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vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隱藏</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">序言</div> </a> </li> <li id="toc-定義" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#定義"> <div class="vector-toc-text"> <span class="vector-toc-numb">一</span> <span>定義</span> </div> </a> <button aria-controls="toc-定義-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>切換定義子章節</span> </button> <ul id="toc-定義-sublist" class="vector-toc-list"> <li id="toc-單位元" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#單位元"> <div class="vector-toc-text"> <span class="vector-toc-numb">一.一</span> <span>單位元</span> </div> </a> <ul id="toc-單位元-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-結合律" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#結合律"> <div class="vector-toc-text"> <span class="vector-toc-numb">一.二</span> <span>結合律</span> </div> </a> <ul id="toc-結合律-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-交換律" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#交換律"> <div class="vector-toc-text"> <span class="vector-toc-numb">一.三</span> <span>交換律</span> </div> </a> <ul id="toc-交換律-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-分配律" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#分配律"> <div class="vector-toc-text"> <span class="vector-toc-numb">一.四</span> <span>分配律</span> </div> </a> <ul id="toc-分配律-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-注" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#注"> <div class="vector-toc-text"> <span class="vector-toc-numb">二</span> <span>注</span> </div> </a> <ul id="toc-注-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="切換目次" > <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">切換目次</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">二元運算</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="前往別種語言的條目。有六四種語言可用" > <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-64" 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">六四種語言</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%85%D9%84%D9%8A%D8%A9_%D8%AB%D9%86%D8%A7%D8%A6%D9%8A%D8%A9" title="عملية ثنائية – 阿拉伯文" lang="ar" hreflang="ar" data-title="عملية ثنائية" data-language-autonym="العربية" data-language-local-name="阿拉伯文" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Operaci%C3%B3n_binaria" title="Operación binaria – 阿斯圖里亞文" lang="ast" hreflang="ast" data-title="Operación binaria" data-language-autonym="Asturianu" data-language-local-name="阿斯圖里亞文" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D1%96%D0%BD%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%8B%D1%8F" title="Бінарная аперацыя – 白俄羅斯文" lang="be" hreflang="be" data-title="Бінарная аперацыя" data-language-autonym="Беларуская" data-language-local-name="白俄羅斯文" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Бинарна операция – 保加利亞文" lang="bg" hreflang="bg" data-title="Бинарна операция" data-language-autonym="Български" data-language-local-name="保加利亞文" 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%85%E0%A6%AA%E0%A6%BE%E0%A6%B0%E0%A7%87%E0%A6%B6%E0%A6%A8_(%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4)" title="অপারেশন (গণিত) – 孟加拉文" lang="bn" hreflang="bn" data-title="অপারেশন (গণিত)" data-language-autonym="বাংলা" data-language-local-name="孟加拉文" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Binarna_operacija" title="Binarna operacija – 波士尼亞文" lang="bs" hreflang="bs" data-title="Binarna operacija" data-language-autonym="Bosanski" data-language-local-name="波士尼亞文" 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/Operaci%C3%B3_bin%C3%A0ria" title="Operació binària – 加泰蘭文" lang="ca" hreflang="ca" data-title="Operació binària" data-language-autonym="Català" data-language-local-name="加泰蘭文" 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/%DA%A9%D8%B1%D8%AF%D8%A7%D8%B1_(%D8%A8%DB%8C%D8%B1%DA%A9%D8%A7%D8%B1%DB%8C)" title="کردار (بیرکاری) – 中庫德文" lang="ckb" hreflang="ckb" data-title="کردار (بیرکاری)" data-language-autonym="کوردی" data-language-local-name="中庫德文" 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/Bin%C3%A1rn%C3%AD_operace" title="Binární operace – 捷克文" lang="cs" hreflang="cs" data-title="Binární operace" data-language-autonym="Čeština" data-language-local-name="捷克文" 