Asociativitāte — Vikipēdija

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<span class="vector-toc-numb">2</span> <span>Piemēri</span> </div> </a> <button aria-controls="toc-Piemēri-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>Pārslēgt Piemēri apakšsadaļu</span> </button> <ul id="toc-Piemēri-sublist" class="vector-toc-list"> <li id="toc-Asociatīvas_operācijas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Asociatīvas_operācijas"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Asociatīvas operācijas</span> </div> </a> <ul id="toc-Asociatīvas_operācijas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Neasociatīvas_operācijas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Neasociatīvas_operācijas"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Neasociatīvas operācijas</span> </div> </a> <ul id="toc-Neasociatīvas_operācijas-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Skatīt_arī" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Skatīt_arī"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Skatīt arī</span> </div> </a> <ul id="toc-Skatīt_arī-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Atsauces" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Atsauces"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Atsauces</span> </div> </a> <ul id="toc-Atsauces-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ārējās_saites" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ārējās_saites"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Ārējās saites</span> </div> </a> <ul id="toc-Ārējās_saites-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="Saturs" 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="Pārslēgt satura rādītāju" > <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">Pārslēgt satura rādītāju</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">Asociativitāte</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="Pāriet uz rakstu citā valodā. Pieejams 67 valodās" > <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-67" 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">67 valodas</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%AA%D8%AC%D9%85%D9%8A%D8%B9%D9%8A%D8%A9" title="عملية تجميعية – arābu" lang="ar" hreflang="ar" data-title="عملية تجميعية" data-language-autonym="العربية" data-language-local-name="arābu" 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/Asociativid%C3%A1" title="Asociatividá – astūriešu" lang="ast" hreflang="ast" data-title="Asociatividá" data-language-autonym="Asturianu" data-language-local-name="astūriešu" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%D1%8B%D2%A1_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Ассоциативлыҡ (математика) – baškīru" lang="ba" hreflang="ba" data-title="Ассоциативлыҡ (математика)" data-language-autonym="Башҡортса" data-language-local-name="baškīru" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D1%81%D0%B0%D1%86%D1%8B%D1%8F%D1%82%D1%8B%D1%9E%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%8B%D1%8F" title="Асацыятыўная аперацыя – baltkrievu" lang="be" hreflang="be" data-title="Асацыятыўная аперацыя" data-language-autonym="Беларуская" data-language-local-name="baltkrievu" 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%90%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Асоциативност – bulgāru" lang="bg" hreflang="bg" data-title="Асоциативност" data-language-autonym="Български" data-language-local-name="bulgāru" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Asocijativnost" title="Asocijativnost – bosniešu" lang="bs" hreflang="bs" data-title="Asocijativnost" data-language-autonym="Bosanski" data-language-local-name="bosniešu" 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/Propietat_associativa" title="Propietat associativa – katalāņu" lang="ca" hreflang="ca" data-title="Propietat associativa" data-language-autonym="Català" data-language-local-name="katalāņu" 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/%DB%8C%DB%95%DA%A9%D8%AA%D8%B1%D8%A8%DB%95%D8%B3%D8%AA%D9%86" title="یەکتربەستن – centrālkurdu" lang="ckb" hreflang="ckb" data-title="یەکتربەستن" data-language-autonym="کوردی" data-language-local-name="centrālkurdu" 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/Asociativita" title="Asociativita – čehu" lang="cs" hreflang="cs" data-title="Asociativita" data-language-autonym="Čeština" data-language-local-name="čehu" 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%90%D1%81%D1%81%D0%B0%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%C4%83%D1%85_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Ассациативлăх (математика) – čuvašu" lang="cv" hreflang="cv" data-title="Ассациативлăх (математика)" data-language-autonym="Чӑвашла" data-language-local-name="čuvašu" 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/Associativitet" title="Associativitet – dāņu" lang="da" hreflang="da" data-title="Associativitet" data-language-autonym="Dansk" data-language-local-name="dāņu" 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/Assoziativgesetz" title="Assoziativgesetz – vācu" lang="de" hreflang="de" data-title="Assoziativgesetz" data-language-autonym="Deutsch" data-language-local-name="vācu" 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%A0%CF%81%CE%BF%CF%83%CE%B5%CF%84%CE%B1%CE%B9%CF%81%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE_%CE%B9%CE%B4%CE%B9%CF%8C%CF%84%CE%B7%CF%84%CE%B1" title="Προσεταιριστική ιδιότητα – grieķu" lang="el" hreflang="el" data-title="Προσεταιριστική ιδιότητα" data-language-autonym="Ελληνικά" data-language-local-name="grieķu" 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/Associative_property" title="Associative property – angļu" lang="en" hreflang="en" data-title="Associative property" data-language-autonym="English" data-language-local-name="angļu" 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/Asocieco" title="Asocieco – esperanto" lang="eo" hreflang="eo" data-title="Asocieco" data-language-autonym="Esperanto" data-language-local-name="esperanto" 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/Asociatividad_(%C3%A1lgebra)" title="Asociatividad (álgebra) – spāņu" lang="es" hreflang="es" data-title="Asociatividad (álgebra)" data-language-autonym="Español" data-language-local-name="spāņu" 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/Assotsiatiivsus" title="Assotsiatiivsus – igauņu" lang="et" hreflang="et" data-title="Assotsiatiivsus" data-language-autonym="Eesti" data-language-local-name="igauņu" 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/Elkarkortasun" title="Elkarkortasun – basku" lang="eu" hreflang="eu" data-title="Elkarkortasun" data-language-autonym="Euskara" data-language-local-name="basku" 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%AE%D8%A7%D8%B5%DB%8C%D8%AA_%D8%B4%D8%B1%DA%A9%D8%AA%E2%80%8C%D9%BE%D8%B0%DB%8C%D8%B1%DB%8C" title="خاصیت شرکت‌پذیری – persiešu" lang="fa" hreflang="fa" data-title="خاصیت شرکت‌پذیری" data-language-autonym="فارسی" data-language-local-name="persiešu" 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/Liit%C3%A4nn%C3%A4isyys" title="Liitännäisyys – somu" lang="fi" hreflang="fi" data-title="Liitännäisyys" data-language-autonym="Suomi" data-language-local-name="somu" 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/Associativit%C3%A9" title="Associativité – franču" lang="fr" hreflang="fr" data-title="Associativité" data-language-autonym="Français" data-language-local-name="franču" 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/Asotsiatiifgesets" title="Asotsiatiifgesets – ziemeļfrīzu" lang="frr" hreflang="frr" data-title="Asotsiatiifgesets" data-language-autonym="Nordfriisk" data-language-local-name="ziemeļfrīzu" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Oibr%C3%ADocht_chomhthiomsaitheach" title="Oibríocht chomhthiomsaitheach – īru" lang="ga" hreflang="ga" data-title="Oibríocht chomhthiomsaitheach" data-language-autonym="Gaeilge" data-language-local-name="īru" 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/Asociatividade_(%C3%A1lxebra)" title="Asociatividade (álxebra) – galisiešu" lang="gl" hreflang="gl" data-title="Asociatividade (álxebra)" data-language-autonym="Galego" data-language-local-name="galisiešu" 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%90%D7%A1%D7%95%D7%A6%D7%99%D7%90%D7%98%D7%99%D7%91%D7%99%D7%AA" title="פעולה אסוציאטיבית – ivrits" lang="he" hreflang="he" data-title="פעולה אסוציאטיבית" data-language-autonym="עברית" data-language-local-name="ivrits" 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/Asocijativnost" title="Asocijativnost – horvātu" lang="hr" hreflang="hr" data-title="Asocijativnost" data-language-autonym="Hrvatski" data-language-local-name="horvātu" 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/Asszociativit%C3%A1s" title="Asszociativitás – ungāru" lang="hu" hreflang="hu" data-title="Asszociativitás" data-language-autonym="Magyar" data-language-local-name="ungāru" 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%B6%D5%B8%D6%82%D5%A3%D5%B8%D6%80%D5%A4%D5%A1%D5%AF%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Զուգորդականություն – armēņu" lang="hy" hreflang="hy" data-title="Զուգորդականություն" data-language-autonym="Հայերեն" data-language-local-name="armēņu" 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/Associativitate" title="Associativitate – interlingva" lang="ia" hreflang="ia" data-title="Associativitate" data-language-autonym="Interlingua" data-language-local-name="interlingva" 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/Sifat_asosiatif" title="Sifat asosiatif – indonēziešu" lang="id" hreflang="id" data-title="Sifat asosiatif" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonēziešu" 