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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">ابزارهای شخصی</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="منوی کاربری" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_fa.wikipedia.org&uselang=fa"><span>کمک مالی</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D9%88%DB%8C%DA%98%D9%87:%D8%A7%DB%8C%D8%AC%D8%A7%D8%AF_%D8%AD%D8%B3%D8%A7%D8%A8_%DA%A9%D8%A7%D8%B1%D8%A8%D8%B1%DB%8C&returnto=%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" title="از شما دعوت می‌شود که یک حساب ایجاد کنید و وارد شوید؛ هرچند که این کار اختیاری است."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>ایجاد حساب</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D9%88%DB%8C%DA%98%D9%87:%D9%88%D8%B1%D9%88%D8%AF_%D8%A8%D9%87_%D8%B3%D8%A7%D9%85%D8%A7%D9%86%D9%87&returnto=%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" title="توصیه می‌شود که به سامانه وارد شوید، گرچه اجباری نیست [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>ورود</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> صفحه‌هایی برای ویرایشگرانی که از سامانه خارج شدند <a href="/wiki/%D8%B1%D8%A7%D9%87%D9%86%D9%85%D8%A7:%D9%85%D9%82%D8%AF%D9%85%D9%87" aria-label="دربارهٔ ویرایش‌کردن بیشتر بدانید"><span>بیشتر بدانید</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D9%88%DB%8C%DA%98%D9%87:%D9%85%D8%B4%D8%A7%D8%B1%DA%A9%D8%AA%E2%80%8C%D9%87%D8%A7%DB%8C_%D9%85%D9%86" title="فهرست ویرایش‌ها انجام شده از این نشانی آی‌پی [y]" accesskey="y"><span>مشارکت‌ها</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D9%88%DB%8C%DA%98%D9%87:%D8%A8%D8%AD%D8%AB_%D9%85%D9%86" title="بحث پیرامون ویرایش‌های این نشانی آی‌پی [n]" accesskey="n"><span>بحث</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="وبگاه"> <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="فهرست" 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">فهرست</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">انتقال به نوار کناری</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">نهفتن</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">بخش آغازین</div> </a> </li> <li id="toc-جستارهای_وابسته" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#جستارهای_وابسته"> <div class="vector-toc-text"> <span class="vector-toc-numb">۱</span> <span>جستارهای وابسته</span> </div> </a> <ul id="toc-جستارهای_وابسته-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-پانویس" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#پانویس"> <div class="vector-toc-text"> <span class="vector-toc-numb">۲</span> <span>پانویس</span> </div> </a> <ul id="toc-پانویس-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-منابع" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#منابع"> <div class="vector-toc-text"> <span class="vector-toc-numb">۳</span> <span>منابع</span> </div> </a> <ul id="toc-منابع-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-پیوندهای_بیرونی" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#پیوندهای_بیرونی"> <div class="vector-toc-text"> <span class="vector-toc-numb">۴</span> <span>پیوندهای بیرونی</span> </div> </a> <ul id="toc-پیوندهای_بیرونی-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="فهرست" 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="تغییر وضعیت فهرست محتویات" > <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">تغییر وضعیت فهرست محتویات</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">ترتیب کلی</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="به مقاله‌ای به یک زبان دیگر بروید. به ۲۸ زبان در دسترس است." > <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-28" 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">۲۸ زبان</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%AA%D8%B1%D8%AA%D9%8A%D8%A8_%D9%83%D9%84%D9%8A" title="ترتيب كلي–عربی" lang="ar" hreflang="ar" data-title="ترتيب كلي" data-language-autonym="العربية" data-language-local-name="عربی" 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/Ordre_total" title="Ordre total–کاتالان" lang="ca" hreflang="ca" data-title="Ordre total" data-language-autonym="Català" data-language-local-name="کاتالان" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs badge-Q70893996 mw-list-item" title=""><a href="https://cs.wikipedia.org/wiki/Line%C3%A1rn%C3%AD_uspo%C5%99%C3%A1d%C3%A1n%C3%AD" title="Lineární uspořádání–چکی" lang="cs" hreflang="cs" data-title="Lineární uspořádání" data-language-autonym="Čeština" data-language-local-name="چکی" 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%9B%D0%B8%D0%BD%D0%B8%D0%BB%D0%BB%D0%B5_%D0%B9%C4%95%D1%80%D0%BA%D0%B5%D0%BB%D0%B5%D0%BD%D0%BD%C4%95_%D0%B9%D1%8B%D1%88" title="Линилле йĕркеленнĕ йыш–چوواشی" lang="cv" hreflang="cv" data-title="Линилле йĕркеленнĕ йыш" data-language-autonym="Чӑвашла" data-language-local-name="چوواشی" 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/Total_ordning" title="Total ordning–دانمارکی" lang="da" hreflang="da" data-title="Total ordning" data-language-autonym="Dansk" data-language-local-name="دانمارکی" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Totalordnung" title="Totalordnung–آلمانی" lang="de" hreflang="de" data-title="Totalordnung" data-language-autonym="Deutsch" data-language-local-name="آلمانی" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Total_order" title="Total order–انگلیسی" lang="en" hreflang="en" data-title="Total order" data-language-autonym="English" data-language-local-name="انگلیسی" 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/Totala_ordo" title="Totala ordo–اسپرانتو" lang="eo" hreflang="eo" data-title="Totala ordo" data-language-autonym="Esperanto" data-language-local-name="اسپرانتو" 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/Orden_total" title="Orden total–اسپانیایی" lang="es" hreflang="es" data-title="Orden total" data-language-autonym="Español" data-language-local-name="اسپانیایی" 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/Lineaarne_j%C3%A4rjestus" title="Lineaarne järjestus–استونیایی" lang="et" hreflang="et" data-title="Lineaarne järjestus" data-language-autonym="Eesti" data-language-local-name="استونیایی" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ordre_total" title="Ordre total–فرانسوی" lang="fr" hreflang="fr" data-title="Ordre total" data-language-autonym="Français" data-language-local-name="فرانسوی" 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/Orde_total" title="Orde