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class="vector-toc-link" href="#Notas"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notas</span> </div> </a> <ul id="toc-Notas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véxase_tamén" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véxase_tamén"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Véxase tamén</span> </div> </a> <button aria-controls="toc-Véxase_tamén-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>Mostrar ou agochar a subsección "Véxase tamén"</span> </button> <ul id="toc-Véxase_tamén-sublist" class="vector-toc-list"> <li id="toc-Outros_artigos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Outros_artigos"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Outros artigos</span> </div> </a> <ul id="toc-Outros_artigos-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="Contidos" 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="Mostrar ou agochar a táboa de contidos" > <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">Mostrar ou agochar a táboa de contidos</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">Elemento maiorante e minorante</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 artigo noutra lingua. Dispoñible en 17 linguas" > <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-17" 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">17 linguas</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%AD%D8%AF%D9%88%D8%AF_%D8%B9%D9%84%D9%8A%D8%A7_%D9%88%D8%AF%D9%86%D9%8A%D8%A7" title="حدود عليا ودنيا – árabe" lang="ar" hreflang="ar" data-title="حدود عليا ودنيا" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Fita_superior" title="Fita superior – catalán" lang="ca" hreflang="ca" data-title="Fita superior" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Upper_and_lower_bounds" title="Upper and lower bounds – inglés" lang="en" hreflang="en" data-title="Upper and lower bounds" data-language-autonym="English" data-language-local-name="inglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Elemento_mayorante_y_minorante" title="Elemento mayorante y minorante – español" lang="es" hreflang="es" data-title="Elemento mayorante y minorante" data-language-autonym="Español" data-language-local-name="español" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Goi-borne" title="Goi-borne – éuscaro" lang="eu" hreflang="eu" data-title="Goi-borne" data-language-autonym="Euskara" data-language-local-name="éuscaro" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Majorant_ou_minorant" title="Majorant ou minorant – francés" lang="fr" hreflang="fr" data-title="Majorant ou minorant" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%A1%D7%9D_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="חסם (מתמטיקה) – hebreo" lang="he" hreflang="he" data-title="חסם (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="hebreo" 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/Gornja_i_donja_me%C4%91a" title="Gornja i donja međa – croata" lang="hr" hreflang="hr" data-title="Gornja i donja međa" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Maggiorante_e_minorante" title="Maggiorante e minorante – italiano" lang="it" hreflang="it" data-title="Maggiorante e minorante" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja badge-Q70894304 mw-list-item" title=""><a href="https://ja.wikipedia.org/wiki/%E4%B8%8A%E7%95%8C%E3%81%A8%E4%B8%8B%E7%95%8C" title="上界と下界 – xaponés" lang="ja" hreflang="ja" data-title="上界と下界" data-language-autonym="日本語" data-language-local-name="xaponés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Maggiorant_e_minorant" title="Maggiorant e minorant – Lombard" lang="lmo" hreflang="lmo" data-title="Maggiorant e minorant" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Bovengrens_en_ondergrens" title="Bovengrens en ondergrens – neerlandés" lang="nl" hreflang="nl" data-title="Bovengrens en ondergrens" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Skranke_(matematikk)" title="Skranke (matematikk) – noruegués bokmål" lang="nb" hreflang="nb" data-title="Skranke (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="noruegués bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%9Cst_ve_alt_s%C4%B1n%C4%B1r" title="Üst ve alt sınır – turco" lang="tr" hreflang="tr" data-title="Üst ve alt sınır" 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%92%D0%B5%D1%80%D1%85%D0%BD%D1%8F_%D1%82%D0%B0_%D0%BD%D0%B8%D0%B6%D0%BD%D1%8F_%D0%BC%D0%B5%D0%B6%D0%B0" title="Верхня та нижня межа – ucraíno" lang="uk" hreflang="uk" data-title="Верхня та нижня межа" data-language-autonym="Українська" data-language-local-name="ucraíno" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%B8%8A%E7%95%8C%E5%92%8C%E4%B8%8B%E7%95%8C" title="上界和下界 – chinés" lang="zh" hreflang="zh" data-title="上界和下界" data-language-autonym="中文" data-language-local-name="chinés" 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%95%8C%E9%99%90_(%E6%95%B8%E5%AD%B8)" title="界限 (數學) – cantonés" lang="yue" hreflang="yue" data-title="界限 (數學)" 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/Q13222579#sitelinks-wikipedia" title="Editar