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class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目次" 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">目次</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">非表示</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">ページ先頭</div> </a> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>参考文献</span> </div> </a> <ul id="toc-参考文献-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-関連項目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#関連項目"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>関連項目</span> </div> </a> <ul id="toc-関連項目-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部リンク" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部リンク"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>外部リンク</span> </div> </a> <ul id="toc-外部リンク-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="目次" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="目次の表示・非表示を切り替え" > <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">目次の表示・非表示を切り替え</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">反対称関係</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="特定の記事の別の言語版に移動します。利用可能な言語29件" > <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-29" 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">29の言語版</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D9%84%D8%A7%D9%82%D8%A9_%D8%B6%D8%AF_%D8%AA%D9%86%D8%A7%D8%B8%D8%B1%D9%8A%D8%A9" title="アラビア語: علاقة ضد تناظرية" lang="ar" hreflang="ar" data-title="علاقة ضد تناظرية" data-language-autonym="العربية" data-language-local-name="アラビア語" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Relaci%C3%B3_antisim%C3%A8trica" title="カタロニア語: Relació antisimètrica" lang="ca" hreflang="ca" data-title="Relació antisimètrica" data-language-autonym="Català" data-language-local-name="カタロニア語" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Antisymetrick%C3%A1_relace" title="チェコ語: Antisymetrická relace" lang="cs" hreflang="cs" data-title="Antisymetrická relace" data-language-autonym="Čeština" data-language-local-name="チェコ語" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Antisymmetrische_Relation" title="ドイツ語: Antisymmetrische Relation" lang="de" hreflang="de" data-title="Antisymmetrische Relation" data-language-autonym="Deutsch" data-language-local-name="ドイツ語" 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%91%CE%BD%CF%84%CE%B9%CF%83%CF%85%CE%BC%CE%BC%CE%B5%CF%84%CF%81%CE%B9%CE%BA%CE%AE_%CF%83%CF%87%CE%AD%CF%83%CE%B7" title="ギリシャ語: Αντισυμμετρική σχέση" lang="el" hreflang="el" data-title="Αντισυμμετρική σχέση" data-language-autonym="Ελληνικά" data-language-local-name="ギリシャ語" 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/Antisymmetric_relation" title="英語: Antisymmetric relation" lang="en" hreflang="en" data-title="Antisymmetric relation" data-language-autonym="English" data-language-local-name="英語" 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/Antisimetria_rilato" title="エスペラント語: Antisimetria rilato" lang="eo" hreflang="eo" data-title="Antisimetria rilato" data-language-autonym="Esperanto" data-language-local-name="エスペラント語" 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/Relaci%C3%B3n_antisim%C3%A9trica" title="スペイン語: Relación antisimétrica" lang="es" hreflang="es" data-title="Relación antisimétrica" data-language-autonym="Español" data-language-local-name="スペイン語" 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/Antis%C3%BCmmeetriline_seos" title="エストニア語: Antisümmeetriline seos" lang="et" hreflang="et" data-title="Antisümmeetriline seos" data-language-autonym="Eesti" data-language-local-name="エストニア語" 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/Antisimetria-erlazio" title="バスク語: Antisimetria-erlazio" lang="eu" hreflang="eu" data-title="Antisimetria-erlazio" data-language-autonym="Euskara" data-language-local-name="バスク語" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D9%BE%D8%A7%D8%AF%D9%85%D8%AA%D9%82%D8%A7%D8%B1%D9%86" title="ペルシア語: رابطه پادمتقارن" lang="fa" hreflang="fa" data-title="رابطه