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hechas desde esta dirección IP [n]" accesskey="n"><span>Discusión</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="Sitio"> <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="Contenidos" 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">Contenidos</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ocultar</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">Inicio</div> </a> </li> <li id="toc-Ejemplos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ejemplos"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Ejemplos</span> </div> </a> <ul id="toc-Ejemplos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véase_también" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véase_también"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Véase también</span> </div> </a> <ul id="toc-Véase_también-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enlaces_externos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Enlaces_externos"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Enlaces externos</span> </div> </a> <ul id="toc-Enlaces_externos-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="Contenidos" 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="Cambiar a la tabla de contenidos" > <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">Cambiar a la tabla de contenidos</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">Función identidad</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="Ir a un artículo en otro idioma. Disponible en 41 idiomas" > <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-41" 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">41 idiomas</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%AF%D8%A7%D9%84%D8%A9_%D9%85%D8%B7%D8%A7%D8%A8%D9%82%D8%A9" title="دالة مطابقة (árabe)" lang="ar" hreflang="ar" data-title="دالة مطابقة" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Funkcija_identiteta" title="Funkcija identiteta (bosnio)" lang="bs" hreflang="bs" data-title="Funkcija identiteta" data-language-autonym="Bosanski" data-language-local-name="bosnio" 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/Funci%C3%B3_identitat" title="Funció identitat (catalán)" lang="ca" hreflang="ca" data-title="Funció identitat" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Funzioni_idantit%C3%A0" title="Funzioni idantità (corso)" lang="co" hreflang="co" data-title="Funzioni idantità" data-language-autonym="Corsu" data-language-local-name="corso" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Identita_(matematika)" title="Identita (matematika) (checo)" lang="cs" hreflang="cs" data-title="Identita (matematika)" data-language-autonym="Čeština" data-language-local-name="checo" 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/%C3%87%D0%B0%D0%B2%D0%B0%D1%85%D0%BB%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8" title="Çавахла функци (chuvasio)" lang="cv" hreflang="cv" data-title="Çавахла функци" data-language-autonym="Чӑвашла" data-language-local-name="chuvasio" 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/Identitetsfunktion" title="Identitetsfunktion (danés)" lang="da" hreflang="da" data-title="Identitetsfunktion" data-language-autonym="Dansk" data-language-local-name="danés" 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/Identische_Abbildung" title="Identische Abbildung (alemán)" lang="de" hreflang="de" data-title="Identische Abbildung" data-language-autonym="Deutsch" data-language-local-name="alemán" 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%A4%CE%B1%CF%85%CF%84%CE%BF%CF%84%CE%B9%CE%BA%CE%AE_%CF%83%CF%85%CE%BD%CE%AC%CF%81%CF%84%CE%B7%CF%83%CE%B7" title="Ταυτοτική συνάρτηση (griego)" lang="el" hreflang="el" data-title="Ταυτοτική συνάρτηση" data-language-autonym="Ελληνικά" data-language-local-name="griego" 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/Identity_function" title="Identity function (inglés)" lang="en" hreflang="en" data-title="Identity function" data-language-autonym="English" data-language-local-name="inglés" 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/Identa_funkcio" title="Identa funkcio (esperanto)" lang="eo" hreflang="eo" data-title="Identa funkcio" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Samasusteisendus" title="Samasusteisendus (estonio)" lang="et" hreflang="et" data-title="Samasusteisendus" data-language-autonym="Eesti" data-language-local-name="estonio" 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/Identitate_funtzio" title="Identitate funtzio (euskera)" lang="eu" hreflang="eu" data-title="Identitate funtzio" data-language-autonym="Euskara" data-language-local-name="euskera" 