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href="/w/index.php?title=Speciale:Entra&returnto=Relazione+binaria" title="Si consiglia di effettuare l'accesso, anche se non è obbligatorio [o]" accesskey="o" class=""><span>entra</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="Altre opzioni" > <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="Strumenti personali" > <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">Strumenti 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[n]" accesskey="n"><span>discussioni</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="Sito"> <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="Indice" 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">Indice</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">nascondi</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">Inizio</div> </a> </li> <li id="toc-Definizione" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definizione"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definizione</span> </div> </a> <ul id="toc-Definizione-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tipologia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tipologia"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tipologia</span> </div> </a> <ul id="toc-Tipologia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altri_progetti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altri_progetti"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Altri progetti</span> </div> </a> <ul id="toc-Altri_progetti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collegamenti_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Collegamenti_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Collegamenti esterni</span> </div> </a> <ul id="toc-Collegamenti_esterni-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="Indice" 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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Relazione binaria</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="Vai a una voce in un'altra lingua. Disponibile in 42 lingue" > <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-42" 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">42 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D9%84%D8%A7%D9%82%D8%A9_%D8%AB%D9%86%D8%A7%D8%A6%D9%8A%D8%A9" title="علاقة ثنائية - arabo" lang="ar" hreflang="ar" data-title="علاقة ثنائية" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D1%96%D0%BD%D0%B0%D1%80%D0%BD%D0%B0%D0%B5_%D0%B4%D0%B0%D1%87%D1%8B%D0%BD%D0%B5%D0%BD%D0%BD%D0%B5" title="Бінарнае дачыненне - bielorusso" lang="be" hreflang="be" data-title="Бінарнае дачыненне" data-language-autonym="Беларуская" data-language-local-name="bielorusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B0_%D1%80%D0%B5%D0%BB%D0%B0%D1%86%D0%B8%D1%8F" title="Бинарна релация - bulgaro" lang="bg" hreflang="bg" data-title="Бинарна релация" data-language-autonym="Български" data-language-local-name="bulgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Bin%C3%A1rn%C3%AD_relace" title="Binární relace - ceco" lang="cs" hreflang="cs" data-title="Binární relace" data-language-autonym="Čeština" data-language-local-name="ceco" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BB%C4%83_%D1%82%D0%B8%D0%B2%C4%95%D0%BC" title="Бинарлă тивĕм - ciuvascio" lang="cv" hreflang="cv" data-title="Бинарлă тивĕм" data-language-autonym="Чӑвашла" data-language-local-name="ciuvascio" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Bin%C3%A4re_Relation" title="Binäre Relation - tedesco" lang="de" hreflang="de" data-title="Binäre Relation" data-language-autonym="Deutsch" data-language-local-name="tedesco" 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%A3%CF%87%CE%AD%CF%83%CE%B7_(%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC)" title="Σχέση (μαθηματικά) - greco" lang="el" hreflang="el" data-title="Σχέση (μαθηματικά)" data-language-autonym="Ελληνικά" data-language-local-name="greco" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Binary_relation" title="Binary relation - inglese" lang="en" hreflang="en" data-title="Binary relation" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Duvalenta_rilato" title="Duvalenta rilato - esperanto" lang="eo" hreflang="eo" data-title="Duvalenta rilato" 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/Relaci%C3%B3n_binaria" title="Relación binaria - spagnolo" lang="es" hreflang="es" data-title="Relación binaria" data-language-autonym="Español" data-language-local-name="spagnolo" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Binaarne_seos" title="Binaarne seos - estone" lang="et" hreflang="et" data-title="Binaarne seos" data-language-autonym="Eesti" data-language-local-name="estone" 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/Erlazio_bitar" title="Erlazio