as ligazóns 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href="/w/index.php?title=Especial:Libro&bookcmd=book_creator&referer=Elemento+maiorante+e+minorante"><span>Crear un libro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=Elemento_maiorante_e_minorante&action=show-download-screen"><span>Descargar como PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Elemento_maiorante_e_minorante&printable=yes" title="Versión para imprimir da páxina [p]" accesskey="p"><span>Versión para imprimir</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Noutros proxectos </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q13222579" title="Ligazón ao elemento conectado no repositorio de datos [g]" accesskey="g"><span>Elemento de 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="Ferramentas das páxinas"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aparencia"> <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">Aparencia</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover á barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">agochar</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">Na Galipedia, a Wikipedia en galego.</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="gl" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Illustration_of_supremum.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Illustration_of_supremum.svg/300px-Illustration_of_supremum.svg.png" decoding="async" width="300" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Illustration_of_supremum.svg/450px-Illustration_of_supremum.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Illustration_of_supremum.svg/600px-Illustration_of_supremum.svg.png 2x" data-file-width="282" data-file-height="90" /></a><figcaption> Un conxunto M (en azul) con elementos maiorantes (en vermello e verde) e o seu maiorante mínimo ou supremo (só o verde)</figcaption></figure> <p>En matemáticas, particularmente na <a href="/wiki/Teor%C3%ADa_da_orde" title="Teoría da orde">teoría da orde</a>, un <b>elemento</b> <b>maiorante</b> dun subconxunto <span class="texhtml mvar" style="font-style:italic;">M</span> dalgún <a href="/w/index.php?title=Orde_previa&action=edit&redlink=1" class="new" title="Orde previa (a páxina aínda non existe)">conxunto preordenado</a> <span class="texhtml">(<i>K</i>, ≤)</span> é un elemento de <span class="texhtml mvar" style="font-style:italic;">K</span> que é maior ou igual que todos os elementos de <span class="texhtml mvar" style="font-style:italic;">M</span>. <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>1<span>]</span></a></sup> Do mesmo modo un <b>elemento minorante</b> de <span class="texhtml mvar" style="font-style:italic;">M</span> defínese como un elemento de <span class="texhtml mvar" style="font-style:italic;">K</span> que é menor ou igual a todos os elementos de <span class="texhtml mvar" style="font-style:italic;">M</span>. Un conxunto cun maiorante (respectivamente, minorante) dise que está <b>limitado superiormente</b> ou <b>maiorizado</b> (respectivamente <b>limitado inferiormente</b> ou <b>minorizado</b>) por ese límite. </p><p>Entre tódolos maiorantes do conxunto <span class="texhtml mvar" style="font-style:italic;">M</span> que pertencen a <span class="texhtml mvar" style="font-style:italic;">K</span>, denominamos supremo de <span class="texhtml mvar" style="font-style:italic;">M</span> ao menor de todos estes maiorantes. Se o supremo pertence tamén a <span class="texhtml mvar" style="font-style:italic;">M</span> denominase máximo de <span class="texhtml mvar" style="font-style:italic;">M</span>. No diagrama de exemplo se o elemento verde pertenecese a <span class="texhtml mvar" style="font-style:italic;">M</span> sería máximo, se non pertence daquela é supremo. </p><p>Simetricamente para os minorantes distinguimos ínfimo de mínimo. </p><p><br /> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Exemplos">Exemplos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&veaction=edit&section=1" title="Editar a sección: «Exemplos»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&action=edit&section=1" title="Editar o código fonte da sección: Exemplos"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Por exemplo, 4 e <span class="texhtml">5</span> son minorantes para o conxunto <span class="texhtml"><i>S</i> = {5, 8, 42, 34, 13934}</span> (como un subconxunto dos <a href="/wiki/N%C3%BAmero_enteiro" title="Número enteiro">enteiros</a> ou dos <a href="/wiki/N%C3%BAmero_real" title="Número real">números reais</a>, etc.). Por outra banda, <span class="texhtml">6</span> non é un elemento minorante para <span class="texhtml mvar" style="font-style:italic;">S</span> xa que non é menor que todos os elementos de <span class="texhtml mvar" style="font-style:italic;">S</span> . <span class="texhtml">13934</span> e outros números <i>x</i> tales que <span class="texhtml">x ≥ 13934</span> sería maiorantes para <i>S</i> . </p><p>O conxunto <span class="texhtml"><i>S</i> = {42}</span> ten o número <span class="texhtml">42</span> tanto coma maiorante coma minorante. </p><p>Cada subconxunto