total–گالیسیایی" lang="gl" hreflang="gl" data-title="Orde total" data-language-autonym="Galego" data-language-local-name="گالیسیایی" 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%A1%D7%93%D7%A8_%D7%9E%D7%9C%D7%90" title="סדר מלא–عبری" lang="he" hreflang="he" data-title="סדר מלא" data-language-autonym="עברית" data-language-local-name="عبری" 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/Totalno_ure%C4%91en_skup" title="Totalno uređen skup–کروات" lang="hr" hreflang="hr" data-title="Totalno uređen skup" data-language-autonym="Hrvatski" data-language-local-name="کروات" 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/Urutan_total" title="Urutan total–اندونزیایی" lang="id" hreflang="id" data-title="Urutan total" data-language-autonym="Bahasa Indonesia" data-language-local-name="اندونزیایی" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ordine_totale" title="Ordine totale–ایتالیایی" lang="it" hreflang="it" data-title="Ordine totale" data-language-autonym="Italiano" data-language-local-name="ایتالیایی" 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/%E5%85%A8%E9%A0%86%E5%BA%8F" title="全順序–ژاپنی" lang="ja" hreflang="ja" data-title="全順序" data-language-autonym="日本語" data-language-local-name="ژاپنی" 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/%EC%A0%84%EC%88%9C%EC%84%9C_%EC%A7%91%ED%95%A9" title="전순서 집합–کره‌ای" lang="ko" hreflang="ko" data-title="전순서 집합" data-language-autonym="한국어" data-language-local-name="کره‌ای" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Totale_orde" title="Totale orde–هلندی" lang="nl" hreflang="nl" data-title="Totale orde" data-language-autonym="Nederlands" data-language-local-name="هلندی" 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/Total_orden" title="Total orden–نروژی بوک‌مُل" lang="nb" hreflang="nb" data-title="Total orden" data-language-autonym="Norsk bokmål" data-language-local-name="نروژی بوک‌مُل" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Porz%C4%85dek_liniowy" title="Porządek liniowy–لهستانی" lang="pl" hreflang="pl" data-title="Porządek liniowy" data-language-autonym="Polski" data-language-local-name="لهستانی" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Rela%C8%9Bie_de_ordine_total%C4%83" title="Relație de ordine totală–رومانیایی" lang="ro" hreflang="ro" data-title="Relație de ordine totală" data-language-autonym="Română" data-language-local-name="رومانیایی" 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%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE_%D1%83%D0%BF%D0%BE%D1%80%D1%8F%D0%B4%D0%BE%D1%87%D0%B5%D0%BD%D0%BD%D0%BE%D0%B5_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Линейно упорядоченное множество–روسی" lang="ru" hreflang="ru" data-title="Линейно упорядоченное множество" data-language-autonym="Русский" data-language-local-name="روسی" 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/Line%C3%A1rne_usporiadan%C3%A1_mno%C5%BEina" title="Lineárne usporiadaná množina–اسلواکی" lang="sk" hreflang="sk" data-title="Lineárne usporiadaná množina" data-language-autonym="Slovenčina" data-language-local-name="اسلواکی" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Linj%C3%A4r_ordning" title="Linjär ordning–سوئدی" lang="sv" hreflang="sv" data-title="Linjär ordning" data-language-autonym="Svenska" data-language-local-name="سوئدی" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%BE_%D0%B2%D0%BF%D0%BE%D1%80%D1%8F%D0%B4%D0%BA%D0%BE%D0%B2%D0%B0%D0%BD%D0%B0_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD%D0%B0" title="Лінійно впорядкована множина–اوکراینی" lang="uk" hreflang="uk" data-title="Лінійно впорядкована множина" data-language-autonym="Українська" data-language-local-name="اوکراینی" 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/Th%E1%BB%A9_t%E1%BB%B1_to%C3%A0n_ph%E1%BA%A7n" title="Thứ tự toàn phần–ویتنامی" lang="vi" hreflang="vi" data-title="Thứ tự toàn phần" data-language-autonym="Tiếng Việt" data-language-local-name="ویتنامی" 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/%E5%85%A8%E5%BA%8F%E5%85%B3%E7%B3%BB" title="全序关系–چینی" lang="zh" hreflang="zh" data-title="全序关系" data-language-autonym="中文" data-language-local-name="چینی" 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/Q369377#sitelinks-wikipedia" title="ویرایش پیوندهای بین‌زبانی" class="wbc-editpage">ویرایش پیوندها</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div 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href="/w/index.php?title=%D9%88%DB%8C%DA%98%D9%87:DownloadAsPdf&page=%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8_%DA%A9%D9%84%DB%8C&action=show-download-screen"><span>بارگیری به‌صورت PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8_%DA%A9%D9%84%DB%8C&printable=yes" title="نسخهٔ قابل چاپ این صفحه [p]" accesskey="p"><span>نسخهٔ قابل چاپ</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"> در پروژه‌های دیگر </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/Q369377" title="پیوند به آیتم متصل‌شدۀ مخزن داده‌ها [g]" accesskey="g"><span>آیتم ویکی‌داده</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="ابزارهای صفحه"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="ظاهر"> <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">ظاهر</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">انتقال به نوار کناری</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">نهفتن</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">از ویکی‌پدیا، دانشنامهٔ آزاد</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-rtl mw-parser-output" lang="fa" dir="rtl"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">ترتیبی ریاضیاتی که در آن تمام عناصر با هم مقایسه پذیرند</div> <style data-mw-deduplicate="TemplateStyles:r33182279">.mw-parser-output .stack{box-sizing:border-box}.mw-parser-output .stack>div{margin:1px;overflow:hidden}@media all and (min-width:720px){.mw-parser-output .stack-clear-right{float:right;clear:right}.mw-parser-output .stack-clear-left{float:left;clear:left}.mw-parser-output .stack-right{float:right}.mw-parser-output .stack-left{float:left}.mw-parser-output .stack-margin-clear-right{float:right;clear:right;margin-left:1em}.mw-parser-output .stack-margin-clear-left{float:left;clear:left;margin-right:1em}.mw-parser-output .stack-margin-right{float:right;margin-left:1em}.mw-parser-output .stack-margin-left{float:left;margin-right:1em}}</style><div