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/Tengiregla" title="Tengiregla – islandiešu" lang="is" hreflang="is" data-title="Tengiregla" data-language-autonym="Íslenska" data-language-local-name="islandiešu" 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/Associativit%C3%A0" title="Associatività – itāļu" lang="it" hreflang="it" data-title="Associatività" data-language-autonym="Italiano" data-language-local-name="itāļu" 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/%E7%B5%90%E5%90%88%E6%B3%95%E5%89%87" title="結合法則 – japāņu" lang="ja" hreflang="ja" data-title="結合法則" data-language-autonym="日本語" data-language-local-name="japāņu" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D1%82%D1%96%D0%BA_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Ассоциативтік операция – kazahu" lang="kk" hreflang="kk" data-title="Ассоциативтік операция" data-language-autonym="Қазақша" data-language-local-name="kazahu" 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/%EA%B2%B0%ED%95%A9%EB%B2%95%EC%B9%99" title="결합법칙 – korejiešu" lang="ko" hreflang="ko" data-title="결합법칙" data-language-autonym="한국어" data-language-local-name="korejiešu" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Associativitas_(mathematica)" title="Associativitas (mathematica) – latīņu" lang="la" hreflang="la" data-title="Associativitas (mathematica)" data-language-autonym="Latina" data-language-local-name="latīņu" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Asociatyvumas" title="Asociatyvumas – lietuviešu" lang="lt" hreflang="lt" data-title="Asociatyvumas" data-language-autonym="Lietuvių" data-language-local-name="lietuviešu" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D1%81%D0%BE%D1%86%D0%B8%D1%98%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Асоцијативност – maķedoniešu" lang="mk" hreflang="mk" data-title="Асоцијативност" data-language-autonym="Македонски" data-language-local-name="maķedoniešu" 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%B8%E0%B4%BE%E0%B4%B9%E0%B4%9A%E0%B4%B0%E0%B5%8D%E0%B4%AF%E0%B4%A8%E0%B4%BF%E0%B4%AF%E0%B4%AE%E0%B4%82" title="സാഹചര്യനിയമം – malajalu" lang="ml" hreflang="ml" data-title="സാഹചര്യനിയമം" data-language-autonym="മലയാളം" data-language-local-name="malajalu" 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/Kalis_sekutuan" title="Kalis sekutuan – malajiešu" lang="ms" hreflang="ms" data-title="Kalis sekutuan" data-language-autonym="Bahasa Melayu" data-language-local-name="malajiešu" 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/Associativiteit_(wiskunde)" title="Associativiteit (wiskunde) – holandiešu" lang="nl" hreflang="nl" data-title="Associativiteit (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="holandiešu" 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/Assosiativitet" title="Assosiativitet – jaunnorvēģu" lang="nn" hreflang="nn" data-title="Assosiativitet" data-language-autonym="Norsk nynorsk" data-language-local-name="jaunnorvēģu" 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/Assosiativ_lov" title="Assosiativ lov – norvēģu bukmols" lang="nb" hreflang="nb" data-title="Assosiativ lov" data-language-autonym="Norsk bokmål" data-language-local-name="norvēģu bukmols" 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/Associativitat" title="Associativitat – oksitāņu" lang="oc" hreflang="oc" data-title="Associativitat" data-language-autonym="Occitan" data-language-local-name="oksitāņu" 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/%C5%81%C4%85czno%C5%9B%C4%87_(matematyka)" title="Łączność (matematyka) – poļu" lang="pl" hreflang="pl" data-title="Łączność (matematyka)" data-language-autonym="Polski" data-language-local-name="poļu" 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/Associatividade" title="Associatividade – portugāļu" lang="pt" hreflang="pt" data-title="Associatividade" data-language-autonym="Português" data-language-local-name="portugāļu" 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/Asociativitate" title="Asociativitate – rumāņu" lang="ro" hreflang="ro" data-title="Asociativitate" data-language-autonym="Română" data-language-local-name="rumāņu" 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%90%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D1%8C_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Ассоциативность (математика) – krievu" lang="ru" hreflang="ru" data-title="Ассоциативность (математика)" data-language-autonym="Русский" data-language-local-name="krievu" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Asocijativnost" title="Asocijativnost – serbu–horvātu" lang="sh" hreflang="sh" data-title="Asocijativnost" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbu–horvātu" 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/Associativity" title="Associativity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Associativity" 