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<div id="vector-appearance-dropdown" class="vector-dropdown " title="Změnit vzhled velikosti písma, šířky stránky a barvy" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Vzhled" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Vzhled</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_cs.wikipedia.org&uselang=cs" class=""><span>Podpořte Wikipedii</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Vytvo%C5%99it_%C3%BA%C4%8Det&returnto=Asociativita" title="Doporučujeme vytvořit si účet a přihlásit se, ovšem není to povinné" class=""><span>Vytvoření účtu</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speci%C3%A1ln%C3%AD:P%C5%99ihl%C3%A1sit&returnto=Asociativita" title="Doporučujeme vám přihlásit se, ovšem není to povinné. [o]" accesskey="o" class=""><span>Přihlášení</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Další možnosti" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Osobní nástroje" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Osobní nástroje</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Uživatelské menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_cs.wikipedia.org&uselang=cs"><span>Podpořte Wikipedii</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Vytvo%C5%99it_%C3%BA%C4%8Det&returnto=Asociativita" title="Doporučujeme vytvořit si účet a přihlásit se, ovšem není to povinné"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Vytvoření účtu</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:P%C5%99ihl%C3%A1sit&returnto=Asociativita" title="Doporučujeme vám přihlásit se, ovšem není to povinné. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Přihlášení</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Stránky pro odhlášené editory <a href="/wiki/N%C3%A1pov%C4%9Bda:%C3%9Avod" aria-label="Více informací o editování"><span>dozvědět se více</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_p%C5%99%C3%ADsp%C4%9Bvky" title="Seznam editací provedených z této IP adresy [y]" accesskey="y"><span>Příspěvky</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_diskuse" title="Diskuse o editacích provedených z této IP adresy [n]" accesskey="n"><span>Diskuse</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Obsah" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</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">(úvod)</div> </a> </li> <li id="toc-Definice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definice"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definice</span> </div> </a> <ul id="toc-Definice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Příklady" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Příklady"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Příklady</span> </div> </a> <ul id="toc-Příklady-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vlastnosti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vlastnosti"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Vlastnosti</span> </div> </a> <ul id="toc-Vlastnosti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Odkazy</span> </div> </a> <button aria-controls="toc-Odkazy-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>Přepnout podsekci Odkazy</span> </button> <ul id="toc-Odkazy-sublist" class="vector-toc-list"> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Literatura" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Literatura"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Literatura</span> </div> </a> <ul id="toc-Literatura-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> </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="Obsah" 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="Přepnout obsah" > <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">Přepnout obsah</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">Asociativita</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="Přejděte k článku v jiném jazyce. Je dostupný v 67 jazycích" > <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 jazyků</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 – arabština" lang="ar" hreflang="ar" data-title="عملية تجميعية" data-language-autonym="العربية" data-language-local-name="arabština" 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 – asturština" lang="ast" hreflang="ast" data-title="Asociatividá" data-language-autonym="Asturianu" data-language-local-name="asturština" 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) – baškirština" lang="ba" hreflang="ba" data-title="Ассоциативлыҡ (математика)" data-language-autonym="Башҡортса" data-language-local-name="baškirština" 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 – běloruština" lang="be" hreflang="be" data-title="Асацыятыўная