class="stack stack-left"><div> <table class="wikitable collapsible collapsed" style="float:right; margin-top:0;padding-top:0;"> <tbody><tr> <th style="font-size:90%;padding-left:0.5em;padding-right:0.5em;"><span style="font-size: 120%;"><a href="/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">روابط دوتایی</a> <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%AA%D8%B1%D8%A7%DB%8C%D8%A7" title="رابطه ترایا">ترایا</a></span>  </th></tr> <tr> <td><table style="text-align:center;"><tbody><tr style="vertical-align:top"><td style="padding-left:0.3em;padding-right:0.3em;;text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D9%85%D8%AA%D9%82%D8%A7%D8%B1%D9%86" title="رابطه متقارن">متقارن</a></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D9%BE%D8%A7%D8%AF%D9%85%D8%AA%D9%82%D8%A7%D8%B1%D9%86" title="رابطه پادمتقارن">پادمتقارن</a></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/w/index.php?title=%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%DA%A9%D8%A7%D9%86%DA%A9%D8%B3&action=edit&redlink=1" class="new" title="رابطه کانکس (صفحه وجود ندارد)">کانکس</a></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/w/index.php?title=%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%AE%D9%88%D8%B4-%D8%A8%D9%86%DB%8C%D8%A7%D9%86&action=edit&redlink=1" class="new" title="رابطه خوش-بنیان (صفحه وجود ندارد)">خوش-بنیان</a></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/wiki/%D8%AC%D9%88%DB%8C%D9%86_%D9%88_%D9%85%DB%8C%D8%AA" title="جوین و میت"> <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 \vee }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vee }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b76220c6805c9b465d6efbc7686c624f49f3023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \vee }"></span> دارد</a></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/wiki/%D8%AC%D9%88%DB%8C%D9%86_%D9%88_%D9%85%DB%8C%D8%AA" title="جوین و میت"> <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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> دارد</a></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%A8%D8%A7%D8%B2%D8%AA%D8%A7%D8%A8%DB%8C" title="رابطه بازتابی">بازتابی</a></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%A8%D8%A7%D8%B2%D8%AA%D8%A7%D8%A8%DB%8C#غیربازتابی" title="رابطه بازتابی">غیربازتابی</a></td><td style="padding-left:0.3em;padding-right:0.3em;"> <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D9%86%D8%A7%D9%85%D8%AA%D9%82%D8%A7%D8%B1%D9%86" title="رابطه نامتقارن">نامتقارن</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D9%87%D9%85%E2%80%8C%D8%A7%D8%B1%D8%B2%DB%8C" title="رابطه هم‌ارزی">رابطه هم‌ارزی</a></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/w/index.php?title=%D9%BE%DB%8C%D8%B4%E2%80%8C%D8%AA%D8%B1%D8%AA%DB%8C%DB%8C%D8%A8&action=edit&redlink=1" class="new" title="پیش‌ترتییب (صفحه وجود ندارد)">پیش‌ترتییب <span style="font-size: 77%; font-weight: normal;display:inline;">(شبه‌ترتیب)</span></a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/wiki/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87_%D8%AC%D8%B2%D8%A6%DB%8C%E2%80%8C%D9%85%D8%B1%D8%AA%D8%A8" title="مجموعه جزئی‌مرتب">ترتیب جزئی</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/w/index.php?title=%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8_%D8%B6%D8%B9%DB%8C%D9%81&action=edit&redlink=1" class="new" title="ترتیب ضعیف (صفحه وجود ندارد)">پیش-ترتیب کلی</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a class="mw-selflink selflink">ترتیب کلی</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/w/index.php?title=%D9%BE%DB%8C%D8%B4-%D8%AE%D9%88%D8%B4%E2%80%8C%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8&action=edit&redlink=1" class="new" title="پیش-خوش‌ترتیب (صفحه وجود ندارد)">پیش-خوش‌ترتیب</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/w/index.php?title=%D8%AE%D9%88%D8%B4-%D8%B4%D8%A8%D9%87-%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8&action=edit&redlink=1" class="new" title="خوش-شبه-ترتیب (صفحه وجود ندارد)">خوش-شبه-ترتیب</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/wiki/%D8%AE%D9%88%D8%B4%E2%80%8C%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8" title="خوش‌ترتیب">خوش‌ترتیب</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/wiki/%D9%85%D8%B4%D8%A8%DA%A9%D9%87_(%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8)" title="مشبکه (ترتیب)">مشبکه</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/wiki/%D8%AC%D9%88%DB%8C%D9%86-%D9%86%DB%8C%D9%85-%D9%85%D8%B4%D8%A8%DA%A9%D9%87" class="mw-redirect" title="جوین-نیم-مشبکه">جوین-نیم-مشبکه</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/wiki/%D9%85%DB%8C%D8%AA-%D9%86%DB%8C%D9%85-%D9%85%D8%B4%D8%A8%DA%A9%D9%87" class="mw-redirect" title="میت-نیم-مشبکه">میت-نیم-مشبکه</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/wiki/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87_%D8%AC%D8%B2%D8%A6%DB%8C%E2%80%8C%D9%85%D8%B1%D8%AA%D8%A8#ترتیب_جزئی_قطعی" title="مجموعه جزئی‌مرتب">جزئی‌مرتب قطعی</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a href="/w/index.php?title=%D9%85%D8%AC%D9%88%D8%B9%D9%87_%D8%B6%D8%B9%DB%8C%D9%81%E2%80%8C%D9%85%D8%B1%D8%AA%D8%A8&action=edit&redlink=1" class="new" title="مجوعه ضعیف‌مرتب (صفحه وجود ندارد)">مجوعه ضعیف‌مرتب</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> <a class="mw-selflink-fragment" href="#ترتیب_کلی_قطعی">ترتیب کلی قطعی</a></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:red;" title="Red X">✗</span></td><td> <span style="color:green;" title="Green tick">✓</span></td><td> <span style="color:green;" title="Green tick">✓</span></td></tr><tr style="vertical-align:top"><td style="text-align:right;padding-left:0.6em;font-weight:bold;padding-right:1.2em;"> تعاریف: برای تمام <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/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> و <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/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> ها و <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 S\neq \varnothing }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>≠</mo> <mi class="MJX-variant">∅</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\neq \varnothing }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b16a4e19ae4c143c619cab08c890e1e8ff20e0f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.406ex; height:2.676ex;" alt="{\displaystyle