B4%EB%B3%B4%ED%98%B8" class="mw-redirect" title="정보보호">정보보호</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%95%94%ED%98%B8%ED%95%99" title="암호학">암호학</a></li> <li><a href="/wiki/%EB%AC%BC%EB%A6%AC_%EB%B3%B4%EC%95%88" title="물리 보안">물리 보안</a></li> <li><a href="/wiki/%EC%95%A0%ED%94%8C%EB%A6%AC%EC%BC%80%EC%9D%B4%EC%85%98_%EB%B3%B4%EC%95%88" title="애플리케이션 보안">애플리케이션 보안</a></li> <li><a href="/wiki/%EC%9D%B8%ED%84%B0%EB%84%B7_%EB%B3%B4%EC%95%88" title="인터넷 보안">인터넷 보안</a></li> <li><a href="/wiki/%EB%84%A4%ED%8A%B8%EC%9B%8C%ED%81%AC_%EB%B3%B4%EC%95%88" title="네트워크 보안">네트워크 보안</a></li> <li><a href="/wiki/%ED%95%B4%ED%82%B9" title="해킹">해킹</a></li> <li><a href="/wiki/%EC%86%8C%ED%94%84%ED%8A%B8%EC%9B%A8%EC%96%B4_%ED%81%AC%EB%9E%98%ED%82%B9" title="소프트웨어 크래킹">크래킹</a></li></ul> </div></td></tr></tbody></table></div> <div 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