аперацыя" data-language-autonym="Беларуская" data-language-local-name="běloruština" 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 – bulharština" lang="bg" hreflang="bg" data-title="Асоциативност" data-language-autonym="Български" data-language-local-name="bulharština" 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 – bosenština" lang="bs" hreflang="bs" data-title="Asocijativnost" data-language-autonym="Bosanski" data-language-local-name="bosenština" 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 – katalánština" lang="ca" hreflang="ca" data-title="Propietat associativa" data-language-autonym="Català" data-language-local-name="katalánština" 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 – kurdština (sorání)" lang="ckb" hreflang="ckb" data-title="یەکتربەستن" data-language-autonym="کوردی" data-language-local-name="kurdština (sorání)" class="interlanguage-link-target"><span>کوردی</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) – čuvaština" lang="cv" hreflang="cv" data-title="Ассациативлăх (математика)" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" 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 – dánština" lang="da" hreflang="da" data-title="Associativitet" data-language-autonym="Dansk" data-language-local-name="dánština" 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 – němčina" lang="de" hreflang="de" data-title="Assoziativgesetz" data-language-autonym="Deutsch" data-language-local-name="němčina" 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 – řečtina" lang="el" hreflang="el" data-title="Προσεταιριστική ιδιότητα" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" 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 – angličtina" lang="en" hreflang="en" data-title="Associative property" data-language-autonym="English" data-language-local-name="angličtina" 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) – španělština" lang="es" hreflang="es" data-title="Asociatividad (álgebra)" data-language-autonym="Español" data-language-local-name="španělština" 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 – estonština" lang="et" hreflang="et" data-title="Assotsiatiivsus" data-language-autonym="Eesti" data-language-local-name="estonština" 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 – baskičtina" lang="eu" hreflang="eu" data-title="Elkarkortasun" data-language-autonym="Euskara" data-language-local-name="baskičtina" 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 – perština" lang="fa" hreflang="fa" data-title="خاصیت شرکت‌پذیری" data-language-autonym="فارسی" data-language-local-name="perština" 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 – finština" lang="fi" hreflang="fi" data-title="Liitännäisyys" data-language-autonym="Suomi" data-language-local-name="finština" 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 – francouzština" lang="fr" hreflang="fr" data-title="Associativité" data-language-autonym="Français" data-language-local-name="francouzština" 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 – fríština (severní)" lang="frr" hreflang="frr" data-title="Asotsiatiifgesets" data-language-autonym="Nordfriisk" data-language-local-name="fríština (severní)" 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 – irština" lang="ga" hreflang="ga" data-title="Oibríocht chomhthiomsaitheach" data-language-autonym="Gaeilge" data-language-local-name="irština" 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) – galicijština" lang="gl" hreflang="gl" data-title="Asociatividade (álxebra)" data-language-autonym="Galego" data-language-local-name="galicijština" 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 – hebrejština" lang="he" hreflang="he" data-title="פעולה אסוציאטיבית" data-language-autonym="עברית" data-language-local-name="hebrejština" 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 – chorvatština" lang="hr" hreflang="hr" data-title="Asocijativnost" data-language-autonym="Hrvatski" data-language-local-name="chorvatština" 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 – maďarština" lang="hu" hreflang="hu" data-title="Asszociativitás" data-language-autonym="Magyar" data-language-local-name="maďarština" 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 – arménština" lang="hy" hreflang="hy" data-title="Զուգորդականություն" data-language-autonym="Հայերեն" data-language-local-name="arménština" 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 – interlingua" lang="ia" hreflang="ia" data-title="Associativitate" data-language-autonym="Interlingua" data-language-local-name="interlingua" 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 – indonéština" lang="id" hreflang="id" data-title="Sifat asosiatif" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" 