S\neq \varnothing }"></span> :</td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}&aRb\\\Rightarrow {}&bRa\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mi>a</mi> <mi>R</mi> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">⇒</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mtd> <mtd> <mi>b</mi> <mi>R</mi> <mi>a</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&aRb\\\Rightarrow {}&bRa\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a18cac1ed3115c87d45b4d751de57124233a6e00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:7.712ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}&aRb\\\Rightarrow {}&bRa\end{aligned}}}"></span></td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}aRb{\text{ and }}&bRa\\\Rightarrow a={}&b\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>a</mi> <mi>R</mi> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> and </mtext> </mrow> </mtd> <mtd> <mi>b</mi> <mi>R</mi> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">⇒</mo> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mtd> <mtd> <mi>b</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}aRb{\text{ and }}&bRa\\\Rightarrow a={}&b\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9cc3f46e9f0b647ce6771396a975ef8d364674d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.643ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}aRb{\text{ and }}&bRa\\\Rightarrow a={}&b\end{aligned}}}"></span></td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}a\neq {}&b\Rightarrow \\aRb{\text{ or }}&bRa\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>a</mi> <mo>≠</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mtd> <mtd> <mi>b</mi> <mo stretchy="false">⇒</mo> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> <mi>R</mi> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> or </mtext> </mrow> </mtd> <mtd> <mi>b</mi> <mi>R</mi> <mi>a</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}a\neq {}&b\Rightarrow \\aRb{\text{ or }}&bRa\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c73cadd7ab7bf3b5257f5c505c756ec098902f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.97ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}a\neq {}&b\Rightarrow \\aRb{\text{ or }}&bRa\end{aligned}}}"></span></td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\min S\\{\text{exists}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mo movablelimits="true" form="prefix">min</mo> <mi>S</mi> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>exists</mtext> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\min S\\{\text{exists}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7ec5a418cceeb68b9945ca75d31604719db4660" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:6.513ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}\min S\\{\text{exists}}\end{aligned}}}"></span></td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}a\vee b\\{\text{exists}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>a</mi> <mo>∨</mo> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>exists</mtext> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}a\vee b\\{\text{exists}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3386379a9406067b50b99e12241e9d7fab3369b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:6.395ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}a\vee b\\{\text{exists}}\end{aligned}}}"></span></td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}a\wedge b\\{\text{exists}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>a</mi> <mo>∧</mo> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>exists</mtext> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}a\wedge b\\{\text{exists}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abff244e064dd72fd16781277ad3440b35bd767d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:6.395ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}a\wedge b\\{\text{exists}}\end{aligned}}}"></span></td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle aRa}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>R</mi> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle aRa}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba7fc1d9d50c65105d5edcb3478b5ca4172c54d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.224ex; height:2.176ex;" alt="{\displaystyle aRa}"></span></td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{not }}aRa}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>not </mtext> </mrow> <mi>a</mi> <mi>R</mi> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{not }}aRa}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8263f0c706367e5306eae1b9353034024639da23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.164ex; height:2.176ex;" alt="{\displaystyle {\text{not }}aRa}"></span></td><td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}aRb\Rightarrow \\{\text{not }}bRa\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>a</mi> <mi>R</mi> <mi>b</mi> <mo stretchy="false">⇒</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>not </mtext> </mrow> <mi>b</mi> <mi>R</mi> <mi>a</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}aRb\Rightarrow \\{\text{not }}bRa\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1aec245f8776556d3ad3fcdc18d4ba61929eccb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.683ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}aRb\Rightarrow \\{\text{not }}bRa\end{aligned}}}"></span></td></tr></tbody></table> </td></tr> <tr> <td align="CENTER"> <p>علامت "<span style="color:green;" title="Green tick">✓</span>" نشان‌دهنده آن است که ویژگی ستونی در تعریف آن سطر لازم است.<br /> برای مثال تعریف رابطه هم‌ارزی لازم دارد تا متقارن باشد.