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%AA%D8%A7%D8%A8%D8%B9_%D9%87%D9%85%D8%A7%D9%86%DB%8C" title="تابع همانی (persa)" lang="fa" hreflang="fa" data-title="تابع همانی" data-language-autonym="فارسی" data-language-local-name="persa" 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/Identiteettifunktio" title="Identiteettifunktio (finés)" lang="fi" hreflang="fi" data-title="Identiteettifunktio" data-language-autonym="Suomi" data-language-local-name="finés" 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/Application_identit%C3%A9" title="Application identité (francés)" lang="fr" hreflang="fr" data-title="Application identité" data-language-autonym="Français" data-language-local-name="francés" 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/Funci%C3%B3n_identidade" title="Función identidade (gallego)" lang="gl" hreflang="gl" data-title="Función identidade" data-language-autonym="Galego" data-language-local-name="gallego" 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%95%D7%A0%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%94%D7%96%D7%94%D7%95%D7%AA" title="פונקציית הזהות (hebreo)" lang="he" hreflang="he" data-title="פונקציית הזהות" data-language-autonym="עברית" data-language-local-name="hebreo" 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%A4%E0%A4%A4%E0%A5%8D%E0%A4%B8%E0%A4%AE%E0%A4%95_%E0%A4%AB%E0%A4%B2%E0%A4%A8" title="तत्समक फलन (hindi)" lang="hi" hreflang="hi" data-title="तत्समक फलन" 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/Funkcija_identiteta" title="Funkcija identiteta (croata)" lang="hr" hreflang="hr" data-title="Funkcija identiteta" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fungsi_identitas" title="Fungsi identitas (indonesio)" lang="id" hreflang="id" data-title="Fungsi identitas" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesio" 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/Samsemdarv%C3%B6rpun" title="Samsemdarvörpun (islandés)" lang="is" hreflang="is" data-title="Samsemdarvörpun" data-language-autonym="Íslenska" data-language-local-name="islandés" 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/Funzione_identit%C3%A0" title="Funzione identità (italiano)" lang="it" hreflang="it" data-title="Funzione identità" data-language-autonym="Italiano" data-language-local-name="italiano" 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/%E6%81%92%E7%AD%89%E5%86%99%E5%83%8F" title="恒等写像 (japonés)" lang="ja" hreflang="ja" data-title="恒等写像" data-language-autonym="日本語" data-language-local-name="japonés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%95%AD%EB%93%B1_%ED%95%A8%EC%88%98" title="항등 함수 (coreano)" lang="ko" hreflang="ko" data-title="항등 함수" 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/Aplicaziun_identica" title="Aplicaziun identica (lombardo)" lang="lmo" hreflang="lmo" data-title="Aplicaziun identica" data-language-autonym="Lombard" data-language-local-name="lombardo" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%8F%E0%A4%95%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%AE%E0%A4%95_%E0%A4%AB%E0%A4%B2%E0%A4%A8" title="एकात्मक फलन (nepalí)" lang="ne" hreflang="ne" data-title="एकात्मक फलन" data-language-autonym="नेपाली" data-language-local-name="nepalí" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Identieke_afbeelding" title="Identieke afbeelding (neerlandés)" lang="nl" hreflang="nl" data-title="Identieke afbeelding" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Funkcja_to%C5%BCsamo%C5%9Bciowa" title="Funkcja tożsamościowa (polaco)" lang="pl" hreflang="pl" data-title="Funkcja tożsamościowa" data-language-autonym="Polski" data-language-local-name="polaco" 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/Fun%C3%A7%C3%A3o_identidade" title="Função identidade (portugués)" lang="pt" hreflang="pt" data-title="Função identidade" data-language-autonym="Português" data-language-local-name="portugués" 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/Identitate_(matematic%C4%83)" title="Identitate (matematică) (rumano)" lang="ro" hreflang="ro" data-title="Identitate (matematică)" data-language-autonym="Română" data-language-local-name="rumano" 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%A2%D0%BE%D0%B6%D0%B4%D0%B5%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%BD%D0%BE%D0%B5_%D0%BE%D1%82%D0%BE%D0%B1%D1%80%D0%B0%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Тождественное отображение (ruso)" lang="ru" hreflang="ru" data-title="Тождественное отображение" data-language-autonym="Русский" data-language-local-name="ruso" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Identi%C4%8Dna_funkcija" title="Identična funkcija (esloveno)" lang="sl" hreflang="sl" data-title="Identična