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 – islandština" lang="is" hreflang="is" data-title="Tengiregla" data-language-autonym="Íslenska" data-language-local-name="islandština" 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 – italština" lang="it" hreflang="it" data-title="Associatività" data-language-autonym="Italiano" data-language-local-name="italština" 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 – japonština" lang="ja" hreflang="ja" data-title="結合法則" data-language-autonym="日本語" data-language-local-name="japonština" 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 – kazaština" lang="kk" hreflang="kk" data-title="Ассоциативтік операция" data-language-autonym="Қазақша" data-language-local-name="kazaština" 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 – korejština" lang="ko" hreflang="ko" data-title="결합법칙" data-language-autonym="한국어" data-language-local-name="korejština" 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) – latina" lang="la" hreflang="la" data-title="Associativitas (mathematica)" data-language-autonym="Latina" data-language-local-name="latina" 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 – litevština" lang="lt" hreflang="lt" data-title="Asociatyvumas" data-language-autonym="Lietuvių" data-language-local-name="litevština" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Asociativit%C4%81te" title="Asociativitāte – lotyština" lang="lv" hreflang="lv" data-title="Asociativitāte" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%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 – makedonština" lang="mk" hreflang="mk" data-title="Асоцијативност" data-language-autonym="Македонски" data-language-local-name="makedonština" 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 – malajálamština" lang="ml" hreflang="ml" data-title="സാഹചര്യനിയമം" data-language-autonym="മലയാളം" data-language-local-name="malajálamština" 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 – malajština" lang="ms" hreflang="ms" data-title="Kalis sekutuan" data-language-autonym="Bahasa Melayu" data-language-local-name="malajština" 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) – nizozemština" lang="nl" hreflang="nl" data-title="Associativiteit (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="nizozemština" 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 – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Assosiativitet" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (nynorsk)" 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 – norština (bokmål)" lang="nb" hreflang="nb" data-title="Assosiativ lov" data-language-autonym="Norsk bokmål" data-language-local-name="norština (bokmål)" 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 – okcitánština" lang="oc" hreflang="oc" data-title="Associativitat" data-language-autonym="Occitan" data-language-local-name="okcitánština" 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) – polština" lang="pl" hreflang="pl" data-title="Łączność (matematyka)" data-language-autonym="Polski" data-language-local-name="polština" 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 – portugalština" lang="pt" hreflang="pt" data-title="Associatividade" data-language-autonym="Português" data-language-local-name="portugalština" 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 – rumunština" lang="ro" hreflang="ro" data-title="Asociativitate" data-language-autonym="Română" data-language-local-name="rumunština" 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) – ruština" lang="ru" hreflang="ru" data-title="Ассоциативность (математика)" data-language-autonym="Русский" data-language-local-name="ruština" 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 – srbochorvatština" lang="sh" hreflang="sh" data-title="Asocijativnost" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvatština" 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 – slovenština" lang="sk" hreflang="sk" data-title="Asociatívnosť" data-language-autonym="Slovenčina" data-language-local-name="slovenština" 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 – slovinština" lang="sl" hreflang="sl" data-title="Asociativnost" data-language-autonym="Slovenščina" data-language-local-name="slovinština" 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 – albánština" lang="sq" hreflang="sq" data-title="Vetia e shoqërimit" data-language-autonym="Shqip" data-language-local-name="albánština" 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 – srbština" lang="sr" hreflang="sr" data-title="Асоцијативност" data-language-autonym="Српски / srpski" data-language-local-name="srbština" 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 – švédština" lang="sv" hreflang="sv" data-title="Associativitet" data-language-autonym="Svenska" data-language-local-name="švédština" 