<br /> به صورت ضمنی همه این تعاریف <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%AA%D8%B1%D8%A7%DB%8C%D8%A7" title="رابطه ترایا">ترایا</a> و <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%A8%D8%A7%D8%B2%D8%AA%D8%A7%D8%A8%DB%8C" title="رابطه بازتابی">بازتابی</a> می‌باشند. علامت "<span style="color:red;" title="Red X">✗</span>" نشان‌دهنده آن است که ویژگی به طور کلی تضمین نمی‌شود (می‌تواند برقرار باشد، یا نباشد). </p><p>تمام روابط بالا مستلزم آن است که <a href="/w/index.php?title=%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D9%87%D9%85%DA%AF%D9%88%D9%86&action=edit&redlink=1" class="new" title="رابطه همگون (صفحه وجود ندارد)">رابطه همگون</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 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> <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%AA%D8%B1%D8%A7%DB%8C%D8%A7" title="رابطه ترایا">ترایا</a> باشد: برای تمام <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/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> و <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/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> و <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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> ها، اگر <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 aRb}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>R</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle aRb}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8b0b52168739fd16b254298771ec07b900e5a6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.991ex; height:2.176ex;" alt="{\displaystyle aRb}"></span> و <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 bRc}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mi>R</mi> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle bRc}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93a62ff0d4c99429cb3465edecb65d2b1a53cf30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.768ex; height:2.176ex;" alt="{\displaystyle bRc}"></span> آنگاه <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 aRc}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>R</mi> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle aRc}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fa8a450af6aba1999bff8edea021e583b059b01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.001ex; height:2.176ex;" alt="{\displaystyle aRc}"></span>. </p> </td></tr></tbody></table></div></div> <p>در <a href="/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA" title="ریاضیات">ریاضیات</a>، یک <b>ترتیب کلی</b> (به <a href="/wiki/%D8%B2%D8%A8%D8%A7%D9%86_%D8%A7%D9%86%DA%AF%D9%84%DB%8C%D8%B3%DB%8C" title="زبان انگلیسی">انگلیسی</a>: <span lang="en" title="متن به زبان انگلیسی"><bdi>Total Order</bdi></span>) (اسامی دیگر این رابطه: ترتیب ساده (به <a href="/wiki/%D8%B2%D8%A8%D8%A7%D9%86_%D8%A7%D9%86%DA%AF%D9%84%DB%8C%D8%B3%DB%8C" title="زبان انگلیسی">انگلیسی</a>: <span lang="en" title="متن به زبان انگلیسی"><bdi>Simple Order</bdi></span>)<sup id="cite_ref-FOOTNOTEBirkhoff19672_1-0" class="reference"><a href="#cite_note-FOOTNOTEBirkhoff19672-1"><span class="cite-bracket">[</span>۱<span class="cite-bracket">]</span></a></sup>، ترتیب خطی (به <a href="/wiki/%D8%B2%D8%A8%D8%A7%D9%86_%D8%A7%D9%86%DA%AF%D9%84%DB%8C%D8%B3%DB%8C" title="زبان انگلیسی">انگلیسی</a>: <span lang="en" title="متن به زبان انگلیسی"><bdi>Linear Order</bdi></span>)، ترتیب کانکس (به <a href="/wiki/%D8%B2%D8%A8%D8%A7%D9%86_%D8%A7%D9%86%DA%AF%D9%84%DB%8C%D8%B3%DB%8C" title="زبان انگلیسی">انگلیسی</a>: <span lang="en" title="متن به زبان انگلیسی"><bdi>Connex Order</bdi></span>)<sup id="cite_ref-FOOTNOTESchmidtStröhlein199332_2-0" class="reference"><a href="#cite_note-FOOTNOTESchmidtStröhlein199332-2"><span class="cite-bracket">[</span>۲<span class="cite-bracket">]</span></a></sup>، ترتیب پر (به <a href="/wiki/%D8%B2%D8%A8%D8%A7%D9%86_%D8%A7%D9%86%DA%AF%D9%84%DB%8C%D8%B3%DB%8C" title="زبان انگلیسی">انگلیسی</a>: <span lang="en" title="متن به زبان انگلیسی"><bdi>Full Order</bdi></span>)<sup id="cite_ref-FOOTNOTEFuchs19632_3-0" class="reference"><a href="#cite_note-FOOTNOTEFuchs19632-3"><span class="cite-bracket">[</span>۳<span class="cite-bracket">]</span></a></sup>)، رابطه دوتایی روی مجموعه ای چون <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/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> است که پاد-تقارنی، ترایایی و کانکس باشد. مجموعه مجهز به ترتیبی کلی را <b>زنجیر</b> (به <a href="/wiki/%D8%B2%D8%A8%D8%A7%D9%86_%D8%A7%D9%86%DA%AF%D9%84%DB%8C%D8%B3%DB%8C" title="زبان انگلیسی">انگلیسی</a>: <span lang="en" title="متن به زبان انگلیسی"><bdi>Chain</bdi></span>)<sup id="cite_ref-FOOTNOTEDaveyPriestley19903_4-0" class="reference"><a href="#cite_note-FOOTNOTEDaveyPriestley19903-4"><span class="cite-bracket">[</span>۴<span class="cite-bracket">]</span></a></sup> یا <b>مجموعه با ترتیب کلی</b><sup id="cite_ref-FOOTNOTEDaveyPriestley19903_4-1" class="reference"><a href="#cite_note-FOOTNOTEDaveyPriestley19903-4"><span class="cite-bracket">[</span>۴<span class="cite-bracket">]</span></a></sup> یا مجموعه با ترتیب ساده<sup id="cite_ref-FOOTNOTEBirkhoff19672_1-1" class="reference"><a href="#cite_note-FOOTNOTEBirkhoff19672-1"><span class="cite-bracket">[</span>۱<span class="cite-bracket">]</span></a></sup> یا مجموعه با ترتیب خطی<sup id="cite_ref-FOOTNOTESchmidtStröhlein199332_2-1" class="reference"><a href="#cite_note-FOOTNOTESchmidtStröhlein199332-2"><span class="cite-bracket">[</span>۲<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEDaveyPriestley19903_4-2" class="reference"><a href="#cite_note-FOOTNOTEDaveyPriestley19903-4"><span class="cite-bracket">[</span>۴<span class="cite-bracket">]</span></a></sup> (یا مخفف آن به صورت toset<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>۵<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>۶<span class="cite-bracket">]</span></a></sup>) یا <b>توست</b> (که مخفف Totally Ordered SET است) هم می گویند. </p><p>به طور صوری، یک رابطه دوتایی چون <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 \leq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≤</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/440568a09c3bfdf0e1278bfa79eb137c04e94035" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \leq }"></span> ترتیبی کلی روی مجموعه ای چون <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/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> است به طوری که دو گزاره زیر برای تمام <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/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> و <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/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> و <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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> در <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/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> برقرار باشند: </p><p>بازتابی : <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\leq