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/Asociat%C3%ADvnos%C5%A5" title="Asociatívnosť – slovāku" lang="sk" hreflang="sk" data-title="Asociatívnosť" data-language-autonym="Slovenčina" data-language-local-name="slovāku" 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/Asociativnost" title="Asociativnost – slovēņu" lang="sl" hreflang="sl" data-title="Asociativnost" data-language-autonym="Slovenščina" data-language-local-name="slovēņu" 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/Vetia_e_shoq%C3%ABrimit" title="Vetia e shoqërimit – albāņu" lang="sq" hreflang="sq" data-title="Vetia e shoqërimit" data-language-autonym="Shqip" data-language-local-name="albāņu" 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%90%D1%81%D0%BE%D1%86%D0%B8%D1%98%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82" title="Асоцијативност – serbu" lang="sr" hreflang="sr" data-title="Асоцијативност" data-language-autonym="Српски / srpski" data-language-local-name="serbu" 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/Associativitet" title="Associativitet – zviedru" lang="sv" hreflang="sv" data-title="Associativitet" data-language-autonym="Svenska" data-language-local-name="zviedru" 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%9A%E0%AF%87%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%AA%E0%AF%8D_%E0%AE%AA%E0%AE%A3%E0%AF%8D%E0%AE%AA%E0%AF%81" title="சேர்ப்புப் பண்பு – tamilu" lang="ta" hreflang="ta" data-title="சேர்ப்புப் பண்பு" data-language-autonym="தமிழ்" data-language-local-name="tamilu" 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%AA%E0%B8%A1%E0%B8%9A%E0%B8%B1%E0%B8%95%E0%B8%B4%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%80%E0%B8%9B%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%99%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88" title="สมบัติการเปลี่ยนหมู่ – taju" lang="th" hreflang="th" data-title="สมบัติการเปลี่ยนหมู่" data-language-autonym="ไทย" data-language-local-name="taju" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Birle%C5%9Fme_%C3%B6zelli%C4%9Fi_(ikili_i%C5%9Flemler)" title="Birleşme özelliği (ikili işlemler) – turku" lang="tr" hreflang="tr" data-title="Birleşme özelliği (ikili işlemler)" data-language-autonym="Türkçe" data-language-local-name="turku" 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%90%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%82%D0%B8%D0%B2%D0%BB%D1%8B%D0%BA" title="Ассоциативлык – tatāru" lang="tt" hreflang="tt" data-title="Ассоциативлык" data-language-autonym="Татарча / tatarça" data-language-local-name="tatāru" 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%90%D1%81%D0%BE%D1%86%D1%96%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Асоціативність – ukraiņu" lang="uk" hreflang="uk" data-title="Асоціативність" data-language-autonym="Українська" data-language-local-name="ukraiņu" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Assotsiativlik" title="Assotsiativlik – uzbeku" lang="uz" hreflang="uz" data-title="Assotsiativlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeku" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Propiet%C3%A0_asociativa" title="Propietà asociativa – Venetian" lang="vec" hreflang="vec" data-title="Propietà asociativa" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%C3%ADnh_k%E1%BA%BFt_h%E1%BB%A3p" title="Tính kết hợp – vjetnamiešu" lang="vi" hreflang="vi" data-title="Tính kết hợp" data-language-autonym="Tiếng Việt" data-language-local-name="vjetnamiešu" 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/%E7%BB%93%E5%90%88%E5%BE%8B" title="结合律 – vu ķīniešu" lang="wuu" hreflang="wuu" data-title="结合律" data-language-autonym="吴语" data-language-local-name="vu ķīniešu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%A1%D7%90%D7%A6%D7%99%D7%90%D7%98%D7%99%D7%95%D7%95%D7%99%D7%98%D7%A2%D7%98" title="אסאציאטיוויטעט – jidišs" lang="yi" hreflang="yi" 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Vikidatos</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Lapas rīki"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izskats"> <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">Izskats</div> <button class="vector-pinnable-header-toggle-button 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Asociativitāte ir viena no <a href="/wiki/Grupa_(matem%C4%81tika)" title="Grupa (matemātika)">grupas</a> <a href="/wiki/Aksioma" title="Aksioma">aksiomām</a>. Intuitīvi asociativitāte nozīmē to, ka izteiksmes vērtība nav atkarīga no tā, kā saliek iekavas. To, cik lielā mērā operācija ir asociatīva, raksturo <i><a href="/w/index.php?title=Asociators&action=edit&redlink=1" class="new" title="Asociators (vēl nav uzrakstīts)">asociators</a></i>. </p><p>Ja izteiksmē vairākas reizes pēc kārtas parādās viena un tā pati asociatīva binārā operācija (piemēram, <a href="/wiki/Saskait%C4%AB%C5%A1ana" title="Saskaitīšana">saskaitīšana</a> vai <a href="/wiki/Reizin%C4%81%C5%A1ana" title="Reizināšana">reizināšana</a>), tad izteiksmes vērtība nav atkarīga no šo operāciju izpildes secības, tāpēc iekavas parasti neliek. Piemēram, </p> <dl><dd>(<i>a</i> + <i>b</i>) + <i>c</i> = <i>a</i> + (<i>b</i> + <i>c</i>) = <i>a</i> + <i>b</i> + <i>c</i>,</dd> <dd>(<i>a</i> · <i>b</i>) · <i>c</i> = <i>a</i> · (<i>b</i> · <i>c</i>) = <i>a</i> · <i>b</i> · <i>c</i>.