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%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BB%C4%83_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8" title="Бинарлă операци – 楚瓦什文" lang="cv" hreflang="cv" data-title="Бинарлă операци" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什文" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Bin%C3%A6r_operator" title="Binær operator – 丹麥文" lang="da" hreflang="da" data-title="Binær operator" data-language-autonym="Dansk" data-language-local-name="丹麥文" 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/Zweistellige_Verkn%C3%BCpfung" title="Zweistellige Verknüpfung – 德文" lang="de" hreflang="de" data-title="Zweistellige Verknüpfung" data-language-autonym="Deutsch" data-language-local-name="德文" 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%94%CF%85%CE%B1%CE%B4%CE%B9%CE%BA%CE%AE_%CF%80%CF%81%CE%AC%CE%BE%CE%B7" title="Δυαδική πράξη – 希臘文" lang="el" hreflang="el" data-title="Δυαδική πράξη" data-language-autonym="Ελληνικά" data-language-local-name="希臘文" 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/Binary_operation" title="Binary operation – 英文" lang="en" hreflang="en" data-title="Binary operation" data-language-autonym="English" data-language-local-name="英文" 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/Duvalenta_operacio" title="Duvalenta operacio – 世界文" lang="eo" hreflang="eo" data-title="Duvalenta operacio" data-language-autonym="Esperanto" data-language-local-name="世界文" 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/Operaci%C3%B3n_binaria" title="Operación binaria – 西班牙文" lang="es" hreflang="es" data-title="Operación binaria" data-language-autonym="Español" data-language-local-name="西班牙文" 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/Binaarne_tehe" title="Binaarne tehe – 愛沙尼亞文" lang="et" hreflang="et" data-title="Binaarne tehe" data-language-autonym="Eesti" data-language-local-name="愛沙尼亞文" 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/Eragiketa_bitar" title="Eragiketa bitar – 巴斯克文" lang="eu" hreflang="eu" data-title="Eragiketa bitar" data-language-autonym="Euskara" data-language-local-name="巴斯克文" 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%B9%D9%85%D9%84_%D8%AF%D9%88%D8%AA%D8%A7%DB%8C%DB%8C" title="عمل دوتایی – 波斯文" lang="fa" hreflang="fa" data-title="عمل دوتایی" data-language-autonym="فارسی" data-language-local-name="波斯文" 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/Bin%C3%A4%C3%A4rioperaatio" title="Binäärioperaatio – 芬蘭文" lang="fi" hreflang="fi" data-title="Binäärioperaatio" data-language-autonym="Suomi" data-language-local-name="芬蘭文" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Op%C3%A9ration_binaire" title="Opération binaire – 法文" lang="fr" hreflang="fr" data-title="Opération binaire" data-language-autonym="Français" data-language-local-name="法文" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Obrachadh_c%C3%A0raideach" title="Obrachadh càraideach – 蘇格蘭蓋爾文" lang="gd" hreflang="gd" data-title="Obrachadh càraideach" data-language-autonym="Gàidhlig" data-language-local-name="蘇格蘭蓋爾文" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Operaci%C3%B3n_binaria" title="Operación binaria – 加利西亞文" lang="gl" hreflang="gl" data-title="Operación binaria" data-language-autonym="Galego" data-language-local-name="加利西亞文" 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%A4%D7%A2%D7%95%D7%9C%D7%94_%D7%91%D7%99%D7%A0%D7%90%D7%A8%D7%99%D7%AA" title="פעולה בינארית – 希伯來文" lang="he" hreflang="he" data-title="פעולה בינארית" data-language-autonym="עברית" data-language-local-name="希伯來文" 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/Binarna_operacija" title="Binarna operacija – 克羅埃西亞文" lang="hr" hreflang="hr" data-title="Binarna operacija" data-language-autonym="Hrvatski" data-language-local-name="克羅埃西亞文" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Operation_binari" title="Operation binari – 國際文" lang="ia" hreflang="ia" data-title="Operation binari" data-language-autonym="Interlingua" data-language-local-name="國際文" 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/Operasi_biner" title="Operasi biner – 印尼文" lang="id" hreflang="id" data-title="Operasi biner" data-language-autonym="Bahasa Indonesia" data-language-local-name="印尼文" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/A%C3%B0ger%C3%B0_(st%C3%A6r%C3%B0fr%C3%A6%C3%B0i)" title="Aðgerð (stærðfræði) – 冰島文" lang="is" hreflang="is" data-title="Aðgerð (stærðfræði)" data-language-autonym="Íslenska" data-language-local-name="冰島文" 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/Operazione_binaria" title="Operazione binaria – 義大利文" lang="it" hreflang="it" data-title="Operazione binaria" data-language-autonym="Italiano" data-language-local-name="義大利文" 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/%E4%BA%8C%E9%A0%85%E6%BC%94%E7%AE%97" title="二項演算 – 日文" lang="ja" hreflang="ja" data-title="二項演算" data-language-autonym="日本語" data-language-local-name="日文" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko badge-Q70893996 mw-list-item" title=""><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%ED%95%AD_%EC%97%B0%EC%82%B0" title="이항 연산 – 韓文" lang="ko" hreflang="ko" data-title="이항 연산" data-language-autonym="한국어" data-language-local-name="韓文" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Kiryar_(matemat%C3%AEk)" title="Kiryar (matematîk) – 庫德文" lang="ku" hreflang="ku" data-title="Kiryar (matematîk)" data-language-autonym="Kurdî" data-language-local-name="庫德文" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bin%C4%81ra_oper%C4%81cija" title="Bināra operācija – 拉脫維亞文" lang="lv" hreflang="lv" data-title="Bināra operācija" data-language-autonym="Latviešu" data-language-local-name="拉脫維亞文" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Operasi_biner" title="Operasi biner – 米南卡堡文" lang="min" hreflang="min" data-title="Operasi biner" data-language-autonym="Minangkabau" data-language-local-name="米南卡堡文" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A6%E0%B5%8D%E0%B4%B5%E0%B4%AF%E0%B4%BE%E0%B4%99%E0%B5%8D%E0%B4%95%E0%B4%B8%E0%B4%82%E0%B4%95%E0%B5%8D%E0%B4%B0%E0%B4%BF%E0%B4%AF" title="ദ്വയാങ്കസംക്രിയ – 馬來亞拉姆文" lang="ml" hreflang="ml" data-title="ദ്വയാങ്കസംക്രിയ" data-language-autonym="മലയാളം" data-language-local-name="馬來亞拉姆文" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Operasi_dedua" title="Operasi dedua – 馬來文" lang="ms" hreflang="ms" data-title="Operasi dedua" data-language-autonym="Bahasa Melayu" data-language-local-name="馬來文" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Binaire_operatie" title="Binaire operatie – 荷蘭文" lang="nl" hreflang="nl" data-title="Binaire operatie" data-language-autonym="Nederlands" data-language-local-name="荷蘭文" 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/Bin%C3%A6r_operasjon" title="Binær operasjon – 耐諾斯克挪威文" lang="nn" hreflang="nn" data-title="Binær operasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="耐諾斯克挪威文" 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/Bin%C3%A6r_operasjon" title="Binær operasjon – 巴克摩挪威文" lang="nb" hreflang="nb" data-title="Binær operasjon" data-language-autonym="Norsk bokmål" data-language-local-name="巴克摩挪威文" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/L%C3%A8i_de_composicion_int%C3%A8rna" title="Lèi de composicion intèrna – 奧克西坦文" lang="oc" hreflang="oc" data-title="Lèi de composicion intèrna" data-language-autonym="Occitan" data-language-local-name="奧克西坦文" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Dzia%C5%82anie_dwuargumentowe" title="Działanie dwuargumentowe – 波蘭文" lang="pl" hreflang="pl" data-title="Działanie dwuargumentowe" data-language-autonym="Polski" data-language-local-name="波蘭文" 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/Operassion" title="Operassion – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Operassion" data-language-autonym="Piemontèis" data-language-local-name="皮埃蒙特文" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Opera%C3%A7%C3%A3o_bin%C3%A1ria" title="Operação binária – 葡萄牙文" lang="pt" hreflang="pt" data-title="Operação binária" data-language-autonym="Português" data-language-local-name="葡萄牙文" 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/Opera%C8%9Bie_binar%C4%83" title="Operație binară – 羅馬尼亞文" lang="ro" hreflang="ro" data-title="Operație binară" data-language-autonym="Română" data-language-local-name="羅馬尼亞文" 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%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Бинарная операция – 俄文" lang="ru" hreflang="ru" data-title="Бинарная операция" data-language-autonym="Русский" data-language-local-name="俄文" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Opirazzioni_binaria" title="Opirazzioni binaria – 