a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>≤</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\leq a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f33338c098fb2384f5c7f4615729d0e0f8d744a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.558ex; height:2.176ex;" alt="{\displaystyle a\leq a}"></span> </p> <dl><dd><a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D9%BE%D8%A7%D8%AF%D9%85%D8%AA%D9%82%D8%A7%D8%B1%D9%86" title="رابطه پادمتقارن">پادتقارنی</a>: اگر <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\leq 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\leq b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41558abc50886fdf38817495b243958d7b3dd39b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.326ex; height:2.343ex;" alt="{\displaystyle a\leq b}"></span> و <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\leq a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>≤</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\leq a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d38bff9a811bdd9b92516d9c2694712555b99952" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.326ex; height:2.343ex;" alt="{\displaystyle b\leq a}"></span> آنگاه <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=b}"> <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=b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1956b03d1314c7071ac1f45ed7b1e29422dcfcc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.326ex; height:2.176ex;" alt="{\displaystyle a=b}"></span>؛</dd> <dd><a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%AA%D8%B1%D8%A7%DB%8C%D8%A7" title="رابطه ترایا">ترایایی</a>: اگر <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\leq 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\leq b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41558abc50886fdf38817495b243958d7b3dd39b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.326ex; height:2.343ex;" alt="{\displaystyle a\leq b}"></span> و <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\leq c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>≤</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\leq c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04cbc237b132cef779abc512c9c8e288781a808e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.103ex; height:2.343ex;" alt="{\displaystyle b\leq c}"></span> آنگاه <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\leq c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>≤</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\leq c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb1c962997d8a303e076777cd6d6bc732f360ac8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.335ex; height:2.176ex;" alt="{\displaystyle a\leq c}"></span>؛</dd> <dd><a href="/w/index.php?title=%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%DA%A9%D8%A7%D9%86%DA%A9%D8%B3&action=edit&redlink=1" class="new" title="رابطه کانکس (صفحه وجود ندارد)">کانکسی</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\leq 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\leq b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41558abc50886fdf38817495b243958d7b3dd39b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.326ex; height:2.343ex;" alt="{\displaystyle a\leq b}"></span> یا <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\leq a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>≤</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\leq a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d38bff9a811bdd9b92516d9c2694712555b99952" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.326ex; height:2.343ex;" alt="{\displaystyle b\leq a}"></span></dd></dl> <p>خاصیت پاد-تقارنی برخی از حالات نامطلوب مثل زمانی که هم <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/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> بر <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/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> تقدم داشته باشد و هم <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/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> بر <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/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> را حذف می کند.<sup id="cite_ref-Nederpelt.2004_7-0" class="reference"><a href="#cite_note-Nederpelt.2004-7"><span class="cite-bracket">[</span>۷<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="صفحه / موقعیت: 325">: 325 </span></sup> رابطه ای که خاصیت <i>کانکس</i> بودن را داشته باشد، هر جفت از عناصر مجموعه آن تحت رابطه مورد نظر قابل مقایسه اند. همچنین کانکس بودن بدین معناست که چنین رابطه ای را می توان با کمک نمودار به صورت خطی از عناصر ترسیم کرد، به همین دلیل است که آن را <i>خطی</i> هم می نامند.<sup id="cite_ref-Nederpelt.2004_7-1" class="reference"><a href="#cite_note-Nederpelt.2004-7"><span class="cite-bracket">[</span>۷<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="صفحه / موقعیت: 330">: 330 </span></sup> خاصیت کانکس همچنین <a href="/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D9%87_%D8%A8%D8%A7%D8%B2%D8%AA%D8%A7%D8%A8%DB%8C" title="رابطه بازتابی">بازتابی</a> بودن را نیز نتیجه می دهد، یعنی برای هر عنصر <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/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> نتیجه می شود <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\leq a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>≤</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\leq a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f33338c098fb2384f5c7f4615729d0e0f8d744a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.558ex; height:2.176ex;" alt="{\displaystyle a\leq a}"></span>. لذا، ترتیب کلی حالت خاصی از یک ترتیب جزئی نیز است، چرا که اگر خاصیت کانکس بودن را در ترتیب کلی تضعیف کنیم به ترتیب جزئی میرسیم. یک توسیع از رابطه با ترتیب جزئی به رابطه با ترتیب کلی را توسیع خطی از آن رابطه ترتیب جزئی نیز می گویند. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="جستارهای_وابسته"><span id=".D8.AC.D8.B3.D8.AA.D8.A7.D8.B1.D9.87.D8.A7.DB.8C_.D9.88.D8.A7.D8.A8.D8.B3.D8.AA.D9.87"></span>جستارهای وابسته</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8_%DA%A9%D9%84%DB%8C&action=edit&section=1" title="ویرایش بخش: جستارهای وابسته"><span>ویرایش</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87_%D8%AC%D8%B2%D8%A6%DB%8C%E2%80%8C%D9%85%D8%B1%D8%AA%D8%A8" title="مجموعه جزئی‌مرتب">ترتیب جزئی</a></li> <li><a href="/wiki/%D8%AE%D9%88%D8%B4%E2%80%8C%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8%DB%8C" class="mw-redirect" title="خوش‌ترتیبی">خوش‌ترتیبی</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="پانویس"><span id=".D9.BE.D8.A7.D9.86.D9.88.DB.8C.D8.B3"></span>پانویس</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8_%DA%A9%D9%84%DB%8C&action=edit&section=2" title="ویرایش بخش: پانویس"><span>ویرایش</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r37199623">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-columns-2 mw-content-ltr" dir="ltr"> <ol class="references"> <li id="cite_note-FOOTNOTEBirkhoff19672-1" class="mw-cite-dir-ltr"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-FOOTNOTEBirkhoff19672_1-0">۱٫۰</a></sup> <sup><a href="#cite_ref-FOOTNOTEBirkhoff19672_1-1">۱٫۱</a></sup></span> <span class="reference-text"><a href="#CITEREFBirkhoff1967">Birkhoff 1967</a>, p. 2.</span> </li> <li id="cite_note-FOOTNOTESchmidtStröhlein199332-2" class="mw-cite-dir-ltr"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-FOOTNOTESchmidtStröhlein199332_2-0">۲٫۰</a></sup> <sup><a href="#cite_ref-FOOTNOTESchmidtStröhlein199332_2-1">۲٫۱</a></sup></span> <span class="reference-text"><a href="#CITEREFSchmidtStröhlein1993">Schmidt & Ströhlein 1993</a>, p. 32.</span> </li> <li id="cite_note-FOOTNOTEFuchs19632-3" class="mw-cite-dir-ltr"><span class="mw-cite-backlink"><a href="#cite_ref-FOOTNOTEFuchs19632_3-0">↑</a></span> <span class="reference-text"><a href="#CITEREFFuchs1963">Fuchs 1963</a>, p. 2.</span> </li> <li id="cite_note-FOOTNOTEDaveyPriestley19903-4" class="mw-cite-dir-ltr"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-FOOTNOTEDaveyPriestley19903_4-0">۴٫۰</a></sup> <sup><a href="#cite_ref-FOOTNOTEDaveyPriestley19903_4-1">۴٫۱</a></sup> <sup><a href="#cite_ref-FOOTNOTEDaveyPriestley19903_4-2">۴٫۲</a></sup></span> <span class="reference-text"><a href="#CITEREFDaveyPriestley1990">Davey & Priestley 1990</a>, p. 3.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r39868036">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFStrohmeierGenillardWeber1990" class="citation journal cs1 cs1-prop-foreign-lang-source">Strohmeier, Alfred; Genillard, Christian; Weber, Mats (1990-08-01). "Ordering of characters and strings". <i>ACM SIGAda Ada Letters</i> (به انگلیسی) (7): 84. <a href="/wiki/%D8%B4%D9%86%D8%A7%D8%B3%D8%A7%DA%AF%D8%B1_%D8%A7%D8%B4%DB%8C%D8%A7%D8%A1_%D8%AF%DB%8C%D8%AC%DB%8C%D8%AA%D8%A7%D9%84" title="شناساگر اشیاء دیجیتال">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F101120.101136">10.1145/101120.101136</a>. <a href="/wiki/%D8%B3%D9%85%D8%A7%D9%86%D8%AA%DB%8C%DA%A9_%D8%A7%D8%B3%DA%A9%D8%A7%D9%84%D8%B1" title="سمانتیک اسکالر">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:38115497">38115497</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ACM+SIGAda+Ada+Letters&rft.atitle=Ordering+of+characters+and+strings&rft.issue=7&rft.pages=84&rft.date=1990-08-01&rft_id=info%3Adoi%2F10.1145%2F101120.101136&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A38115497%23id-name%3DS2CID&rft.aulast=Strohmeier&rft.aufirst=Alfred&rft.au=Genillard%2C+Christian&rft.au=Weber%2C+Mats&rfr_id=info%3Asid%2Ffa.wikipedia.org%3A%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r39868036"><cite id="CITEREFGanapathy1992" class="citation journal cs1">Ganapathy, Jayanthi (1992). <a rel="nofollow" class="external text" href="https://archive.org/details/sim_pi-mu-epsilon-journal_fall-1992_9_7/page/462">"Maximal Elements and Upper Bounds in Posets"</a>. <i>Pi Mu Epsilon Journal</i>. <b>9</b> (7): 462–464. <a href="/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%87_%D8%A7%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF_%D8%A8%DB%8C%D9%86%E2%80%8C%D8%A7%D9%84%D9%85%D9%84%D9%84%DB%8C_%D9%BE%DB%8C%D8%A7%DB%8C%D9%86%D8%AF" title="شماره استاندارد بین‌المللی پیایند">ISSN</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0031-952X">0031-952X</a>. <a href="/wiki/%D8%AC%DB%8C%E2%80%8C%D8%A7%D8%B3%D8%AA%D9%88%D8%B1" title="جی‌استور">JSTOR</a> <a rel="nofollow" class="external text" href="//www.jstor.org/stable/24340068">24340068</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pi+Mu+Epsilon+Journal&rft.atitle=Maximal+Elements+and+Upper+Bounds+in+Posets&rft.volume=9&rft.issue=7&rft.pages=462-464&rft.date=1992&rft_id=%2F%2Fwww.jstor.org%2Fstable%2F24340068%23id-name%3DJSTOR&rft.issn=0031-952X&rft.aulast=Ganapathy&rft.aufirst=Jayanthi&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_pi-mu-epsilon-journal_fall-1992_9_7%2Fpage%2F462&rfr_id=info%3Asid%2Ffa.wikipedia.org%3A%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" class="Z3988"></span></span> </li> <li id="cite_note-Nederpelt.2004-7"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Nederpelt.2004_7-0">۷٫۰</a></sup> <sup><a href="#cite_ref-Nederpelt.2004_7-1">۷٫۱</a></sup></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r39868036"><cite id="CITEREFNederpelt2004" class="citation book cs1">Nederpelt, Rob (2004). <i>Logical Reasoning: A First Course</i>. Texts in Computing. Vol. 3 (3rd, Revised ed.). King's College Publications. <a href="/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%87_%D8%A7%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF_%D8%A8%DB%8C%D9%86%E2%80%8C%D8%A7%D9%84%D9%85%D9%84%D9%84%DB%8C_%DA%A9%D8%AA%D8%A7%D8%A8" title="شماره استاندارد بین‌المللی کتاب">ISBN</a> <a href="/wiki/%D9%88%DB%8C%DA%98%D9%87:%D9%85%D9%86%D8%A7%D8%A8%D8%B9_%DA%A9%D8%AA%D8%A7%D8%A8/0-9543006-7-X" title="ویژه:منابع کتاب/0-9543006-7-X"><bdi>0-9543006-7-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Logical+Reasoning%3A+A+First+Course&rft.series=Texts+in+Computing&rft.edition=3rd%2C+Revised&rft.pub=King%27s+College+Publications&rft.date=2004&rft.isbn=0-9543006-7-X&rft.aulast=Nederpelt&rft.aufirst=Rob&rfr_id=info%3Asid%2Ffa.wikipedia.org%3A%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="منابع"><span id=".D9.85.D9.86.D8.A7.D8.A8.D8.B9"></span>منابع</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8_%DA%A9%D9%84%DB%8C&action=edit&section=3" title="ویرایش بخش: منابع"><span>ویرایش</span></a><span class="mw-editsection-bracket">]</span></span></div> <div dir="ltr" class="mw-content-ltr"> <style data-mw-deduplicate="TemplateStyles:r32987365">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-100{font-size:100%}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}</style><div class="refbegin refbegin-columns references-column-count references-column-count-2" style="column-count: 2;"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r39868036"><cite id="CITEREFGarrett_Birkhoff1967" class="citation book cs1"><a href="/w/index.php?title=Garrett_Birkhoff&action=edit&redlink=1" class="new" title="Garrett Birkhoff (صفحه وجود ندارد)">Garrett Birkhoff</a> (1967). <i>Lattice Theory</i>. Colloquium Publications. Vol. 25. Providence: Am. Math. Soc.