</dd></dl> <p>Taču šāda īpašība nav spēkā, ja izteiksmē ir <i>dažādas</i> asociatīvas binārās operācijas. Piemēram, </p> <dl><dd>(1 + 2) · 3 ≠ 1 + (2 · 3),</dd></dl> <p>jo kreisā puse ir vienāda ar 3 · 3 = 9, bet labā — ar 1 + 6 = 7. </p><p>Asociativitātei līdzīga īpašība ir <a href="/wiki/Komutativit%C4%81te" title="Komutativitāte">komutativitāte</a>. Komutativitāte nozīmē to, ka operācijas <i>argumentu</i> secībai nav nozīmes (nevis operāciju <i>izpildes</i> secībai). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definīcija"><span id="Defin.C4.ABcija"></span>Definīcija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativit%C4%81te&veaction=edit&section=1" title="Labot sadaļu: Definīcija" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativit%C4%81te&action=edit&section=1" title="Labot sadaļas vikikodu: Definīcija"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Bin%C4%81ra_oper%C4%81cija" title="Bināra operācija">Bināru operāciju</a> "<span style="font-family: 'Arial Unicode MS', 'Lucida Sans Unicode', Gentium, GentiumAlt, tahoma, Code2000, 'Doulos SIL', Gentium, 'TITUS Cyberbit Basic', 'Lucida Grande', 'DejaVu Sans', 'Bitstream Vera Sans', 'Bitstream Cyberbit', Arial, sans-serif;" dir="ltr">∗</span>" <a href="/wiki/Kopa" title="Kopa">kopā</a> <i>S</i> sauc par <i>asociatīvu</i>, ja jebkuriem trijiem kopas <i>S</i> elementiem <i>x</i>, <i>y</i>, <i>z</i> izpildās īpašība (<i>x</i> <span style="font-family: 'Arial Unicode MS', 'Lucida Sans Unicode', Gentium, GentiumAlt, tahoma, Code2000, 'Doulos SIL', Gentium, 'TITUS Cyberbit Basic', 'Lucida Grande', 'DejaVu Sans', 'Bitstream Vera Sans', 'Bitstream Cyberbit', Arial, sans-serif;" dir="ltr">∗</span> <i>y</i>) <span style="font-family: 'Arial Unicode MS', 'Lucida Sans Unicode', Gentium, GentiumAlt, tahoma, Code2000, 'Doulos SIL', Gentium, 'TITUS Cyberbit Basic', 'Lucida Grande', 'DejaVu Sans', 'Bitstream Vera Sans', 'Bitstream Cyberbit', Arial, sans-serif;" dir="ltr">∗</span> <i>z</i> = <i>x</i> <span style="font-family: 'Arial Unicode MS', 'Lucida Sans Unicode', Gentium, GentiumAlt, tahoma, Code2000, 'Doulos SIL', Gentium, 'TITUS Cyberbit Basic', 'Lucida Grande', 'DejaVu Sans', 'Bitstream Vera Sans', 'Bitstream Cyberbit', Arial, sans-serif;" dir="ltr">∗</span> (<i>y</i> <span style="font-family: 'Arial Unicode MS', 'Lucida Sans Unicode', Gentium, GentiumAlt, tahoma, Code2000, 'Doulos SIL', Gentium, 'TITUS Cyberbit Basic', 'Lucida Grande', 'DejaVu Sans', 'Bitstream Vera Sans', 'Bitstream Cyberbit', Arial, sans-serif;" dir="ltr">∗</span> <i>z</i>). Formāli to pieraksta šādi: </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,z\in S:(x\ast y)\ast z=x\ast (y\ast z),}"> <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>z</mi> <mo>∈</mo> <mi>S</mi> <mo>:</mo> <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> <mo stretchy="false">(</mo> <mi>y</mi> <mo>∗</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x,y,z\in S:(x\ast y)\ast z=x\ast (y\ast z),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b54f65bb7c155f37a9abb1229a8fd302206625d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.5ex; height:2.843ex;" alt="{\displaystyle \forall x,y,z\in S:(x\ast y)\ast z=x\ast (y\ast z),}"></span></dd></dl> <p>kur "∀" ir <a href="/w/index.php?title=Univers%C4%81lkvantors&action=edit&redlink=1" class="new" title="Universālkvantors (vēl nav uzrakstīts)">universālkvantors</a> (lasa kā "visiem") un "∈" apzīmē piederību kopai (lasa kā "pieder"). </p> <div class="mw-heading mw-heading2"><h2 id="Piemēri"><span id="Piem.C4.93ri"></span>Piemēri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativit%C4%81te&veaction=edit&section=2" title="Labot sadaļu: Piemēri" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativit%C4%81te&action=edit&section=2" title="Labot sadaļas vikikodu: Piemēri"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Asociatīvas_operācijas"><span id="Asociat.C4.ABvas_oper.C4.81cijas"></span>Asociatīvas operācijas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativit%C4%81te&veaction=edit&section=3" title="Labot sadaļu: Asociatīvas operācijas" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativit%C4%81te&action=edit&section=3" title="Labot sadaļas vikikodu: Asociatīvas operācijas"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th width="160px">Operācija </th> <th width="300px">Operācijas īpašība </th> <th>Piemērs </th></tr> <tr> <th><a