bitar - basco" lang="eu" hreflang="eu" data-title="Erlazio bitar" data-language-autonym="Euskara" data-language-local-name="basco" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%AF%D9%88%D8%AA%D8%A7%DB%8C%DB%8C" title="رابطه دوتایی - persiano" lang="fa" hreflang="fa" data-title="رابطه دوتایی" data-language-autonym="فارسی" data-language-local-name="persiano" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Bin%C3%A4%C3%A4rirelaatio" title="Binäärirelaatio - finlandese" lang="fi" hreflang="fi" data-title="Binäärirelaatio" data-language-autonym="Suomi" data-language-local-name="finlandese" 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/Relation_binaire" title="Relation binaire - francese" lang="fr" hreflang="fr" data-title="Relation binaire" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Relaci%C3%B3n_binaria" title="Relación binaria - galiziano" lang="gl" hreflang="gl" data-title="Relación binaria" data-language-autonym="Galego" data-language-local-name="galiziano" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%99%D7%97%D7%A1_(%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%A7%D7%91%D7%95%D7%A6%D7%95%D7%AA)" title="יחס (תורת הקבוצות) - ebraico" lang="he" hreflang="he" data-title="יחס (תורת הקבוצות)" data-language-autonym="עברית" data-language-local-name="ebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8D%E0%A4%B5%E0%A4%AF%E0%A5%80_%E0%A4%B8%E0%A4%AE%E0%A5%8D%E0%A4%AC%E0%A4%A8%E0%A5%8D%E0%A4%A7" title="द्वयी सम्बन्ध - hindi" lang="hi" hreflang="hi" data-title="द्वयी सम्बन्ध" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Binarne_relacije" title="Binarne relacije - croato" lang="hr" hreflang="hr" data-title="Binarne relacije" data-language-autonym="Hrvatski" data-language-local-name="croato" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Relation_binari" title="Relation binari - interlingua" lang="ia" hreflang="ia" data-title="Relation binari" 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/Relasi_biner" title="Relasi biner - indonesiano" lang="id" hreflang="id" data-title="Relasi biner" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BA%8C%E9%A0%85%E9%96%A2%E4%BF%82" title="二項関係 - giapponese" lang="ja" hreflang="ja" data-title="二項関係" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Assa%C9%A3_imisin" title="Assaɣ imisin - cabilo" lang="kab" hreflang="kab" data-title="Assaɣ imisin" data-language-autonym="Taqbaylit" data-language-local-name="cabilo" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%ED%95%AD_%EA%B4%80%EA%B3%84" title="이항 관계 - coreano" lang="ko" hreflang="ko" data-title="이항 관계" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Relazion_binaria" title="Relazion binaria - lombardo" lang="lmo" hreflang="lmo" data-title="Relazion binaria" data-language-autonym="Lombard" data-language-local-name="lombardo" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-nl badge-Q17437796 badge-featuredarticle mw-list-item" title="voce in vetrina"><a href="https://nl.wikipedia.org/wiki/Tweeplaatsige_relatie" title="Tweeplaatsige relatie - olandese" lang="nl" hreflang="nl" data-title="Tweeplaatsige relatie" data-language-autonym="Nederlands" data-language-local-name="olandese" 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/Relasjon_i_matematikk" title="Relasjon i matematikk - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Relasjon i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese 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/Bin%C3%A6r_relasjon" title="Binær relasjon - norvegese bokmål" lang="nb" hreflang="nb" data-title="Binær relasjon" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese 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/Relacion_bin%C3%A0ria" title="Relacion binària - occitano" lang="oc" hreflang="oc" data-title="Relacion binària" data-language-autonym="Occitan" data-language-local-name="occitano" 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/Relacja_dwuargumentowa" title="Relacja dwuargumentowa - polacco" lang="pl" hreflang="pl" data-title="Relacja dwuargumentowa" data-language-autonym="Polski" data-language-local-name="polacco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Relassion_binaria" title="Relassion binaria - piemontese" lang="pms" hreflang="pms" data-title="Relassion binaria" data-language-autonym="Piemontèis" data-language-local-name="piemontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Rela%C3%A7%C3%A3o_bin%C3%A1ria" title="Relação binária - portoghese" lang="pt" hreflang="pt" data-title="Relação binária" data-language-autonym="Português" data-language-local-name="portoghese" 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/Rela%C8%9Bie_binar%C4%83" title="Relație binară - rumeno" lang="ro" hreflang="ro" data-title="Relație