funkcija" data-language-autonym="Slovenščina" data-language-local-name="esloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Identitetsfunktion" title="Identitetsfunktion (sueco)" lang="sv" hreflang="sv" data-title="Identitetsfunktion" data-language-autonym="Svenska" data-language-local-name="sueco" 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%AE%E0%AF%81%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AF%8A%E0%AE%B0%E0%AF%81%E0%AE%AE%E0%AF%88%E0%AE%9A%E0%AF%8D_%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%81" title="முற்றொருமைச் சார்பு (tamil)" lang="ta" hreflang="ta" data-title="முற்றொருமைச் சார்பு" data-language-autonym="தமிழ்" data-language-local-name="tamil" 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%9F%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B9%8C%E0%B8%8A%E0%B8%B1%E0%B8%99%E0%B9%80%E0%B8%AD%E0%B8%81%E0%B8%A5%E0%B8%B1%E0%B8%81%E0%B8%A9%E0%B8%93%E0%B9%8C" title="ฟังก์ชันเอกลักษณ์ (tailandés)" lang="th" hreflang="th" data-title="ฟังก์ชันเอกลักษณ์" data-language-autonym="ไทย" data-language-local-name="tailandés" 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/Birim_fonksiyon" title="Birim fonksiyon (turco)" lang="tr" hreflang="tr" data-title="Birim fonksiyon" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%BE%D1%82%D0%BE%D0%B6%D0%BD%D0%B5_%D0%B2%D1%96%D0%B4%D0%BE%D0%B1%D1%80%D0%B0%D0%B6%D0%B5%D0%BD%D0%BD%D1%8F" title="Тотожне відображення (ucraniano)" lang="uk" hreflang="uk" data-title="Тотожне відображення" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%A0m_%C4%91%E1%BB%93ng_nh%E1%BA%A5t" title="Hàm đồng nhất (vietnamita)" lang="vi" hreflang="vi" data-title="Hàm đồng nhất" 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/%E6%81%86%E7%AD%89%E5%87%BD%E6%95%B8" title="恆等函數 (chino)" lang="zh" hreflang="zh" data-title="恆等函數" data-language-autonym="中文" data-language-local-name="chino" 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/%E6%81%86%E7%AD%89%E5%87%BD%E6%95%B8" title="恆等函數 (cantonés)" lang="yue" hreflang="yue" data-title="恆等函數" data-language-autonym="粵語" data-language-local-name="cantonés" 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/Q321119#sitelinks-wikipedia" title="Editar enlaces interlingüísticos" class="wbc-editpage">Editar enlaces</a></span></div> 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</div> <div id="siteSub" class="noprint">De Wikipedia, la enciclopedia libre</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="es" dir="ltr"><p>En <a href="/wiki/Matem%C3%A1ticas" title="Matemáticas">matemáticas</a> una <b>función identidad</b> es una <a href="/wiki/Funci%C3%B3n_matem%C3%A1tica" class="mw-redirect" title="Función matemática">función matemática</a>, de un conjunto <i>M</i> a sí mismo, que devuelve su propio largo. En <a href="/wiki/Notaci%C3%B3n_matem%C3%A1tica" title="Notación matemática">notación matemática</a>: </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 {\begin{array}{rccl}{\text{id}}_{M}:&M&\longrightarrow &M\\&m&\mapsto &n={\text{id}}_{M}(m)=m\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right center center left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>id</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo>:</mo> </mtd> <mtd> <mi>M</mi> </mtd> <mtd> <mo stretchy="false">⟶</mo> </mtd> <mtd> <mi>M</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>m</mi> </mtd> <mtd> <mo stretchy="false">↦</mo> </mtd> <mtd> <mi>n</mi> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>id</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>m</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{rccl}{\text{id}}_{M}:&M&\longrightarrow &M\\&m&\mapsto &n={\text{id}}_{M}(m)=m\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a775ac36b3661608d9846053117ea25dab92afc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:36.538ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{rccl}{\text{id}}_{M}:&M&\longrightarrow &M\\&m&\mapsto &n={\text{id}}_{M}(m)=m\end{array}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Ejemplos">Ejemplos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funci%C3%B3n_identidad&action=edit&section=1" title="Editar sección: Ejemplos"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Archivo:Funci%C3%B3n_Cu_id.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Funci%C3%B3n_Cu_id.svg/280px-Funci%C3%B3n_Cu_id.svg.png" decoding="async" width="280" height="280" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Funci%C3%B3n_Cu_id.svg/420px-Funci%C3%B3n_Cu_id.