پادمتقارن" data-language-autonym="فارسی" data-language-local-name="ペルシア語" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Relation_antisym%C3%A9trique" title="フランス語: Relation antisymétrique" lang="fr" hreflang="fr" data-title="Relation antisymétrique" data-language-autonym="Français" data-language-local-name="フランス語" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl badge-Q70894304 mw-list-item" title=""><a href="https://gl.wikipedia.org/wiki/Relaci%C3%B3n_antisim%C3%A9trica" title="ガリシア語: Relación antisimétrica" lang="gl" hreflang="gl" data-title="Relación antisimétrica" data-language-autonym="Galego" data-language-local-name="ガリシア語" 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%99%D7%97%D7%A1_%D7%90%D7%A0%D7%98%D7%99-%D7%A1%D7%99%D7%9E%D7%98%D7%A8%D7%99" title="ヘブライ語: יחס אנטי-סימטרי" lang="he" hreflang="he" data-title="יחס אנטי-סימטרי" data-language-autonym="עברית" data-language-local-name="ヘブライ語" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Antisimetri%C4%8Dna_relacija" title="クロアチア語: Antisimetrična relacija" lang="hr" hreflang="hr" data-title="Antisimetrična relacija" data-language-autonym="Hrvatski" data-language-local-name="クロアチア語" 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/Antiszimmetrikus_rel%C3%A1ci%C3%B3" title="ハンガリー語: Antiszimmetrikus reláció" lang="hu" hreflang="hu" data-title="Antiszimmetrikus reláció" data-language-autonym="Magyar" data-language-local-name="ハンガリー語" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%BD%D1%82%D0%B8%D1%81%D0%B8%D0%BC%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D2%9B%D0%B0%D1%82%D1%8B%D0%BD%D0%B0%D1%81" title="カザフ語: Антисимметриялық қатынас" lang="kk" hreflang="kk" data-title="Антисимметриялық қатынас" data-language-autonym="Қазақша" data-language-local-name="カザフ語" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%98%EB%8C%80%EC%B9%AD%EA%B4%80%EA%B3%84" title="韓国語: 반대칭관계" lang="ko" hreflang="ko" data-title="반대칭관계" data-language-autonym="한국어" data-language-local-name="韓国語" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-no badge-Q70894304 mw-list-item" title=""><a href="https://no.wikipedia.org/wiki/Antisymmetrisk_relasjon" title="ノルウェー語(ブークモール): Antisymmetrisk relasjon" lang="nb" hreflang="nb" data-title="Antisymmetrisk relasjon" data-language-autonym="Norsk bokmål" data-language-local-name="ノルウェー語(ブークモール)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Relacja_antysymetryczna" title="ポーランド語: Relacja antysymetryczna" lang="pl" hreflang="pl" data-title="Relacja antysymetryczna" data-language-autonym="Polski" data-language-local-name="ポーランド語" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Rela%C3%A7%C3%A3o_antissim%C3%A9trica" title="ポルトガル語: Relação antissimétrica" lang="pt" hreflang="pt" data-title="Relação antissimétrica" data-language-autonym="Português" data-language-local-name="ポルトガル語" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BD%D1%82%D0%B8%D1%81%D0%B8%D0%BC%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D0%B5_%D0%BE%D1%82%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%B8%D0%B5" title="ロシア語: Антисимметричное отношение" lang="ru" hreflang="ru" data-title="Антисимметричное отношение" data-language-autonym="Русский" data-language-local-name="ロシア語" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Antisymetrick%C3%A1_rel%C3%A1cia" title="スロバキア語: Antisymetrická relácia" lang="sk" hreflang="sk" data-title="Antisymetrická relácia" data-language-autonym="Slovenčina" data-language-local-name="スロバキア語" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Antisymmetrisk_relation" title="スウェーデン語: Antisymmetrisk relation" lang="sv" hreflang="sv" data-title="Antisymmetrisk relation" data-language-autonym="Svenska" data-language-local-name="スウェーデン語" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8E%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AF%8D%E0%AE%9A%E0%AE%AE%E0%AE%9A%E0%AF%8D%E0%AE%9A%E0%AF%80%E0%AE%B0%E0%AF%8D_%E0%AE%89%E0%AE%B1%E0%AE%B5%E0%AF%81" title="タミル語: எதிர்சமச்சீர் உறவு" lang="ta" hreflang="ta" data-title="எதிர்சமச்சீர் உறவு" data-language-autonym="தமிழ்" data-language-local-name="タミル語" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BD%D1%82%D0%B8%D1%81%D0%B8%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B5_%D0%B2%D1%96%D0%B4%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%BD%D1%8F" title="ウクライナ語: Антисиметричне відношення" lang="uk" hreflang="uk" data-title="Антисиметричне відношення" data-language-autonym="Українська" data-language-local-name="ウクライナ語" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%AA%D9%86%D8%A7%D8%B8%D8%B1_%D8%B4%DA%A9%D9%86_%D8%AA%D8%B9%D9%84%D9%82" title="ウルドゥー語: متناظر شکن تعلق" lang="ur" hreflang="ur" data-title="متناظر شکن تعلق" data-language-autonym="اردو" data-language-local-name="ウルドゥー語" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Quan_h%E1%BB%87_ph%E1%BA%A3n_%C4%91%E1%BB%91i_x%E1%BB%A9ng" title="ベトナム語: Quan hệ phản đối xứng" lang="vi" hreflang="vi" data-title="Quan hệ phản đối xứng" data-language-autonym="Tiếng Việt" data-language-local-name="ベトナム語" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8F%8D%E5%AF%B9%E7%A7%B0%E5%85%B3%E7%B3%BB" title="中国語: 反对称关系" lang="zh" hreflang="zh" data-title="反对称关系" data-language-autonym="中文" data-language-local-name="中国語" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q583760#sitelinks-wikipedia" title="言語間リンクを編集" class="wbc-editpage">リンクを編集</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="名前空間"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82" title="本文を閲覧 [c]" accesskey="c"><span>ページ</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%E3%83%8E%E3%83%BC%E3%83%88:%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82" rel="discussion" title="本文ページについての議論 [t]" accesskey="t"><span>ノート</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="別の言語に切り替える" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button 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id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">ツール</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">非表示</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="その他の操作" > <div class="vector-menu-heading"> 操作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82"><span>閲覧</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82&action=edit" title="このページのソースコードを編集する [e]" accesskey="e"><span>編集</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82&action=history"><span>履歴表示</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 全般 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%83%AA%E3%83%B3%E3%82%AF%E5%85%83/%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82" 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title="このページのこの版への固定リンク"><span>この版への固定リンク</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82&action=info" title="このページについての詳細情報"><span>ページ情報</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%81%93%E3%81%AE%E3%83%9A%E3%83%BC%E3%82%B8%E3%82%92%E5%BC%95%E7%94%A8&page=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82&id=83275771&wpFormIdentifier=titleform" title="このページの引用方法"><span>このページを引用</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:UrlShortener&url=https%3A%2F%2Fja.wikipedia.org%2Fwiki%2F%25E5%258F%258D%25E5%25AF%25BE%25E7%25A7%25B0%25E9%2596%25A2%25E4%25BF%2582"><span>短縮URLを取得する</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:QrCode&url=https%3A%2F%2Fja.wikipedia.org%2Fwiki%2F%25E5%258F%258D%25E5%25AF%25BE%25E7%25A7%25B0%25E9%2596%25A2%25E4%25BF%2582"><span>QRコードをダウンロード</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> 印刷/書き出し </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:%E3%83%96%E3%83%83%E3%82%AF&bookcmd=book_creator&referer=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82"><span>ブックの新規作成</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%E7%89%B9%E5%88%A5:DownloadAsPdf&page=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82&action=show-download-screen"><span>PDF 形式でダウンロード</span></a></li><li id="t-print" class="mw-list-item"><a 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aria-label="表示"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">表示</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">非表示</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">出典: フリー百科事典『ウィキペディア（Wikipedia）』</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ja" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r101304250">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%;font-size:90%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-出典の明記 plainlinks metadata ambox ambox-content ambox-出典の明記" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/50px-Question_book-4.