binară" data-language-autonym="Română" data-language-local-name="rumeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%BE%D0%B5_%D0%BE%D1%82%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%B8%D0%B5" title="Бинарное отношение - russo" lang="ru" hreflang="ru" data-title="Бинарное отношение" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Bin%C3%A1rna_rel%C3%A1cia" title="Binárna relácia - slovacco" lang="sk" hreflang="sk" data-title="Binárna relácia" data-language-autonym="Slovenčina" data-language-local-name="slovacco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B0_%D1%80%D0%B5%D0%BB%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Бинарна релација - serbo" lang="sr" hreflang="sr" data-title="Бинарна релација" data-language-autonym="Српски / srpski" data-language-local-name="serbo" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Bin%C3%A4r_relation" title="Binär relation - svedese" lang="sv" hreflang="sv" data-title="Binär relation" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%88%E0%AE%B0%E0%AF%81%E0%AE%B1%E0%AF%81%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81_%E0%AE%89%E0%AE%B1%E0%AE%B5%E0%AF%81" title="ஈருறுப்பு உறவு - tamil" lang="ta" hreflang="ta" data-title="ஈருறுப்பு உறவு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D1%96%D0%BD%D0%B0%D1%80%D0%BD%D0%B5_%D0%B2%D1%96%D0%B4%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%BD%D1%8F" title="Бінарне відношення - ucraino" lang="uk" hreflang="uk" data-title="Бінарне відношення" data-language-autonym="Українська" data-language-local-name="ucraino" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%D8%AB%D9%86%DB%8C%DB%81_%D8%AA%D8%B9%D9%84%D9%82" title="تثنیہ تعلق - urdu" lang="ur" hreflang="ur" data-title="تثنیہ تعلق" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Quan_h%E1%BB%87_hai_ng%C3%B4i" title="Quan hệ hai ngôi - vietnamita" lang="vi" hreflang="vi" data-title="Quan hệ hai ngôi" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%8C%E5%85%83%E5%85%B3%E7%B3%BB" title="二元关系 - cinese" lang="zh" hreflang="zh" data-title="二元关系" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q130901#sitelinks-wikipedia" title="Modifica collegamenti interlinguistici" class="wbc-editpage">Modifica collegamenti</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="Namespace"> <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/Relazione_binaria" title="Vedi la voce [c]" accesskey="c"><span>Voce</span></a></li><li id="ca-talk" 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class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q130901" title="Collegamento all'elemento connesso dell'archivio dati [g]" accesskey="g"><span>Elemento Wikidata</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="Strumenti pagine"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspetto"> <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">Aspetto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">nascondi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Da Wikipedia, l'enciclopedia libera.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><p>In <a href="/wiki/Matematica" title="Matematica">matematica</a>, una <b>relazione binaria</b> definita di un <a href="/wiki/Insieme" title="Insieme">insieme</a>, anche detta <b>relazione</b> o <b>corrispondenza</b> tra due oggetti, è un elenco di <a href="/wiki/Coppia_(matematica)" title="Coppia (matematica)">coppie ordinate</a> di elementi appartenenti all'insieme. In modo equivalente, una relazione binaria è un sottoinsieme del <a href="/wiki/Prodotto_cartesiano" title="Prodotto cartesiano">prodotto cartesiano</a> di un insieme con se stesso. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definizione">Definizione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relazione_binaria&veaction=edit&section=1" title="Modifica la sezione Definizione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relazione_binaria&action=edit&section=1" title="Edit section's source code: Definizione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dati due <a href="/wiki/Insieme" title="Insieme">insiemi</a> <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> e <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 B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>, il loro <a href="/wiki/Prodotto_cartesiano" title="Prodotto cartesiano">prodotto cartesiano</a> è l'insieme delle <a href="/wiki/Coppia_(matematica)" title="Coppia (matematica)">coppie ordinate</a> definito nel modo seguente:<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> </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 A\times B:=\{(a,b):a\in A\;\mathrm {e} \;b\in B\}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>×</mo> <mi>B</mi> <mo>:=</mo> <mo fence="false" stretchy="false">{</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>:</mo> <mi>a</mi> <mo>∈</mo> <mi>A</mi> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mspace