西西里文" lang="scn" hreflang="scn" data-title="Opirazzioni binaria" data-language-autonym="Sicilianu" data-language-local-name="西西里文" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Binarna_operacija" title="Binarna operacija – 塞爾維亞克羅埃西亞文" lang="sh" hreflang="sh" data-title="Binarna operacija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞爾維亞克羅埃西亞文" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Binary_operation" title="Binary operation – Simple English" lang="en-simple" hreflang="en-simple" data-title="Binary operation" 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/Bin%C3%A1rna_oper%C3%A1cia" title="Binárna operácia – 斯洛伐克文" lang="sk" hreflang="sk" data-title="Binárna operácia" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克文" 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/Dvo%C4%8Dlena_operacija" title="Dvočlena operacija – 斯洛維尼亞文" lang="sl" hreflang="sl" data-title="Dvočlena operacija" data-language-autonym="Slovenščina" data-language-local-name="斯洛維尼亞文" 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/Veprimi_binar" title="Veprimi binar – 阿爾巴尼亞文" lang="sq" hreflang="sq" data-title="Veprimi binar" data-language-autonym="Shqip" data-language-local-name="阿爾巴尼亞文" 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%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Бинарна операција – 塞爾維亞文" lang="sr" hreflang="sr" data-title="Бинарна операција" data-language-autonym="Српски / srpski" data-language-local-name="塞爾維亞文" 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/Bin%C3%A4r_operator" title="Binär operator – 瑞典文" lang="sv" hreflang="sv" data-title="Binär operator" data-language-autonym="Svenska" data-language-local-name="瑞典文" 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%88%E0%AE%B0%E0%AF%81%E0%AE%B1%E0%AF%81%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%9A%E0%AF%8D_%E0%AE%9A%E0%AF%86%E0%AE%AF%E0%AE%B2%E0%AE%BF" title="ஈருறுப்புச் செயலி – 坦米爾文" lang="ta" hreflang="ta" data-title="ஈருறுப்புச் செயலி" data-language-autonym="தமிழ்" data-language-local-name="坦米爾文" 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%81%E0%B8%B2%E0%B8%A3%E0%B8%94%E0%B8%B3%E0%B9%80%E0%B8%99%E0%B8%B4%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%97%E0%B8%A7%E0%B8%B4%E0%B8%A0%E0%B8%B2%E0%B8%84" title="การดำเนินการทวิภาค – 泰文" lang="th" hreflang="th" data-title="การดำเนินการทวิภาค" data-language-autonym="ไทย" data-language-local-name="泰文" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Operasyong_tambalan" title="Operasyong tambalan – 塔加路族文" lang="tl" hreflang="tl" data-title="Operasyong tambalan" data-language-autonym="Tagalog" data-language-local-name="塔加路族文" 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/%C4%B0kili_i%C5%9Flem" title="İkili işlem – 土耳其文" lang="tr" hreflang="tr" data-title="İkili işlem" data-language-autonym="Türkçe" data-language-local-name="土耳其文" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D1%96%D0%BD%D0%B0%D1%80%D0%BD%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%96%D1%8F" title="Бінарна операція – 烏克蘭文" lang="uk" hreflang="uk" data-title="Бінарна операція" data-language-autonym="Українська" data-language-local-name="烏克蘭文" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A9p_to%C3%A1n_hai_ng%C3%B4i" title="Phép toán hai ngôi – 越南文" lang="vi" hreflang="vi" data-title="Phép toán hai ngôi" data-language-autonym="Tiếng Việt" data-language-local-name="越南文" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97" title="二元运算 – 吳語" lang="wuu" hreflang="wuu" data-title="二元运算" data-language-autonym="吴语" data-language-local-name="吳語" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Бинарн операция – 卡爾梅克文" lang="xal" hreflang="xal" data-title="Бинарн операция" data-language-autonym="Хальмг" data-language-local-name="卡爾梅克文" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%91%D7%99%D7%A0%D7%90%D7%A8%D7%99%D7%A9%D7%A2_%D7%90%D7%A4%D7%A2%D7%A8%D7%90%D7%A6%D7%99%D7%A2" title="בינארישע אפעראציע – 意第緒文" lang="yi" hreflang="yi" data-title="בינארישע אפעראציע" data-language-autonym="ייִדיש" data-language-local-name="意第緒文" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97" title="二元运算 – 中文" lang="zh" hreflang="zh" data-title="二元运算" data-language-autonym="中文" data-language-local-name="中文" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97" title="二元運算 – 粵語" lang="yue" hreflang="yue" data-title="二元運算" data-language-autonym="粵語" data-language-local-name="粵語" class="interlanguage-link-target"><span>粵語</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/Q164307#sitelinks-wikipedia" title="修跨語鏈" class="wbc-editpage">纂鏈</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="名集"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" 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							cdx-fr-css-icon--close"></span></button></header><div class="cdx-dialog__body">此為底本，未經<a href="/wiki/%E8%AA%AA%E6%98%8E:%E6%A0%A1%E5%B0%8D" title="說明:校對">審校</a>。