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/75px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/100px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><b>この記事は<a href="/wiki/Wikipedia:%E6%A4%9C%E8%A8%BC%E5%8F%AF%E8%83%BD%E6%80%A7" title="Wikipedia:検証可能性">検証可能</a>な<a href="/wiki/Wikipedia:%E4%BF%A1%E9%A0%BC%E3%81%A7%E3%81%8D%E3%82%8B%E6%83%85%E5%A0%B1%E6%BA%90" title="Wikipedia:信頼できる情報源">参考文献や出典</a>が全く示されていないか、不十分です。</b><span class="hide-when-compact"> <a href="/wiki/Wikipedia:%E5%87%BA%E5%85%B8%E3%82%92%E6%98%8E%E8%A8%98%E3%81%99%E3%82%8B" title="Wikipedia:出典を明記する">出典を追加</a>して記事の信頼性向上にご協力ください。<small>（<a href="/wiki/Template:%E5%87%BA%E5%85%B8%E3%81%AE%E6%98%8E%E8%A8%98/doc" title="Template:出典の明記/doc">このテンプレートの使い方</a>）</small><br /><small><span class="plainlinks">出典検索<a href="/wiki/Template:Find_sources_mainspace" title="Template:Find sources mainspace"><sup>?</sup></a>: <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&as_eq=wikipedia&q=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22&num=50">"反対称関係"</a> – <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&q=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22&tbm=nws">ニュース</a> <b>·</b> <a rel="nofollow" class="external text" href="//www.google.co.jp/search?hl=ja&tbs=bks:1&q=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22">書籍</a> <b>·</b> <a rel="nofollow" class="external text" href="//scholar.google.co.jp/scholar?num=100&hl=ja&q=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22">スカラー</a> <b>·</b> <a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/opensearch/search?lang=ja&q=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22&range=2&count=200&sortorder=1&type=0">CiNii</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstage.jst.go.jp/result/global/-char/ja?globalSearchKey=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22">J-STAGE</a> <b>·</b> <a rel="nofollow" class="external text" href="https://ndlsearch.ndl.go.jp/api/openurl?any=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22">NDL</a> <b>·</b> <a rel="nofollow" class="external text" href="https://dlib.jp/?q=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22">dlib.jp</a> <b>·</b> <a rel="nofollow" class="external text" href="https://jpsearch.go.jp/csearch/jps-cross?csid=jps-cross&keyword=%22%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82%22">ジャパンサーチ</a> <b>·</b> <a rel="nofollow" class="external text" href="https://wikipedialibrary.wmflabs.org/partners/">TWL</a></span></small></span> <span class="date-container"><i>(<span class="date"><span title="2015年3月">2015年3月</span></span>)</i></span></div></td></tr></tbody></table> <p><b>反対称関係</b>（はんたいしょうかんけい、<a href="/wiki/%E8%8B%B1%E8%AA%9E" title="英語">英</a>: <span lang="en">antisymmetric relation</span>）とは、<a href="/wiki/%E9%9B%86%E5%90%88" title="集合">集合</a> <span lang="en" class="texhtml mvar" style="font-style:italic;">X</span> に関する<a href="/wiki/%E4%BA%8C%E9%A0%85%E9%96%A2%E4%BF%82" title="二項関係">二項関係</a> <span lang="en" class="texhtml mvar" style="font-style:italic;">R</span> であって、次の条件を満たすものをいう。 </p> <dl><dd><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,y\in X\ (xRy\land yRx\;\Rightarrow \;x=y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>∈</mo> <mi>X</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>x</mi> <mi>R</mi> <mi>y</mi> <mo>∧</mo> <mi>y</mi> <mi>R</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mo stretchy="false">⇒</mo> <mspace width="thickmathspace" /> <mi>x</mi> <mo>=</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x,y\in X\ (xRy\land yRx\;\Rightarrow \;x=y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c076c1cf145891a7871fc272ee7f6496e0b67fbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.591ex; height:2.843ex;" alt="{\displaystyle \forall x,y\in X\ (xRy\land yRx\;\Rightarrow \;x=y)}"></span></dd></dl> <p>すなわち、<span lang="en" class="texhtml mvar" style="font-style:italic;">X</span> の任意の元 <span lang="en" class="texhtml mvar" style="font-style:italic;">x</span> と <span lang="en" class="texhtml mvar" style="font-style:italic;">y</span> に対して「<span lang="en" class="texhtml mvar" style="font-style:italic;">x</span> から <span lang="en" class="texhtml mvar" style="font-style:italic;">y</span> への関係、および <span lang="en" class="texhtml mvar" style="font-style:italic;">y</span> から <span lang="en" class="texhtml mvar" style="font-style:italic;">x</span> への関係がともに成り立つならば、<span lang="en" class="texhtml mvar" style="font-style:italic;">x</span> = <span lang="en" class="texhtml mvar" style="font-style:italic;">y</span> である」ような関係のことである。この条件を<b>反対称律</b>（<a href="/wiki/%E8%8B%B1%E8%AA%9E" title="英語">英</a>: <span lang="en">antisymmetric law</span>）という。 </p><p>また、反対称律は次の条件と<a href="/wiki/%E5%90%8C%E5%80%A4" title="同値">同値</a>である。 </p> <dl><dd><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,y\in X\ (xRy\land x\neq y\Rightarrow \lnot yRx)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>∈</mo> <mi>X</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>x</mi> <mi>R</mi> <mi>y</mi> <mo>∧</mo> <mi>x</mi> <mo>≠</mo> <mi>y</mi> <mo stretchy="false">⇒</mo> <mi mathvariant="normal">¬</mi> <mi>y</mi> <mi>R</mi> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x,y\in X\ (xRy\land x\neq y\Rightarrow \lnot yRx)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0de1dc71b057b4ce4684ac957a00dce3060d726e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.851ex; height:2.843ex;" alt="{\displaystyle \forall x,y\in X\ (xRy\land x\neq y\Rightarrow \lnot yRx)}"></span></dd></dl> <p>すなわち、反対称関係とは「<span lang="en" class="texhtml mvar" style="font-style:italic;">x</span> から<span lang="en" class="texhtml mvar" style="font-style:italic;">y</span> への関係が成り立ち、かつ <span lang="en" class="texhtml mvar" style="font-style:italic;">x</span> と <span lang="en" class="texhtml mvar" style="font-style:italic;">y</span> が等しくないならば、<span lang="en" class="texhtml mvar" style="font-style:italic;">y</span> から <span lang="en" class="texhtml mvar" style="font-style:italic;">x</span> への関係は成り立たない」ような関係であると定義してもよい。 </p><p>反対称律に加え、<a href="/wiki/%E5%8F%8D%E5%B0%84%E5%BE%8B" class="mw-redirect" title="反射律">反射律</a>および<a href="/wiki/%E6%8E%A8%E7%A7%BB%E5%BE%8B" class="mw-redirect" title="推移律">推移律</a>が成り立つ二項関係を、<a href="/wiki/%E9%A0%86%E5%BA%8F" class="mw-redirect" title="順序">順序</a>関係という。したがって、一般に順序関係は反対称関係である。例えば、<a href="/wiki/%E5%AE%9F%E6%95%B0" title="実数">実数</a>における大小関係 (≦) や集合における包含関係 (⊆) は順序関係であるから、反対称関係でもある。順序関係でなく、反対称関係である関係の例としては、等号なしの大小関係 (＜) が挙げられる。 </p><p>反対称関係は<a href="/wiki/%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82" title="対称関係">対称関係</a>の論理的<a href="/wiki/%E5%90%A6%E5%AE%9A" title="否定">否定</a>ではない。対称関係でも反対称関係でもある関係（等号＝など）もあり、また対称関係でも反対称関係でもない関係もある。対称関係でないものは<a href="/wiki/%E9%9D%9E%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82" title="非対称関係">非対称関係</a>と呼ばれる。なお、ある<a href="/wiki/%E5%A4%89%E6%8F%9B_(%E6%95%B0%E5%AD%A6)" title="変換 (数学)">変換</a>により<a href="/wiki/%E6%AD%A3%E3%81%AE%E6%95%B0%E3%81%A8%E8%B2%A0%E3%81%AE%E6%95%B0" title="正の数と負の数">符号</a>が反転する性質を<a href="/wiki/%E5%8F%8D%E5%AF%BE%E7%A7%B0%E6%80%A7" title="反対称性">反対称性</a>というが、この概念とも直接の関係はない。 </p> <div class="mw-heading mw-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82&action=edit&section=1" title="節を編集: 参考文献"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite style="font-style:normal" class="citation" id="CITEREFLipschutzLipson2007"><a href="https://en.wikipedia.org/wiki/Seymour_Lipschutz" class="extiw" title="en:Seymour Lipschutz">Lipschutz, Seymour</a>; Lipson, Marc (2007), <a rel="nofollow" class="external text" href="https://books.google.co.jp/books?id=9KtFcFa81FcC&pg=PA29"><i>Schaum's outline of theory and problems of discrete mathematics</i></a>, Schaum's outline series (3rd ed.), New York: McGraw-Hill, <style data-mw-deduplicate="TemplateStyles:r101121245">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:var(--color-success,#3a3);margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/978-0-07-151101-8" title="特別:文献資料/978-0-07-151101-8">978-0-07-151101-8</a><span style="display:none;">, <a rel="nofollow" class="external free" href="https://books.google.co.jp/books?id=9KtFcFa81FcC&pg=PA29">https://books.google.co.jp/books?id=9KtFcFa81FcC&pg=PA29</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Schaum%27s+outline+of+theory+and+problems+of+discrete+mathematics&rft.aulast=Lipschutz&rft.aufirst=Seymour&rft.au=Lipschutz%2C%26%2332%3BSeymour&rft.au=Lipson%2C%26%2332%3BMarc&rft.date=2007&rft.series=Schaum%27s+outline+series&rft.edition=3rd&rft.place=New+York&rft.pub=McGraw-Hill&rft.isbn=978-0-07-151101-8&rft_id=https%3A%2F%2Fbooks.google.co.jp%2Fbooks%3Fid%3D9KtFcFa81FcC%26pg%3DPA29&rfr_id=info:sid/ja.wikipedia.org:%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82"><span style="display: none;"> </span></span> <ul><li><cite style="font-style:normal" class="citation book" id="CITEREFLipschutz1995">Lipschutz, Seymour『離散数学　コンピュータサイエンスの基礎数学』成嶋弘監訳、オーム社〈マグロウヒル大学演習〉、1995年3月24日。<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/978-4-274-13005-2" title="特別:文献資料/978-4-274-13005-2">978-4-274-13005-2</a>。</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%E9%9B%A2%E6%95%A3%E6%95%B0%E5%AD%A6%E3%80%80%E3%82%B3%E3%83%B3%E3%83%94%E3%83%A5%E3%83%BC%E3%82%BF%E3%82%B5%E3%82%A4%E3%82%A8%E3%83%B3%E3%82%B9%E3%81%AE%E5%9F%BA%E7%A4%8E%E6%95%B0%E5%AD%A6&rft.aulast=Lipschutz&rft.aufirst=Seymour&rft.au=Lipschutz%2C%26%2332%3BSeymour&rft.date=1995-03-24&rft.series=%E3%83%9E%E3%82%B0%E3%83%AD%E3%82%A6%E3%83%92%E3%83%AB%E5%A4%A7%E5%AD%A6%E6%BC%94%E7%BF%92&rft.pub=%E3%82%AA%E3%83%BC%E3%83%A0%E7%A4%BE&rft.isbn=978-4-274-13005-2&rfr_id=info:sid/ja.wikipedia.org:%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82"><span style="display: none;"> </span></span></li></ul></li></ul> <div class="mw-heading mw-heading2"><h2 id="関連項目"><span id=".E9.96.A2.E9.80.A3.E9.A0.85.E7.9B.AE"></span>関連項目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82&action=edit&section=2" title="節を編集: 関連項目"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="div-col columns column-count column-count-" style="-moz-column-count:; -webkit-column-count:; column-count:; -moz-column-width: 18em; -webkit-column-width: 18em; column-width: 18em;"> <ul><li><a href="/wiki/%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82" title="対称関係">対称関係</a></li> <li><a href="/wiki/%E5%AF%BE%E7%A7%B0%E6%80%A7" title="対称性">対称性</a></li> <li><a href="/wiki/%E4%BA%8C%E9%A0%85%E9%96%A2%E4%BF%82" title="二項関係">二項関係</a></li> <li><a href="/wiki/%E5%8F%8D%E5%AF%BE%E7%A7%B0%E6%80%A7" title="反対称性">反対称性</a></li> <li><a href="/wiki/%E9%9D%9E%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82" title="非対称関係">非対称関係</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="外部リンク"><span id=".E5.A4.96.E9.83.A8.E3.83.AA.E3.83.B3.E3.82.AF"></span>外部リンク</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8F%8D%E5%AF%BE%E7%A7%B0%E9%96%A2%E4%BF%82&action=edit&section=3" title="節を編集: 外部リンク"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>『<a rel="nofollow" class="external text" href="//kotobank.jp/word/%E5%8F%8D%E5%AF%BE%E7%A7%B0%E5%BE%8B">反対称律</a>』 - <a href="/wiki/%E3%82%B3%E3%83%88%E3%83%90%E3%83%B3%E3%82%AF" title="コトバンク">コトバンク</a></li> <li><span class="citation mathworld" id="Reference-Mathworld-Antisymmetric_Relation"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r101121245"><cite id="CITEREFWeisstein" class="citation web cs1 cs1-prop-foreign-lang-source">Weisstein, Eric W. <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/AntisymmetricRelation.html">"Antisymmetric Relation"</a>. <i>mathworld.wolfram.com</i> (英語).</cite><span 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