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 – tamilština" lang="ta" hreflang="ta" data-title="சேர்ப்புப் பண்பு" data-language-autonym="தமிழ்" data-language-local-name="tamilština" 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 – thajština" lang="th" hreflang="th" data-title="สมบัติการเปลี่ยนหมู่" data-language-autonym="ไทย" data-language-local-name="thajština" 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) – turečtina" lang="tr" hreflang="tr" data-title="Birleşme özelliği (ikili işlemler)" data-language-autonym="Türkçe" data-language-local-name="turečtina" 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 – tatarština" lang="tt" hreflang="tt" data-title="Ассоциативлык" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarština" 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 – ukrajinština" lang="uk" hreflang="uk" data-title="Асоціативність" data-language-autonym="Українська" data-language-local-name="ukrajinština" 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 – uzbečtina" lang="uz" hreflang="uz" data-title="Assotsiativlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečtina" 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 – benátština" lang="vec" hreflang="vec" data-title="Propietà asociativa" data-language-autonym="Vèneto" data-language-local-name="benátština" 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 – vietnamština" lang="vi" hreflang="vi" data-title="Tính kết hợp" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" 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 – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="结合律" data-language-autonym="吴语" data-language-local-name="čínština (dialekty Wu)" 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 – jidiš" lang="yi" hreflang="yi" data-title="אסאציאטיוויטעט" data-language-autonym="ייִדיש" data-language-local-name="jidiš" 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/%E7%BB%93%E5%90%88%E5%BE%8B" title="结合律 – čínština" lang="zh" hreflang="zh" data-title="结合律" data-language-autonym="中文" data-language-local-name="čínština" 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/%E7%B5%90%E5%90%88%E5%BE%8B" title="結合律 – kantonština" lang="yue" hreflang="yue" data-title="結合律" data-language-autonym="粵語" data-language-local-name="kantonština" 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/Q177251#sitelinks-wikipedia" title="Editovat mezijazykové odkazy" class="wbc-editpage">Upravit odkazy</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="Jmenné prostory"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Asociativita" 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lang="cs" dir="ltr"><p><b>Asociativita</b> je v <a href="/wiki/Algebra" title="Algebra">algebře</a> vlastnost <a href="/wiki/Bin%C3%A1rn%C3%AD_operace" title="Binární operace">binární</a> <a href="/wiki/Operace_(matematika)" title="Operace (matematika)">operace</a>, která znamená, že nezáleží, jak použijeme závorky ve výrazu, kde je více operandů, tedy v jakém pořadí budeme tento výraz počítat. Například operace sčítání čísel je <b>asociativní</b>, takže <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 1+2+3=(1+2)+3=1+(2+3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>3</mn> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+2+3=(1+2)+3=1+(2+3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e890f26252470cfc3b2d3f21d42ecd67fd9586eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.32ex; height:2.843ex;" alt="{\displaystyle 1+2+3=(1+2)+3=1+(2+3)}"></span>. </p><p>V <a href="/wiki/Informatika" title="Informatika">informatice</a> se často název <b>asociativita</b> používá i pro operace, které asociativní v matematickém smyslu nejsou. Pak rozlišujeme <b>asociativitu zleva doprava</b>, jaká je například u odečítání, kdy <code>a - b - c</code> znamená <code>(a - b) - c</code>, a <b>asociativitu zprava doleva</b>, jaká je třeba u umocňování, kde <code>a ↑ b ↑ c</code> znamená <code>a ↑ (b ↑ c)</code> (místo <code>↑</code> se v některých <a href="/wiki/Programovac%C3%AD_jazyk" title="Programovací jazyk">programovacích jazycích</a> používá <code>**</code>, v jiných <code>^</code>).