href="/wiki/Saskait%C4%AB%C5%A1ana" title="Saskaitīšana">Saskaitīšana</a> </th> <td align="center">(<i>a</i> + <i>b</i>) + <i>c</i> = <i>a</i> + (<i>b</i> + <i>c</i>) </td> <td>(5 + 1) + 3 = 6 + 3 = 9, <br /> 5 + (1 + 3) = 5 + 4 = 9. </td></tr> <tr> <th><a href="/wiki/Reizin%C4%81%C5%A1ana" title="Reizināšana">Reizināšana</a> </th> <td align="center">(<i>a</i> · <i>b</i>) · <i>c</i> = <i>a</i> · (<i>b</i> · <i>c</i>) </td> <td>(2 · 3) · 4 = 6 · 4 = 24, <br /> 2 · (3 · 4) = 2 · 12 = 24. </td></tr> <tr> <th><a href="/wiki/Liel%C4%81kais_kop%C4%ABgais_dal%C4%ABt%C4%81js" title="Lielākais kopīgais dalītājs">Lielākais kopīgais dalītājs</a> </th> <td align="center">LKD(LKD(<i>a</i>, <i>b</i>), <i>c</i>) = LKD(<i>a</i>, LKD(<i>b</i>, <i>c</i>)) </td> <td>LKD(LKD(12, 6), 4) = LKD(6, 4) = 2, <br /> LKD(12, LKD(6, 4)) = LKD(12, 2) = 2. </td></tr> <tr> <th><a href="/wiki/Maz%C4%81kais_kop%C4%ABgais_dal%C4%81mais" title="Mazākais kopīgais dalāmais">Mazākais kopīgais dalāmais</a> </th> <td align="center">MKD(MKD(<i>a</i>, <i>b</i>), <i>c</i>) = MKD(<i>a</i>, MKD(<i>b</i>, <i>c</i>)) </td> <td>MKD(MKD(2, 6), 5) = MKD(6, 5) = 30, <br /> MKD(2, MKD(6, 5)) = MKD(2, 30) = 30. </td></tr> <tr> <th><a href="/wiki/Matricu_reizin%C4%81%C5%A1ana" title="Matricu reizināšana">Matricu reizināšana</a> </th> <td align="center">(<i>A</i> · <i>B</i>) · <i>C</i> = <i>A</i> · (<i>B</i> · <i>C</i>) </td> <td><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={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )},\,B={\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )},\,C={\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>,</mo> <mspace width="thinmathspace" /> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )},\,B={\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )},\,C={\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b1c94512ccda0741b348f27688105bdef45704f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:33.954ex; height:3.343ex;" alt="{\displaystyle A={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )},\,B={\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )},\,C={\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )},}"></span> <p><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 {\begin{aligned}A\cdot B&={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}5&6\\3&5\end{smallmatrix}}{\bigr )},\\B\cdot C&={\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}12&9\\3&4\end{smallmatrix}}{\bigr )},\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>A</mi> <mo>⋅</mo> <mi>B</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>5</mn> </mtd> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>5</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> <mo>⋅</mo> <mi>C</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>12</mn> </mtd> <mtd> <mn>9</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}A\cdot B&={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}5&6\\3&5\end{smallmatrix}}{\bigr )},\\B\cdot C&={\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}12&9\\3&4\end{smallmatrix}}{\bigr )},\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/459930e0bc8e59b16bce87dd0c86ef81538d5866" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.202ex; height:7.176ex;" alt="{\displaystyle {\begin{aligned}A\cdot B&={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}5&6\\3&5\end{smallmatrix}}{\bigr )},\\B\cdot C&={\bigl (}{\begin{smallmatrix}1&4\\2&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}12&9\\3&4\end{smallmatrix}}{\bigr )},\end{aligned}}}"></span> </p><p><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 {\begin{aligned}(A\cdot B)\cdot C&={\bigl (}{\begin{smallmatrix}5&6\\3&5\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}18&17\\15&13\end{smallmatrix}}{\bigr )},\\A\cdot (B\cdot C)&={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}12&9\\3&4\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}18&17\\15&13\end{smallmatrix}}{\bigr )}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mo stretchy="false">(</mo> <mi>A</mi> <mo>⋅</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>C</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>5</mn> </mtd> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>5</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>18</mn> </mtd> <mtd> <mn>17</mn> </mtd> </mtr> <mtr> <mtd> <mn>15</mn> </mtd> <mtd> <mn>13</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo>⋅</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>12</mn> </mtd> <mtd> <mn>9</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mn>18</mn> </mtd> <mtd> <mn>17</mn> </mtd> </mtr> <mtr> <mtd> <mn>15</mn> </mtd> <mtd> <mn>13</mn> </mtd> </mtr> </mtable> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}(A\cdot B)\cdot C&={\bigl (}{\begin{smallmatrix}5&6\\3&5\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}18&17\\15&13\end{smallmatrix}}{\bigr )},\\A\cdot (B\cdot C)&={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}12&9\\3&4\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}18&17\\15&13\end{smallmatrix}}{\bigr )}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1db2415e3ae341f9bca725d644be0f55beed868" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.707ex; margin-bottom: -0.298ex; width:38.077ex; height:7.176ex;" alt="{\displaystyle {\begin{aligned}(A\cdot B)\cdot C&={\bigl (}{\begin{smallmatrix}5&6\\3&5\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}0&1\\3&2\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}18&17\\15&13\end{smallmatrix}}{\bigr )},\\A\cdot (B\cdot C)&={\bigl (}{\begin{smallmatrix}1&2\\1&1\end{smallmatrix}}{\bigr )}\cdot {\bigl (}{\begin{smallmatrix}12&9\\3&4\end{smallmatrix}}{\bigr )}={\bigl (}{\begin{smallmatrix}18&17\\15&13\end{smallmatrix}}{\bigr )}.\end{aligned}}}"></span> </p> </td></tr> <tr> <th><a href="/w/index.php?title=Funkciju_kompoz%C4%ABcija&action=edit&redlink=1" class="new" title="Funkciju kompozīcija (vēl nav uzrakstīts)">Funkciju kompozīcija</a> </th> <td align="center">(<i>f</i> ∘ <i>g</i>) ∘ <i>h</i> = <i>f</i> ∘ (<i>g</i> ∘ <i>h</i>) </td> <td><i>A</i>, <i>B</i>, <i>C</i> — patvaļīgas <a href="/wiki/Kopa" title="Kopa">kopas</a>, <br /> <i>f</i>: <i>A</i> → <i>B</i>, <i>g</i>: <i>B</i> → <i>C</i>, <i>h</i>: <i>C</i> → <i>D</i> — <a href="/wiki/Funkcija" title="Funkcija">funkcijas</a> starp tām. </td></tr> <tr> <th>Punktu saskaitīšana uz eliptiskās līknes<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </th> <td align="center">(<i>A</i> + <i>B</i>) + <i>C</i> = <i>A</i> + (<i>B</i> + <i>C</i>) </td> <td><i>A</i>, <i>B</i>, <i>C</i> ir <a href="/wiki/Punkts_(%C4%A3eometrija)" title="Punkts (ģeometrija)">punkti</a> uz <a href="/w/index.php?title=Eliptisk%C4%81_l%C4%ABkne&action=edit&redlink=1" class="new" title="Eliptiskā līkne (vēl nav uzrakstīts)">eliptiskās līknes</a>. </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Neasociatīvas_operācijas"><span id="Neasociat.C4.ABvas_oper.C4.81cijas"></span>Neasociatīvas operācijas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativit%C4%81te&veaction=edit&section=4" title="Labot sadaļu: Neasociatīvas operācijas" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativit%C4%81te&action=edit&section=4" title="Labot sadaļas vikikodu: Neasociatīvas operācijas"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th width="160px">Operācija </th> <th width="300px">Operācijas īpašība </th> <th>Piemērs </th></tr> <tr> <th><a href="/wiki/At%C5%86em%C5%A1ana" title="Atņemšana">Atņemšana</a> </th> <td align="center">(<i>a</i> − <i>b</i>) − <i>c</i> ≠ <i>a</i> − (<i>b</i> − <i>c</i>) </td> <td>(4 − 2) − 1 = 2 − 1 = 1, <br /> 4 − (2 − 1) = 4 − 1 = 3. </td></tr> <tr> <th><a href="/wiki/Dal%C4%AB%C5%A1ana" title="Dalīšana">Dalīšana</a> </th> <td align="center">(<i>a / b</i>) <i>/</i> <i>c</i> ≠ <i>a</i> <i>/</i> (<i>b / c</i>) </td> <td>(4 <i>/</i> 2) <i>/</i> 2 = 2 <i>/</i> 2 = 1, <br /> 4 <i>/</i> (2 <i>/</i> 2) = 4 <i>/</i> 1 = 4. </td></tr> <tr> <th><a href="/wiki/K%C4%81pin%C4%81%C5%A1ana" title="Kāpināšana">Kāpināšana</a> </th> <td align="center"><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^{(b^{c})}\neq (a^{b})^{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </msup> <mo>≠</mo> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{(b^{c})}\neq (a^{b})^{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/989bfa2cc24145e8ef1b291642e6a0d1b99f4153" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.208ex; height:3.343ex;" alt="{\displaystyle a^{(b^{c})}\neq (a^{b})^{c}}"></span> </td> <td><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 2^{(1^{2})}=2^{1}=2,\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{(1^{2})}=2^{1}=2,\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66e012a5e2fe99b4aae5913ea1eb0f81b776f5fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.938ex; height:3.343ex;" alt="{\displaystyle 2^{(1^{2})}=2^{1}=2,\,}"></span> <br /> <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 (2^{1})^{2}=2^{2}=4.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>4.</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2^{1})^{2}=2^{2}=4.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1799ab48440abd503191fe6ac191884da1d32fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.69ex; height:3.176ex;" alt="{\displaystyle (2^{1})^{2}=2^{2}=4.