width="thickmathspace" /> <mi>b</mi> <mo>∈</mo> <mi>B</mi> <mo fence="false" stretchy="false">}</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\times B:=\{(a,b):a\in A\;\mathrm {e} \;b\in B\}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4f574e6ae343948ac9611f6553f0a45ba644d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.745ex; height:2.843ex;" alt="{\displaystyle A\times B:=\{(a,b):a\in A\;\mathrm {e} \;b\in B\}\ }"></span></dd></dl> <p>Si definisce relazione binaria <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 R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> tra due insiemi non vuoti <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> e <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 B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> un sottoinsieme di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\times B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>×</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\times B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65f31ae45b0098f06b5d22c38d317eb097a88fa9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.348ex; height:2.176ex;" alt="{\displaystyle A\times B}"></span>.<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> Due elementi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> sono messi in relazione da <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 R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> se: </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 (x,y)\in R\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>R</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x,y)\in R\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/106e8ff24ed38b3ee1424d8c382c88db36770547" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.514ex; height:2.843ex;" alt="{\displaystyle (x,y)\in R\ }"></span></dd></dl> <p>ed in tal caso si scrive <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 xRy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mi>R</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle xRy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/324aab4e2674bb19cc073ea887888b98f0fc63d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.249ex; height:2.509ex;" alt="{\displaystyle xRy}"></span>. </p><p>Per le relazioni binarie è molto comune usare notazioni infisse della forma <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 \,xRy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>x</mi> <mi>R</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,xRy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f1778d18f399f34237b7fecd7fb6d817aa38ab1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.636ex; height:2.509ex;" alt="{\displaystyle \,xRy}"></span> per esprimere il fatto che la coppia <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 \langle x,y\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle x,y\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9df1806ebe1fed1a728b18aed82c30be8b2a0acb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.328ex; height:2.843ex;" alt="{\displaystyle \langle x,y\rangle }"></span> appartiene ad <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 R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>, cioè per individuare singoli. Tipicamente per indicare che il numero reale <i>x</i> è minore del numero reale <i>y</i> è usuale scrivere <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x<y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo><</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x<y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aeb239de6fee56ea8b6a65f7858d95b87632069f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.176ex;" alt="{\displaystyle x<y}"></span>, mentre per ricondursi strettamente alla definizione generale si dovrebbe scrivere <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 \langle x,y\rangle \in <}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>∈<</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle x,y\rangle \in <}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2f8b2f01ea3ae6ef9a661be3dea749ed86d2f23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.332ex; height:2.843ex;" alt="{\displaystyle \langle x,y\rangle \in <}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Tipologia">Tipologia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relazione_binaria&veaction=edit&section=2" title="Modifica la sezione Tipologia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relazione_binaria&action=edit&section=2" title="Edit section's source code: Tipologia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La nozione di relazione è estremamente generale e da certi punti di vista, assai generica. La