<sup id="cite_ref-FOOTNOTEHerout2001263_1-0" class="reference"><a href="#cite_note-FOOTNOTEHerout2001263-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definice">Definice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativita&veaction=edit&section=1" title="Editace sekce: Definice" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativita&action=edit&section=1" title="Editovat zdrojový kód sekce Definice"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Bin%C3%A1rn%C3%AD_operace" title="Binární operace">Binární operace</a> ∗ (tj. abstraktní operace se dvěma operandy symbolizovaná znakem ∗) je na množině <i>S</i> <b>asociativní</b>, jestliže platí </p> <dl><dd>(<i>x</i> ∗ <i>y</i>) ∗ <i>z</i> = <i>x ∗ (</i>y<i> ∗ </i>z<i>)</i></dd></dl> <p>pro každé <i>x</i>, <i>y</i> a <i>z</i> v <i>S</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Příklady"><span id="P.C5.99.C3.ADklady"></span>Příklady</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativita&veaction=edit&section=2" title="Editace sekce: Příklady" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativita&action=edit&section=2" title="Editovat zdrojový kód sekce Příklady"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nejznámější příklady asociativních binárních operací jsou <a href="/wiki/S%C4%8D%C3%ADt%C3%A1n%C3%AD" title="Sčítání">sčítání</a> (<i>a</i> + <i>b</i>) a <a href="/wiki/N%C3%A1soben%C3%AD" title="Násobení">násobení</a> (<i>a</i> . <i>b</i>) <a href="/wiki/Re%C3%A1ln%C3%A9_%C4%8D%C3%ADslo" title="Reálné číslo">reálných čísel</a>. </p> <dl><dd>(2 + 3) + 8 = 5 + 8 = 13 = 2 + 11 = 2 + (3 + 8)</dd> <dd>(7×3)×2 = 21×2 = 42 = 7×6 = 7×(3×2)</dd></dl> <p>Další ukázky asociativních binárních operací jsou například: <a href="/wiki/S%C4%8D%C3%ADt%C3%A1n%C3%AD" title="Sčítání">sčítání</a> a <a href="/wiki/N%C3%A1soben%C3%AD" title="Násobení">násobení</a> <a href="/wiki/Komplexn%C3%AD_%C4%8D%C3%ADslo" title="Komplexní číslo">komplexních čísel</a>, sčítání <a href="/wiki/Vektor" title="Vektor">vektorů</a>, <a href="/wiki/Pr%C5%AFnik" title="Průnik">průnik</a> a <a href="/wiki/Sjednocen%C3%AD" title="Sjednocení">sjednocení</a> <a href="/wiki/Mno%C5%BEina" title="Množina">množin</a>, operace <a href="/wiki/Maximum" title="Maximum">maximum</a> a <a href="/wiki/Minimum" title="Minimum">minimum</a>. </p><p>Mezi binární operace, které nejsou asociativní, patří například <a href="/wiki/Od%C4%8D%C3%ADt%C3%A1n%C3%AD" title="Odčítání">odčítání</a> (<i>a</i> − <i>b</i>), <a href="/wiki/D%C4%9Blen%C3%AD" title="Dělení">dělení</a> (<i>a</i> : <i>b</i>) a <a href="/wiki/Umoc%C5%88ov%C3%A1n%C3%AD" title="Umocňování">umocňování</a> (<i>a</i><sup><i>b</i></sup>) čísel nebo <a href="/wiki/Vektorov%C3%BD_sou%C4%8Din" title="Vektorový součin">vektorové násobení</a> vektorů. </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 2-(3-1)=0\quad \neq \quad -2=(2-3)-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>−</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mspace width="1em" /> <mo>≠</mo> <mspace width="1em" /> <mo>−</mo> <mn>2</mn> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>−</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2-(3-1)=0\quad \neq \quad -2=(2-3)-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a63576e242f2dfeee4823b918b4062ba433d0de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.029ex; height:2.843ex;" alt="{\displaystyle 2-(3-1)=0\quad \neq \quad -2=(2-3)-1}"></span>.</dd> <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 2^{(2^{3})}=2^{8}=256\quad \neq \quad 64=4^{3}=(2^{2})^{3}}"> <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>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mo>=</mo> <mn>256</mn> <mspace width="1em" /> <mo>≠</mo> <mspace width="1em" /> <mn>64</mn> <mo>=</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{(2^{3})}=2^{8}=256\quad \neq \quad 64=4^{3}=(2^{2})^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d27e9717167e6375029f337e977a0a769882f6b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.791ex; height:3.509ex;" alt="{\displaystyle 2^{(2^{3})}=2^{8}=256\quad \neq \quad 64=4^{3}=(2^{2})^{3}}"></span></dd></dl> <p>U neasociativních operací je tedy třeba buď důsledně závorkovat, nebo se dohodnout na implicitním pořadí provádění operací – pak se někdy mluví o operacích <i>asociativních zleva</i> či <i>asociativních zprava</i>. Z předvedených příkladů je odčítání levě asociativní, výraz 10 − 5 − 3 se chápe jako (10 − 5) − 3, naopak umocňování je asociativní zprava, <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^{3^{4}}=2^{\left(3^{4}\right)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </msup> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{3^{4}}=2^{\left(3^{4}\right)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/344c7cee01110c4857a8a56309d107ea3872f0fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.701ex; height:3.009ex;" alt="{\displaystyle 2^{3^{4}}=2^{\left(3^{4}\right)}}"></span> (neboť levá asociativita by u mocnění byla neužitečná – stejného výsledku lze díky pravidlům pro mocniny zapsat pomocí součinu exponentů: <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^{3})^{4}=2^{3\cdot 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>3</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>⋅</mo> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2^{3})^{4}=2^{3\cdot 4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2119432ee2a9fe82d4a695b767cdaea4b4db02b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.675ex; height:3.176ex;" alt="{\displaystyle (2^{3})^{4}=2^{3\cdot 4}}"></span>).