\,}"></span> </td></tr> <tr> <th><a href="/w/index.php?title=Oktonioni&action=edit&redlink=1" class="new" title="Oktonioni (vēl nav uzrakstīts)">Oktonionu reizināšana</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </th> <td align="center">(<i>a</i> · <i>b</i>) · <i>c</i> ≠ <i>a</i> · (<i>b</i> · <i>c</i>) </td> <td>(<i>e</i><sub>1</sub> · <i>e</i><sub>2</sub>) · <i>e</i><sub>3</sub> = <i>e</i><sub>4</sub> · <i>e</i><sub>3</sub> = −<i>e</i><sub>6</sub>, <br /> <i>e</i><sub>1</sub> · (<i>e</i><sub>2</sub> · <i>e</i><sub>3</sub>) = <i>e</i><sub>1</sub> · <i>e</i><sub>5</sub> = <i>e</i><sub>6</sub>. </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Skatīt_arī"><span id="Skat.C4.ABt_ar.C4.AB"></span>Skatīt arī</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativit%C4%81te&veaction=edit&section=5" title="Labot sadaļu: Skatīt arī" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativit%C4%81te&action=edit&section=5" title="Labot sadaļas vikikodu: Skatīt arī"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Komutativit%C4%81te" title="Komutativitāte">Komutativitāte</a></li> <li><a href="/w/index.php?title=Distributivit%C4%81te&action=edit&redlink=1" class="new" title="Distributivitāte (vēl nav uzrakstīts)">Distributivitāte</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Atsauces">Atsauces</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativit%C4%81te&veaction=edit&section=6" title="Labot sadaļu: Atsauces" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativit%C4%81te&action=edit&section=6" title="Labot sadaļas vikikodu: Atsauces"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Tas, ka punktu saskaitīšana uz eliptiskās līknes ir asociatīva, nebūt nav acīmredzami, taču to ir iespējams pierādīt. Skatīt, piemēram, <ul><li>Stefan Friedl, <a rel="nofollow" class="external text" href="http://math.rice.edu/~friedl/papers/AAELLIPTIC.PDF">An Elementary Proof of the Group Law for Elliptic Cruves</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140207205732/http://math.rice.edu/~friedl/papers/AAELLIPTIC.PDF">Arhivēts</a> 2014. gada 7. februārī, <i><a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i> vietnē..</li></ul> </span></li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Oktonionu reizināšanas likumi atrodami šeit: <ul><li>John C. Baez, <a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/octonions/octonions.html">The Octonions</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090421054044/http://math.ucr.edu/home/baez/octonions/octonions.html">Arhivēts</a> 2009. gada 21. aprīlī, <i><a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i> vietnē., nodaļa <a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/octonions/node4.html">2.1 The Fano plane</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090703202247/http://math.ucr.edu/home/baez/octonions/node4.html">Arhivēts</a> 2009. gada 3. jūlijā, <i><a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i> vietnē..</li> <li>Oleksandr Pavlyk, <a rel="nofollow" class="external text" href="http://demonstrations.wolfram.com/OctonionsAndTheFanoPlaneMnemonic/">Octonions and the Fano Plane Mnemonic</a>, The Wolfram Demonstrations Project.</li></ul> </span></li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Ārējās_saites"><span id=".C4.80r.C4.93j.C4.81s_saites"></span>Ārējās saites</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativit%C4%81te&veaction=edit&section=7" title="Labot sadaļu: Ārējās saites" class="mw-editsection-visualeditor"><span>labot šo sadaļu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativit%C4%81te&action=edit&section=7" title="Labot sadaļas vikikodu: Ārējās saites"><span>labot pirmkodu</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Eric W. Weisstein, <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Associative.html">Associative</a>, MathWorld.</li> <li><a rel="nofollow" class="external text" href="https://planetmath.org/encyclopedia/Associative.html">Associative</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081229153100/http://planetmath.org/encyclopedia/Associative.html">Arhivēts</a> 2008. gada 29. decembrī, <i><a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></i> vietnē., PlanetMath.</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Saturs iegūts no "<a dir="ltr" href="https://lv.wikipedia.org/w/index.php?title=Asociativitāte&oldid=3468221">https://lv.wikipedia.org/w/index.php?title=Asociativitāte&oldid=3468221</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Kategorijas</a>: <ul><li><a href="/wiki/Kategorija:Abstrakt%C4%81_algebra" title="Kategorija:Abstraktā algebra">Abstraktā algebra</a></li><li><a href="/wiki/Kategorija:Grupu_teorija" title="Kategorija:Grupu teorija">Grupu teorija</a></li><li><a href="/wiki/Kategorija:Bin%C4%81r%C4%81s_oper%C4%81cijas" title="Kategorija:Binārās operācijas">Binārās operācijas</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Šī lapa pēdējoreiz labota: 2021. gada 31. augusts plkst. 01.48.</li> <li id="footer-info-copyright">Teksts ir pieejams saskaņā ar <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution/Share-Alike licenci</a>; var pastāvēt papildu ierobežojumi. 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