sua precisazione comunque ha contribuito in modo decisivo a porre ordine in moltissimi risultati della matematica e delle sue applicazioni che erano stati ottenuti in studi specifici e venivano proposte mediante enunciazioni anche molto scoordinate. La generalità della nozione implica che nella <a href="/wiki/Matematica" title="Matematica">matematica</a> e in tutti i settori applicativi che si servono di modelli matematici si incontrano moltissime relazioni. Come è prevedibile, le svariate relazioni presentano caratteristiche anche molto diverse ed è opportuno classificarle con cura. </p><p>Le relazioni si distinguono sia per la natura dei prodotti cartesiani nei quali si collocano, sia per le loro caratteristiche come insiemi di coppie. </p><p>Secondo il primo punto di vista si distinguono, in particolare, </p> <ul><li>le relazioni fra insiemi finiti (come quelle riguardanti gradi di parentela in un ambito familiare);</li> <li>le relazioni fra insiemi numerabili (come la relazione di divisibilità fra interi positivi);</li> <li>le relazioni fra insiemi continui (come le relazioni fra numeri reali, ad es. curve piane come le spirali, le funzioni di variabile reale o complessa e le superfici nello spazio tridimensionalele).</li></ul> <p>Va osservato che le relazioni binarie finite equivalgono ai <a href="/wiki/Digrafo_(matematica)" title="Digrafo (matematica)">digrafi</a>, cioè ai grafi orientati. </p><p>Dal punto di vista delle caratteristiche degli insiemi di coppie si distinguono i seguenti tipi di relazione: </p> <ul><li><a href="/wiki/Relazione_riflessiva" title="Relazione riflessiva">relazione riflessiva</a></li> <li><a href="/wiki/Relazione_antiriflessiva" class="mw-redirect" title="Relazione antiriflessiva">relazione antiriflessiva</a></li> <li><a href="/wiki/Relazione_simmetrica" title="Relazione simmetrica">relazione simmetrica</a></li> <li><a href="/wiki/Relazione_antisimmetrica" class="mw-redirect" title="Relazione antisimmetrica">relazione antisimmetrica</a></li> <li><a href="/wiki/Preordine" title="Preordine">relazione di preordine</a></li> <li><a href="/wiki/Relazione_transitiva" title="Relazione transitiva">relazione transitiva</a></li> <li><a href="/wiki/Relazione_di_equivalenza" title="Relazione di equivalenza">relazione di equivalenza</a></li> <li><a href="/wiki/Relazione_d%27ordine" title="Relazione d'ordine">relazione d'ordine</a></li> <li><a href="/wiki/Relazione_tricotomica" title="Relazione tricotomica">relazione tricotomica</a></li> <li><a href="/wiki/Funzione_(matematica)" title="Funzione (matematica)">funzione (matematica)</a></li></ul> <p>Alcune possono implicarne altre: ad esempio la <a href="/wiki/Relazione_d%27ordine" title="Relazione d'ordine">relazione d'ordine</a> implica la riflessiva, la antisimmetrica e la transitiva </p><p>Queste proprietà sono in genere riferite alle relazioni di un insieme in sé. </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relazione_binaria&veaction=edit&section=3" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relazione_binaria&action=edit&section=3" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFreed">Reed, Simon</a>, Pag. 1</cite>.</span> </li> <li id="cite_note-2"><a href="#cite_ref-2"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFreed">Reed, Simon</a>, Pag. 2</cite>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relazione_binaria&veaction=edit&section=4" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relazione_binaria&action=edit&section=4" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFreed" class="citation libro" style="font-style:normal"> Michael Reed, Barry Simon, <span style="font-style:italic;">Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis</span>, 2ª ed., San Diego, California, Academic press inc., 1980, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/0-12-585050-6" title="Speciale:RicercaISBN/0-12-585050-6">0-12-585050-6</a>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relazione_binaria&veaction=edit&section=5" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relazione_binaria&action=edit&section=5" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><span class="plainlinks" title="commons:Category:Binary relations"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Binary_relations?uselang=it">Wikimedia Commons</a></span></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/?uselang=it" title="Collabora a Wikimedia Commons"><img alt="Collabora a Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/27px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/36px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/?uselang=it">Wikimedia Commons</a></span> contiene immagini o altri file sulla <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Binary_relations?uselang=it">relazione binaria</a></span></b></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Relazione_binaria&veaction=edit&section=6" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Relazione_binaria&action=edit&section=6" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li> <li><cite id="CITEREFEnciclopedia_della_Matematica" class="citation libro" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/relazione-binaria_(Enciclopedia-della-Matematica)/"><span style="font-style:italic;">relazione binaria</span></a>, in <span style="font-style:italic;">Enciclopedia della Matematica</span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>, 2013.