<sup id="cite_ref-FOOTNOTEHerout2001263_1-1" class="reference"><a href="#cite_note-FOOTNOTEHerout2001263-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Vlastnosti">Vlastnosti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativita&veaction=edit&section=3" title="Editace sekce: Vlastnosti" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativita&action=edit&section=3" title="Editovat zdrojový kód sekce Vlastnosti"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Asociativita operace je důležitá, protože umožňuje nepoužívat závorky a např. zavést <a href="/wiki/Mocnina" class="mw-redirect" title="Mocnina">mocniny</a> s přirozeným mocnitelem. </p> <div class="mw-heading mw-heading2"><h2 id="Odkazy">Odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativita&veaction=edit&section=4" title="Editace sekce: Odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativita&action=edit&section=4" title="Editovat zdrojový kód sekce Odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Reference">Reference</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativita&veaction=edit&section=5" title="Editace sekce: Reference" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativita&action=edit&section=5" title="Editovat zdrojový kód sekce Reference"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-FOOTNOTEHerout2001263-1"><span class="mw-cite-backlink">↑ <a href="#cite_ref-FOOTNOTEHerout2001263_1-0"><sup style="font-style: italic; font-weight: bold; vertical-align: top">a</sup></a> <a href="#cite_ref-FOOTNOTEHerout2001263_1-1"><sup style="font-style: italic; font-weight: bold; vertical-align: top">b</sup></a></span> <span class="reference-text"><a href="#CITEREFHerout2001">Herout 2001</a>, s. 263.</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Literatura">Literatura</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativita&veaction=edit&section=6" title="Editace sekce: Literatura" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativita&action=edit&section=6" title="Editovat zdrojový kód sekce Literatura"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="book" style="font-style:normal;" id="CITEREFHerout2001">HEROUT, Pavel, 2001. <i>Učebnice jazyka C</i>. 3., upravené vyd. České Budějovice: Kopp. 269 s. <span style="white-space:nowrap"><a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Speci%C3%A1ln%C3%AD:Zdroje_knih/80-85828-21-9" title="Speciální:Zdroje knih/80-85828-21-9"><span class="ISBN">80-85828-21-9</span></a></span>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/cs.wikipedia.org:templatecitacemonografie&rft.btitle=U%C4%8Debnice+jazyka+C&rft.isbn=80-85828-21-9&rft.aulast=Herout&rft.aufirst=Pavel&rft.place=%C4%8Cesk%C3%A9+Bud%C4%9Bjovice&rft.pub=Kopp&rft.date=2001&rft.edition=3&rft.tpages=269"><span style="display:none"> </span></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativita&veaction=edit&section=7" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativita&action=edit&section=7" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Komutativita" title="Komutativita">Komutativita</a></li> <li><a href="/wiki/Distributivita" title="Distributivita">Distributivita</a></li> <li><a href="/wiki/Precedence" title="Precedence">Precedence</a></li> <li><a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a></li> <li><a href="/wiki/Algebraick%C3%A1_struktura" title="Algebraická struktura">Algebraická struktura</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Asociativita&veaction=edit&section=8" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Asociativita&action=edit&section=8" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Associative.html">Asociativita</a> v encyklopedii <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a> (anglicky)</li></ul> <table class="plainlinks metadata noprint pahyl" cellpadding="2" style="background: transparent;"> <tbody><tr> <td><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Soubor:Wiki_letter_w.svg" class="mw-file-description" title="Pahýl"><img alt="Pahýl" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a><figcaption>Pahýl</figcaption></figure> </td> <td><i>Tento článek je příliš stručný nebo <a href="/wiki/Wikipedie:Pah%C3%BDl" title="Wikipedie:Pahýl">postrádá důležité informace</a>.<br />Pomozte Wikipedii tím, že jej vhodně <a class="external text" href="https://cs.wikipedia.org/w/index.php?title=Asociativita&action=edit">rozšíříte</a>. 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