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lattice+Theory&rft.place=Providence&rft.series=Colloquium+Publications&rft.pub=Am.+Math.+Soc.&rft.date=1967&rft.au=Garrett+Birkhoff&rfr_id=info%3Asid%2Ffa.wikipedia.org%3A%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r39868036"><cite id="CITEREFBrian_A._DaveyHilary_Ann_Priestley1990" class="citation book cs1">Brian A. Davey; <a href="/w/index.php?title=Hilary_Priestley&action=edit&redlink=1" class="new" title="Hilary Priestley (صفحه وجود ندارد)">Hilary Ann Priestley</a> (1990). <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontola0000dave"><i>Introduction to Lattices and Order</i></a>. Cambridge Mathematical Textbooks. Cambridge University Press. <a href="/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%87_%D8%A7%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF_%D8%A8%DB%8C%D9%86%E2%80%8C%D8%A7%D9%84%D9%85%D9%84%D9%84%DB%8C_%DA%A9%D8%AA%D8%A7%D8%A8" title="شماره استاندارد بین‌المللی کتاب">ISBN</a> <a href="/wiki/%D9%88%DB%8C%DA%98%D9%87:%D9%85%D9%86%D8%A7%D8%A8%D8%B9_%DA%A9%D8%AA%D8%A7%D8%A8/0-521-36766-2" title="ویژه:منابع کتاب/0-521-36766-2"><bdi>0-521-36766-2</bdi></a>. <a href="/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%87_%DA%A9%D9%86%D8%AA%D8%B1%D9%84_%DA%A9%D8%AA%D8%A7%D8%A8%D8%AE%D8%A7%D9%86%D9%87_%DA%A9%D9%86%DA%AF%D8%B1%D9%87" title="شماره کنترل کتابخانه کنگره">LCCN</a> <a rel="nofollow" class="external text" href="//lccn.loc.gov/89009753">89009753</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Lattices+and+Order&rft.series=Cambridge+Mathematical+Textbooks&rft.pub=Cambridge+University+Press&rft.date=1990&rft_id=info%3Alccn%2F89009753&rft.isbn=0-521-36766-2&rft.au=Brian+A.+Davey&rft.au=Hilary+Ann+Priestley&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontola0000dave&rfr_id=info%3Asid%2Ffa.wikipedia.org%3A%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r39868036"><cite id="CITEREFFuchs1963" class="citation book cs1">Fuchs, L (1963). <a rel="nofollow" class="external text" href="https://archive.org/details/partiallyordered0000fuch"><i>Partially Ordered Algebraic Systems</i></a>. Pergamon Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Partially+Ordered+Algebraic+Systems&rft.pub=Pergamon+Press&rft.date=1963&rft.aulast=Fuchs&rft.aufirst=L&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fpartiallyordered0000fuch&rfr_id=info%3Asid%2Ffa.wikipedia.org%3A%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" class="Z3988"></span></li> <li>George Grätzer (1971). <i>Lattice theory: first concepts and distributive lattices.</i> W. H. Freeman and Co. <a href="/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%87_%D8%A7%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF_%D8%A8%DB%8C%D9%86%E2%80%8C%D8%A7%D9%84%D9%85%D9%84%D9%84%DB%8C_%DA%A9%D8%AA%D8%A7%D8%A8" title="شماره استاندارد بین‌المللی کتاب">ISBN</a> <a href="/wiki/%D9%88%DB%8C%DA%98%D9%87:%D9%85%D9%86%D8%A7%D8%A8%D8%B9_%DA%A9%D8%AA%D8%A7%D8%A8/0-7167-0442-0" title="ویژه:منابع کتاب/0-7167-0442-0">0-7167-0442-0</a></li> <li>John G. Hocking and Gail S. Young (1961). <i>Topology.</i> Corrected reprint, Dover, 1988. <a href="/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%87_%D8%A7%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF_%D8%A8%DB%8C%D9%86%E2%80%8C%D8%A7%D9%84%D9%85%D9%84%D9%84%DB%8C_%DA%A9%D8%AA%D8%A7%D8%A8" title="شماره استاندارد بین‌المللی کتاب">ISBN</a> <a href="/wiki/%D9%88%DB%8C%DA%98%D9%87:%D9%85%D9%86%D8%A7%D8%A8%D8%B9_%DA%A9%D8%AA%D8%A7%D8%A8/0-486-65676-4" title="ویژه:منابع کتاب/0-486-65676-4">0-486-65676-4</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r39868036"><cite id="CITEREFSchmidtStröhlein1993" class="citation book cs1"><a href="/w/index.php?title=Gunther_Schmidt&action=edit&redlink=1" class="new" title="Gunther Schmidt (صفحه وجود ندارد)">Schmidt, Gunther</a>; Ströhlein, Thomas (1993). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZgarCAAAQBAJ"><i>Relations and Graphs: Discrete Mathematics for Computer Scientists</i></a>. Berlin: Springer-Verlag. <a href="/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%87_%D8%A7%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF_%D8%A8%DB%8C%D9%86%E2%80%8C%D8%A7%D9%84%D9%85%D9%84%D9%84%DB%8C_%DA%A9%D8%AA%D8%A7%D8%A8" title="شماره استاندارد بین‌المللی کتاب">ISBN</a> <a href="/wiki/%D9%88%DB%8C%DA%98%D9%87:%D9%85%D9%86%D8%A7%D8%A8%D8%B9_%DA%A9%D8%AA%D8%A7%D8%A8/978-3-642-77970-1" title="ویژه:منابع کتاب/978-3-642-77970-1"><bdi>978-3-642-77970-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relations+and+Graphs%3A+Discrete+Mathematics+for+Computer+Scientists&rft.place=Berlin&rft.pub=Springer-Verlag&rft.date=1993&rft.isbn=978-3-642-77970-1&rft.aulast=Schmidt&rft.aufirst=Gunther&rft.au=Str%C3%B6hlein%2C+Thomas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZgarCAAAQBAJ&rfr_id=info%3Asid%2Ffa.wikipedia.org%3A%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" class="Z3988"></span></li></ul> </div> </div> <div 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href="/w/index.php?title=European_Mathematical_Society&action=edit&redlink=1" class="new" title="European Mathematical Society (صفحه وجود ندارد)">EMS Press</a>, 2001 [1994]</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Totally+ordered+set&rft.btitle=Encyclopedia+of+Mathematics&rft.pub=EMS+Press&rft.date=2001&rft_id=https%3A%2F%2Fwww.encyclopediaofmath.org%2Findex.php%3Ftitle%3DTotally_ordered_set&rfr_id=info%3Asid%2Ffa.wikipedia.org%3A%D8%AA%D8%B1%D8%AA%DB%8C%D8%A8+%DA%A9%D9%84%DB%8C" class="Z3988"></span></li></ul> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">برگرفته از «<a dir="ltr" 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