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q130901#P9621" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFBritannica.com" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://www.britannica.com/topic/binary-relation"><span style="font-style:italic;">binary relation</span></a>, su <span style="font-style:italic;"><a href="/wiki/Enciclopedia_Britannica" title="Enciclopedia Britannica">Enciclopedia Britannica</a></span>, Encyclopædia Britannica, Inc.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q130901#P1417" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFFOLDOC" class="citation testo" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Denis Howe, <span style="font-style:italic;"><a href="https://foldoc.org/binary_relation" class="extiw" title="foldoc:binary relation">binary relation</a></span>, in <span style="font-style:italic;"><a href="/wiki/Free_On-line_Dictionary_of_Computing" 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Usa l'anteprima prima di salvare">M</span></a></div></div><span class="navbox_title"><a href="/wiki/Teoria_degli_insiemi" title="Teoria degli insiemi">Teoria degli insiemi</a></span></th></tr><tr><th colspan="1" class="navbox_group"><a href="/wiki/Insieme" title="Insieme">Insiemi numerici</a></th><td colspan="1" class="navbox_list navbox_odd"><a href="/wiki/Numero_naturale" title="Numero naturale">Naturali</a><b> ·</b> <a href="/wiki/Numero_intero" title="Numero intero">Interi</a><b> ·</b> <a href="/wiki/Numero_razionale" title="Numero razionale">Razionali</a><b> ·</b> <a href="/wiki/Numero_reale" title="Numero reale">Reali</a><b> ·</b> <a href="/wiki/Numero_complesso" title="Numero complesso">Complessi</a></td></tr><tr><th colspan="1" class="navbox_group"><a href="/wiki/Teoria_ingenua_degli_insiemi" title="Teoria ingenua degli insiemi">Teoria ingenua degli insiemi</a> (o di <a href="/wiki/Georg_Cantor" title="Georg Cantor">Cantor</a>)</th><td colspan="1" class="navbox_list navbox_even"><a href="/wiki/Insieme_vuoto" title="Insieme vuoto">Insieme vuoto</a><b> ·</b> <a href="/wiki/Insieme_universo" title="Insieme universo">Insieme universo</a><b> ·</b> <a href="/wiki/Sottoinsieme" class="mw-redirect" title="Sottoinsieme">Sottoinsieme</a><b> ·</b> <a href="/wiki/Insieme_potenza" class="mw-redirect" title="Insieme potenza">Insieme potenza</a><b> ·</b> <a href="/wiki/Insieme_complemento" title="Insieme complemento">Insieme complemento</a><b> ·</b> <a href="/wiki/Unione_(insiemistica)" title="Unione (insiemistica)">Unione</a><b> ·</b> <a href="/wiki/Intersezione_(insiemistica)" title="Intersezione (insiemistica)">Intersezione</a><b> ·</b> <a href="/wiki/Coppia_(matematica)" title="Coppia (matematica)">Coppia ordinata</a><b> ·</b> <a href="/wiki/Prodotto_cartesiano" title="Prodotto cartesiano">Prodotto cartesiano</a><b> ·</b> <a href="/wiki/Paradosso_di_Russell" title="Paradosso di Russell">Paradosso di Russell</a><b> ·</b> <a href="/wiki/Paradosso_di_Burali-Forti" title="Paradosso di Burali-Forti">Paradosso di Burali-Forti</a></td></tr><tr><th colspan="1" class="navbox_group"><a href="/wiki/Teoria_assiomatica_degli_insiemi" title="Teoria assiomatica degli insiemi">Teoria assiomatica degli insiemi</a></th><td colspan="1" class="navbox_list navbox_odd"><a href="/wiki/Assioma_(matematica)" title="Assioma (matematica)">Assioma</a><b> ·</b> <a href="/wiki/Assiomi_di_Peano" title="Assiomi di Peano">Assiomi di Peano</a><b> ·</b> <a href="/wiki/Teoria_degli_insiemi_di_Zermelo" title="Teoria degli insiemi di Zermelo">Teoria degli insiemi di Zermelo</a><b> ·</b> <a href="/wiki/Teoria_degli_insiemi_di_Zermelo-Fraenkel" title="Teoria degli insiemi di Zermelo-Fraenkel">Teoria degli insiemi di Zermelo-Fraenkel</a><b> ·</b> <a href="/wiki/Assioma_della_scelta" title="Assioma della scelta">Assioma della scelta</a><b> ·</b> <a href="/wiki/Lemma_di_Zorn" title="Lemma di Zorn">Lemma di Zorn</a><b> ·</b> <a href="/wiki/Teoria_degli_insiemi_di_Von_Neumann-Bernays-G%C3%B6del" title="Teoria degli insiemi di Von Neumann-Bernays-Gödel">Teoria degli insiemi di Von Neumann-Bernays-Gödel</a></td></tr></tbody></table> <div class="noprint" style="width:100%; 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