finito non baleiro dun <a href="/wiki/Orde_total" title="Orde total">conxunto totalmente ordenado</a> ten elemento maiorantes e elemento minorante. </p> <div class="mw-heading mw-heading2"><h2 id="Límites_das_funcións"><span id="L.C3.ADmites_das_funci.C3.B3ns"></span>Límites das funcións</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&veaction=edit&section=2" title="Editar a sección: «Límites das funcións»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&action=edit&section=2" title="Editar o código fonte da sección: Límites das funcións"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As definicións pódense xeneralizar a <a href="/wiki/Funci%C3%B3n" title="Función">funcións</a> e mesmo a conxuntos de funcións. </p><p>Dada unha función f co <a href="/wiki/Dominio_de_definici%C3%B3n" title="Dominio de definición">dominio</a> <span class="texhtml mvar" style="font-style:italic;">D</span> e un conxunto preordenado <span class="texhtml">(<i>K</i>, ≤)</span> como <a href="/wiki/Codominio" title="Codominio">codominio</a>, un elemento <span class="texhtml mvar" style="font-style:italic;"><i>y</i></span> de <span class="texhtml mvar" style="font-style:italic;">K</span> é un límite superior de f se <span class="texhtml"><i>y</i> ≥ <i>f</i>(<i>x</i>)</span> para cada <span class="texhtml mvar" style="font-style:italic;">x</span> en <span class="texhtml mvar" style="font-style:italic;">D</span>. O maiorante chámase óptimo se a igualdade cúmprese para polo menos un valor de <span class="texhtml mvar" style="font-style:italic;">x</span>. </p><p>Do mesmo xeito, unha función <span class="texhtml mvar" style="font-style:italic;">g</span> definida no dominio <span class="texhtml mvar" style="font-style:italic;">D</span> e que teña o mesmo codominio <span class="texhtml">(<i>K</i>, ≤)</span> é maiorante de f, se <span class="texhtml"><i>g</i>(<i>x</i>) ≥ <i>f</i>(<i>x</i>)</span> para cada <span class="texhtml mvar" style="font-style:italic;">x</span> en <span class="texhtml mvar" style="font-style:italic;">D</span>. Ademais, dise que a función <span class="texhtml mvar" style="font-style:italic;">g</span> é maiorante dun conxunto de funcións, se é maiorante de <i>cada</i> función dese conxunto. </p><p>A noción de límite inferior para (conxuntos de) funcións defínese de xeito análogo, substituíndo ≥ por ≤. </p> <div class="mw-heading mw-heading2"><h2 id="Límites_estritos"><span id="L.C3.ADmites_estritos"></span>Límites estritos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&veaction=edit&section=3" title="Editar a sección: «Límites estritos»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&action=edit&section=3" title="Editar o código fonte da sección: Límites estritos"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un maiorante dise que é un maiorante <i>mínimo</i> ou límite superior mínimo ou <a href="/wiki/%C3%8Dnfimo_e_supremo" title="Ínfimo e supremo"> supremo</a> se ningún valor menor é maiorante. Do mesmo xeito, dise que un minorante ou límite inferior ou <i>ínfimo</i>, se ningún valor maior é un minorante. </p> <div class="mw-heading mw-heading2"><h2 id="Notas">Notas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&veaction=edit&section=4" title="Editar a sección: «Notas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&action=edit&section=4" title="Editar o código fonte da sección: Notas"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://www.mathsisfun.com/definitions/upper-bound.html">"upper-bound"</a>. <i>www.mathsisfun.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fgl.wikipedia.org%3AElemento+maiorante+e+minorante&rft.atitle=upper-bound&rft.genre=unknown&rft.jtitle=www.mathsisfun.com&rft_id=https%3A%2F%2Fwww.mathsisfun.com%2Fdefinitions%2Fupper-bound.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Véxase_tamén"><span id="V.C3.A9xase_tam.C3.A9n"></span>Véxase tamén</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&veaction=edit&section=5" title="Editar a sección: «Véxase tamén»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&action=edit&section=5" title="Editar o código fonte da sección: Véxase tamén"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Outros_artigos">Outros artigos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&veaction=edit&section=6" title="Editar a sección: «Outros artigos»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elemento_maiorante_e_minorante&action=edit&section=6" title="Editar o código fonte da sección: Outros artigos"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Elemento_maior_e_menor" title="Elemento maior e menor">Elemento maior e menor</a></li> <li><a href="/wiki/%C3%8Dnfimo_e_supremo" title="Ínfimo e supremo">Ínfimo e supremo</a></li> <li><a href="/wiki/Elemento_maximal_e_minimal" title="Elemento maximal e minimal">Elemento maximal e minimal</a></li></ul> <div role="navigation" class="navbox" aria-labelledby="Control_de_autoridades" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Control_de_autoridades" scope="row" class="navbox-group" style="width:1%;width: 12%; 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