</div></div><div tabindex="0"></div></div><div class="mw-content-ltr mw-parser-output" lang="lzh" dir="ltr"><div style="border:1px solid #A3B1BF; padding:0.5em 2em; width:60%; float:left;"> 註︰蓋當今數學之事，誠難僅以文述，而無符號，故凡數學之文，咸有漢字、拉丁字相易之事，以合文言、數學，則無論文理之人，皆可明之也。</div> <div style="clear:left;"></div> <p><b>二元運算</b>者，四則之抽象也。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="定義"><span id=".E5.AE.9A.E7.BE.A9"></span>定義</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97&action=edit&section=1" title="所纂章名：定義"><span>纂</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>二元運算</b>者（「<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 \circ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∘</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \circ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99add39d2b681e2de7ff62422c32704a05c7ec31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.125ex; margin-bottom: -0.297ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \circ }"></span>」），集與已之直積<a href="/wiki/%E6%98%A0%E5%B0%84" title="映射">映射</a>己也（「<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 \circ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∘</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \circ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99add39d2b681e2de7ff62422c32704a05c7ec31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.125ex; margin-bottom: -0.297ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \circ }"></span> : <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 A\times A\to A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>×</mo> <mi>A</mi> <mo stretchy="false">→</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\times A\to A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c43e04047205125debea8e49d9d98d14cef9f5ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.684ex; height:2.176ex;" alt="{\displaystyle A\times A\to A}"></span>」）。加減乘除，皆二元運算也。甲（a）運算乙（b）而得丙，記曰「<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 a\circ b=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∘</mo> <mi>b</mi> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\circ b=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/515d82dfb34c61ca424373fc3973632e82e0cd3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.527ex; height:2.176ex;" alt="{\displaystyle a\circ b=c}"></span>」，或曰<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 \circ (a,b)=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∘</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \circ (a,b)=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a975dffe032082942330ba1dbe23f04f6da4c7a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.338ex; height:2.843ex;" alt="{\displaystyle \circ (a,b)=c}"></span>，則曰甲為<b>被運算數</b>（古稱<b>實數</b>或<b>實</b>），乙為<b>運算數</b>（古稱<b>法數</b>或<b>法</b>）。<b>廣群</b>者，有二元運算之<a href="/w/index.php?title=%E4%BB%A3%E6%95%B8%E7%B5%90%E6%A7%8B&action=edit&redlink=1" class="new" title="代數結構（查無此頁）">代數結構</a>也。<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>一<span class="cite-bracket">]</span></a></sup> </p><p>若無固定名稱，多以乘法或加法稱之。且以乘法語之。 </p> <div class="mw-heading mw-heading3"><h3 id="單位元"><span id=".E5.96.AE.E4.BD.8D.E5.85.83"></span>單位元</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97&action=edit&section=2" title="所纂章名：單位元"><span>纂</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>有元素（「e」），凡乘物或乘以物，皆得斯物，曰<b>單位元</b>（「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e\circ x=x\circ e=x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>∘</mo> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo>∘</mo> <mi>e</mi> <mo>=</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e\circ x=x\circ e=x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/deceb5a24c8bd26dfe75f97ce8395803122894e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.742ex; height:1.676ex;" alt="{\displaystyle e\circ x=x\circ e=x}"></span>」）。