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Funci%C3%B3n_Cu_id.svg/560px-Funci%C3%B3n_Cu_id.svg.png 2x" data-file-width="500" data-file-height="500" /></a><figcaption></figcaption></figure> <p>La función identidad de <a href="/wiki/N%C3%BAmero_real" title="Número real">números reales</a> puede describirse de la forma siguiente: </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 {\begin{array}{rccl}{\text{id}}_{\mathbb {R} }:&\mathbb {R} &\longrightarrow &\mathbb {R} \\&x&\mapsto &y={\text{id}}_{\mathbb {R} }(x)=x\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right center center left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>id</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mrow> </msub> <mo>:</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mtd> <mtd> <mo stretchy="false">⟶</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>x</mi> </mtd> <mtd> <mo stretchy="false">↦</mo> </mtd> <mtd> <mi>y</mi> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>id</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{rccl}{\text{id}}_{\mathbb {R} }:&\mathbb {R} &\longrightarrow &\mathbb {R} \\&x&\mapsto &y={\text{id}}_{\mathbb {R} }(x)=x\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4958b4a5bbd6799ef7fdb6c31ad25cd3b14733ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.032ex; height:6.176ex;" alt="{\displaystyle {\begin{array}{rccl}{\text{id}}_{\mathbb {R} }:&\mathbb {R} &\longrightarrow &\mathbb {R} \\&x&\mapsto &y={\text{id}}_{\mathbb {R} }(x)=x\end{array}}}"></span></dd></dl> <p>La <a href="/wiki/Funci%C3%B3n_real" title="Función real">función real</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 {\text{id}}_{\mathbb {R} }:\mathbb {R} \longrightarrow \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>id</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mrow> </msub> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">⟶</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{id}}_{\mathbb {R} }:\mathbb {R} \longrightarrow \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f738eb8e4d89d0c7c40c8156dc71d882788fe141" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.747ex; height:2.509ex;" alt="{\displaystyle {\text{id}}_{\mathbb {R} }:\mathbb {R} \longrightarrow \mathbb {R} }"></span> tiene como representación gráfica en <a href="/wiki/Coordenadas_cartesianas" title="Coordenadas cartesianas">coordenadas cartesianas</a> la <a href="/wiki/L%C3%ADnea_recta" class="mw-redirect" title="Línea recta">línea recta</a> que cruza el origen subiendo en un ángulo de 45° hacia la derecha. </p><p>La función identidad en el conjunto <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 M=\left\{0,1\right\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>}</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=\left\{0,1\right\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ec5fbf53d516fb9bff01c26fe3ee56edb18f24d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.224ex; height:2.843ex;" alt="{\displaystyle M=\left\{0,1\right\}}"></span> es la <a href="/wiki/Doble_negaci%C3%B3n" class="mw-disambig" title="Doble negación">doble negación</a>, expresada por <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 \not \neg x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬̸</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \neg x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/065ba35d75daa0efb4563a3bb2d1eb88885b7192" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.881ex; height:2.676ex;" alt="{\displaystyle \not \neg x}"></span> </p><p>Además, para cualquier otra <a href="/wiki/Funci%C3%B3n_matem%C3%A1tica" class="mw-redirect" title="Función matemática">función</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 f:M\longrightarrow N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>M</mi> <mo stretchy="false">⟶</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:M\longrightarrow N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7da4f93277d788280ae6bd537479d2c083952ff2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.817ex; height:2.509ex;" alt="{\displaystyle f:M\longrightarrow N}"></span>se satisfacen las siguientes reglas de composición: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f\circ {\text{id}}_{M}=f,\;\;{\text{id}}_{N}\circ f=f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>∘</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>id</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </msub> <mo>=</mo> <mi>f</mi> <mo>,</mo> <mspace width="thickmathspace" /> <mspace width="thickmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>id</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>∘</mo> <mi>f</mi> <mo>=</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f\circ {\text{id}}_{M}=f,\;\;{\text{id}}_{N}\circ f=f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45b2cf500cd7830dae0718955e5932749a8a6ce3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.554ex; height:2.509ex;" alt="{\displaystyle f\circ {\text{id}}_{M}=f,\;\;{\text{id}}_{N}\circ f=f}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Véase_también"><span id="V.C3.A9ase_tambi.C3.A9n"></span>Véase también</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funci%C3%B3n_identidad&action=edit&section=2" title="Editar sección: Véase también"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Involuci%C3%B3n_(matem%C3%A1tica)" title="Involución (matemática)">Involución (matemática)</a></li> <li><a href="/wiki/Inyecci%C3%B3n_can%C3%B3nica" title="Inyección canónica">Inyección canónica</a></li></ul> <dl><dd><a href="/wiki/Funci%C3%B3n_definida_a_trozos" title="Función definida a trozos">Función definida a trozos</a></dd></dl> <dl><dd><a href="/wiki/Funci%C3%B3n_escal%C3%B3n_de_Heaviside" title="Función escalón de Heaviside">Función escalón de Heaviside</a></dd> <dd><a href="/wiki/Funci%C3%B3n_rectangular" title="Función rectangular">Función rectangular</a></dd> <dd><a href="/wiki/Funci%C3%B3n_escalonada" title="Función escalonada">Función escalonada</a></dd></dl> <dl><dd><a href="/wiki/Funci%C3%B3n_signo" title="Función signo">Función signo</a></dd> <dd><a href="/wiki/Valor_absoluto" title="Valor absoluto">Valor absoluto</a></dd> <dd><a href="/wiki/Funci%C3%B3n_rampa" title="Función rampa">Función rampa</a></dd> <dd><a href="/wiki/Funciones_de_parte_entera" title="Funciones de parte entera">Funciones de parte entera</a></dd> <dd><a href="/wiki/Parte_fraccionaria" title="Parte fraccionaria">Parte fraccionaria</a></dd> <dd><a href="/wiki/Mantisa" title="Mantisa">Mantisa</a></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Enlaces_externos">Enlaces externos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funci%C3%B3n_identidad&action=edit&section=3" title="Editar sección: Enlaces externos"><span>editar</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span id="Reference-Mathworld-Identity_Function" class="citation web"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W</a>. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/IdentityFunction.html">«Identity Function»</a>. En Weisstein, Eric W, ed. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i> <span style="color:var(--color-subtle, #555 );">(en inglés)</span>. <a href="/wiki/Wolfram_Research" title="Wolfram Research">Wolfram Research</a>.</span><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fes.wikipedia.org%3AFunci%C3%B3n+identidad&rft.atitle=Identity+Function&rft.au=Weisstein%2C+Eric+W&rft.aulast=Weisstein%2C+Eric+W&rft.genre=article&rft.jtitle=MathWorld&rft.pub=Wolfram+Research&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FIdentityFunction.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><a rel="nofollow" class="external text" href="https://planetmath.org/5418">Identity map</a> en <a href="/wiki/PlanetMath" title="PlanetMath">PlanetMath</a>.</li></ul> <style data-mw-deduplicate="TemplateStyles:r161257576">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output .mw-authority-control .navbox table{margin:0}.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control .mw-mf-linked-projects{display:flex;padding:0.5em;border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral,#eaecf0);color:var(--color-base,#202122)}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}.mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#a2a9b1);background-color:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .mw-authority-control .navbox-list{border-color:#f8f9fa}.mw-parser-output .mw-authority-control .navbox th{background-color:#eeeeff}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d);background-color:var(--background-color-neutral,#27292d);color:var(--color-base,#eaecf0)}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-night .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .mw-mf-linked-projects{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral,#27292d)!important;color:var(--color-base,#eaecf0)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox{border:1px solid var(--border-color-base,#72777d)!important;background-color:var(--background-color-neutral-subtle,#202122)!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox-list{border-color:#202122!important}html.skin-theme-clientpref-os .mw-parser-output .mw-authority-control .navbox th{background-color:#27292d!important}}</style><div class="mw-authority-control"><div role="navigation" class="navbox" aria-label="Navbox" style="width: inherit;padding:3px"><table class="hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width: 12%; 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