加法單位元謂<a href="/wiki/%E9%9B%B6" class="mw-redirect" title="零">零</a>；乘法單位元曰<a href="/wiki/%E4%B8%80" title="一">一</a>。 </p> <div class="mw-heading mw-heading3"><h3 id="結合律"><span id=".E7.B5.90.E5.90.88.E5.BE.8B"></span>結合律</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97&action=edit&section=3" title="所纂章名：結合律"><span>纂</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>若甲乙之積乘丙，同乎甲乘乙丙之積（「<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\circ (y\circ z)=(x\circ y)\circ z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>∘</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>∘</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>∘</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∘</mo> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\circ (y\circ z)=(x\circ y)\circ z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40ddaafc638b6d08cd7df41f480db7ffbc5f7561" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.643ex; height:2.843ex;" alt="{\displaystyle x\circ (y\circ z)=(x\circ y)\circ z}"></span>」），則曰二元運算合<b>結合律</b>也。 </p><p>其廣群曰<b>半群</b>。若有單位元，則曰<b>半幺群</b>也。 </p> <div class="mw-heading mw-heading3"><h3 id="交換律"><span id=".E4.BA.A4.E6.8F.9B.E5.BE.8B"></span>交換律</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97&action=edit&section=4" title="所纂章名：交換律"><span>纂</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>若甲乘乙必同乎乙乘甲（「<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\circ y=y\circ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>∘</mo> <mi>y</mi> <mo>=</mo> <mi>y</mi> <mo>∘</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\circ y=y\circ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2578d2ab8b7ab36781793b5484c664d7f283e93c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.458ex; height:2.009ex;" alt="{\displaystyle x\circ y=y\circ x}"></span>」），則曰二元運算合<b>交換律</b>也。 </p> <div class="mw-heading mw-heading3"><h3 id="分配律"><span id=".E5.88.86.E9.85.8D.E5.BE.8B"></span>分配律</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97&action=edit&section=5" title="所纂章名：分配律"><span>纂</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>若加、乘皆二元運算，且有 </p> <ul><li>甲乘乙丙之和，同乎甲乙之積加甲丙之積，曰<b>左分配律</b>。（「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\times (y+z)=x\times y+x\times z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>×</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>+</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mo>×</mo> <mi>y</mi> <mo>+</mo> <mi>x</mi> <mo>×</mo> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\times (y+z)=x\times y+x\times z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36d448030d1043b266db87244d3e29604ee3134c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.586ex; height:2.843ex;" alt="{\displaystyle x\times (y+z)=x\times y+x\times z}"></span>」<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>二<span class="cite-bracket">]</span></a></sup>）</li> <li>甲乙之和乘丙，同乎甲丙之積加乙丙之積，曰<b>右分配律</b>。（「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x+y)\times z=x\times z+y\times z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mi>z</mi> <mo>=</mo> <mi>x</mi> <mo>×</mo> <mi>z</mi> <mo>+</mo> <mi>y</mi> <mo>×</mo> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x+y)\times z=x\times z+y\times z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a703281c546d882609f0d1c7bc82d8a0844ce28f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.344ex; height:2.843ex;" alt="{\displaystyle (x+y)\times z=x\times z+y\times z}"></span>」）</li></ul> <p>加乘二法合左右者，則謂二法合<b>分配律</b>也。 </p> <div class="mw-heading mw-heading2"><h2 id="注"><span id=".E6.B3.A8"></span>注</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BA%8C%E5%85%83%E9%81%8B%E7%AE%97&action=edit&section=6" title="所纂章名：注"><span>纂</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">另有代數結構曰<a href="/w/index.php?title=%E5%BB%A3%E7%BE%A4&action=edit&redlink=1" class="new" title="廣群（查無此頁）">廣群</a>。</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">依習，先乘除後加減。</span> </li> </ol></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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