CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-disabled skin-theme-clientpref-day vector-toc-available" lang="th" dir="ltr"> <head> <meta charset="UTF-8"> <title>จำนวนเต็ม - วิกิพีเดีย</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-disabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )thwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat": "thai","wgMonthNames":["","มกราคม","กุมภาพันธ์","มีนาคม","เมษายน","พฤษภาคม","มิถุนายน","กรกฎาคม","สิงหาคม","กันยายน","ตุลาคม","พฤศจิกายน","ธันวาคม"],"wgRequestId":"cbaecbef-dbdc-4a8a-924f-09fb8badfeb3","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"จำนวนเต็ม","wgTitle":"จำนวนเต็ม","wgCurRevisionId":11888802,"wgRevisionId":11888802,"wgArticleId":4763,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["บทความที่ขาดแหล่งอ้างอิง","บทความทั้งหมดที่ขาดแหล่งอ้างอิง","บทความที่มีข้อความภาษาอังกฤษ", "บทความที่มีข้อความภาษาเยอรมัน","บทความที่มีข้อความภาษาฝรั่งเศส","บทความทั้งหมดที่ยังไม่สมบูรณ์","ทฤษฎีกรุป","จำนวน","ทฤษฎีจำนวน","ทฤษฎีเซต","คณิตศาสตร์มูลฐาน","จำนวนเต็ม","บทความเกี่ยวกับ คณิตศาสตร์ ที่ยังไม่สมบูรณ์"],"wgPageViewLanguage":"th","wgPageContentLanguage":"th","wgPageContentModel":"wikitext","wgRelevantPageName":"จำนวนเต็ม","wgRelevantArticleId":4763,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault": true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"th","pageLanguageDir":"ltr","pageVariantFallbacks":"th"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":10000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q12503","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.charinsert-styles":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user": "ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.charinsert","ext.gadget.refToolbar","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions", "wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=th&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=th&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=th&modules=ext.gadget.charinsert-styles&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=th&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Latex_integers.svg/1200px-Latex_integers.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1351"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Latex_integers.svg/800px-Latex_integers.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="901"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Latex_integers.svg/640px-Latex_integers.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="721"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="จำนวนเต็ม - วิกิพีเดีย"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//th.m.wikipedia.org/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1"> <link rel="alternate" type="application/x-wiki" title="แก้ไข" href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="วิกิพีเดีย (th)"> <link rel="EditURI" type="application/rsd+xml" href="//th.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://th.wikipedia.org/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.th"> <link rel="alternate" type="application/atom+xml" title="ฟีดอะตอม วิกิพีเดีย" href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%9B%E0%B8%A3%E0%B8%B1%E0%B8%9A%E0%B8%9B%E0%B8%A3%E0%B8%B8%E0%B8%87%E0%B8%A5%E0%B9%88%E0%B8%B2%E0%B8%AA%E0%B8%B8%E0%B8%94&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-จำนวนเต็ม rootpage-จำนวนเต็ม skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">ข้ามไปเนื้อหา</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="ไซต์"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="เมนูหลัก" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">เมนูหลัก</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">เมนูหลัก</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">ซ่อน</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> การนำทาง </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%AB%E0%B8%A5%E0%B8%B1%E0%B8%81" title="เยี่ยมชมหน้าหลัก [z]" accesskey="z"><span>หน้าหลัก</span></a></li><li id="n-ask" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%96%E0%B8%B2%E0%B8%A1%E0%B8%84%E0%B8%B3%E0%B8%96%E0%B8%B2%E0%B8%A1"><span>ถามคำถาม</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/%E0%B8%AA%E0%B8%96%E0%B8%B2%E0%B8%99%E0%B8%B5%E0%B8%A2%E0%B9%88%E0%B8%AD%E0%B8%A2:%E0%B9%80%E0%B8%AB%E0%B8%95%E0%B8%B8%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%93%E0%B9%8C%E0%B8%9B%E0%B8%B1%E0%B8%88%E0%B8%88%E0%B8%B8%E0%B8%9A%E0%B8%B1%E0%B8%99" title="ค้นหาข้อมูลเบื้องหลังในเหตุการณ์ปัจจุบัน"><span>เหตุการณ์ปัจจุบัน</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AA%E0%B8%B8%E0%B9%88%E0%B8%A1" title="โหลดหน้าแบบสุ่ม [x]" accesskey="x"><span>สุ่มบทความ</span></a></li><li id="n-about" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B9%80%E0%B8%81%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A7%E0%B8%81%E0%B8%B1%E0%B8%9A" title="ทำความรู้จักวิกิพีเดีย"><span>เกี่ยวกับวิกิพีเดีย</span></a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%95%E0%B8%B4%E0%B8%94%E0%B8%95%E0%B9%88%E0%B8%AD" title="วิธีการติดต่อวิกิพีเดีย"><span>ติดต่อเรา</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> มีส่วนร่วม </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%98%E0%B8%B5%E0%B9%83%E0%B8%8A%E0%B9%89:%E0%B8%AA%E0%B8%B2%E0%B8%A3%E0%B8%9A%E0%B8%B1%E0%B8%8D" title="ข้อแนะนำการใช้และแก้ไขวิกิพีเดีย"><span>คำอธิบาย</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%AA%E0%B8%AD%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%83%E0%B8%8A%E0%B9%89%E0%B8%87%E0%B8%B2%E0%B8%99"><span>เริ่มต้นเขียน</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%A8%E0%B8%B2%E0%B8%A5%E0%B8%B2%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%8A%E0%B8%B2%E0%B8%84%E0%B8%A1" title="เกี่ยวกับโครงการ สิ่งที่คุณทำได้ และวิธีการค้นหา"><span>ศาลาประชาคม</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%9B%E0%B8%A3%E0%B8%B1%E0%B8%9A%E0%B8%9B%E0%B8%A3%E0%B8%B8%E0%B8%87%E0%B8%A5%E0%B9%88%E0%B8%B2%E0%B8%AA%E0%B8%B8%E0%B8%94" title="รายการเปลี่ยนแปลงล่าสุดในวิกินี้ [r]" accesskey="r"><span>ปรับปรุงล่าสุด</span></a></li><li id="n-discord" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%94%E0%B8%B4%E0%B8%AA%E0%B8%84%E0%B8%AD%E0%B8%A3%E0%B9%8C%E0%B8%94"><span>ดิสคอร์ด</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%AB%E0%B8%A5%E0%B8%B1%E0%B8%81" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="วิกิพีเดีย" src="/static/images/mobile/copyright/wikipedia-wordmark-th.svg" style="width: 6.4375em; height: 1.6875em;"> <img class="mw-logo-tagline" alt="สารานุกรมเสรี" src="/static/images/mobile/copyright/wikipedia-tagline-th.svg" width="100" height="18" style="width: 6.25em; height: 1.125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%84%E0%B9%89%E0%B8%99%E0%B8%AB%E0%B8%B2" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="ค้นหาวิกิ [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>ค้นหา</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="ค้นหาใน วิกิพีเดีย" aria-label="ค้นหาใน วิกิพีเดีย" autocapitalize="sentences" title="ค้นหาวิกิ [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="พิเศษ:ค้นหา"> </div> <button class="cdx-button cdx-search-input__end-button">ค้นหา</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="เครื่องมือส่วนตัว"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="หน้าตา"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="หน้าตา" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">หน้าตา</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_th.wikipedia.org&uselang=th" class=""><span>บริจาคให้วิกิพีเดีย</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AA%E0%B8%A3%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%9A%E0%B8%B1%E0%B8%8D%E0%B8%8A%E0%B8%B5%E0%B8%9C%E0%B8%B9%E0%B9%89%E0%B9%83%E0%B8%8A%E0%B9%89%E0%B9%83%E0%B8%AB%E0%B8%A1%E0%B9%88&returnto=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="แนะนำให้คุณสร้างบัญชีและเข้าสู่ระบบ แต่ไม่บังคับ" class=""><span>สร้างบัญชี</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%A5%E0%B9%87%E0%B8%AD%E0%B8%81%E0%B8%AD%E0%B8%B4%E0%B8%99&returnto=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="แนะนำให้คุณเข้าสู่ระบบ แต่ไม่บังคับ [o]" accesskey="o" class=""><span>เข้าสู่ระบบ</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="ตัวเลือกเพิ่มเติม" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="เครื่องมือส่วนตัว" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">เครื่องมือส่วนตัว</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="เมนูผู้ใช้" > <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_th.wikipedia.org&uselang=th"><span>บริจาคให้วิกิพีเดีย</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AA%E0%B8%A3%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%9A%E0%B8%B1%E0%B8%8D%E0%B8%8A%E0%B8%B5%E0%B8%9C%E0%B8%B9%E0%B9%89%E0%B9%83%E0%B8%8A%E0%B9%89%E0%B9%83%E0%B8%AB%E0%B8%A1%E0%B9%88&returnto=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="แนะนำให้คุณสร้างบัญชีและเข้าสู่ระบบ แต่ไม่บังคับ"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>สร้างบัญชี</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%A5%E0%B9%87%E0%B8%AD%E0%B8%81%E0%B8%AD%E0%B8%B4%E0%B8%99&returnto=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="แนะนำให้คุณเข้าสู่ระบบ แต่ไม่บังคับ [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>เข้าสู่ระบบ</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"> หน้าสำหรับผู้แก้ไขที่ออกจากระบบ <a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%98%E0%B8%B5%E0%B9%83%E0%B8%8A%E0%B9%89:%E0%B8%9A%E0%B8%97%E0%B8%99%E0%B8%B3" aria-label="เรียนรู้เพิ่มเกี่ยวกับการแก้ไข"><span>เรียนรู้เพิ่มเติม</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/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B9%80%E0%B8%A3%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%89%E0%B8%B1%E0%B8%99%E0%B9%80%E0%B8%82%E0%B8%B5%E0%B8%A2%E0%B8%99" title="รายการการแก้ไขจากเลขที่อยู่ไอพีนี้ [y]" accesskey="y"><span>ส่วนร่วม</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%9E%E0%B8%B9%E0%B8%94%E0%B8%84%E0%B8%B8%E0%B8%A2%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%89%E0%B8%B1%E0%B8%99" title="อภิปรายเกี่ยวกับการแก้ไขจากเลขที่อยู่ไอพีนี้ [n]" accesskey="n"><span>คุย</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="ไซต์"> <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="สารบัญ" 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">สารบัญ</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ซ่อน</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">บทนำ</div> </a> </li> <li id="toc-สมบัติทางพีชคณิต" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#สมบัติทางพีชคณิต"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>สมบัติทางพีชคณิต</span> </div> </a> <ul id="toc-สมบัติทางพีชคณิต-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-สมบัติการเรียงลำดับ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#สมบัติการเรียงลำดับ"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>สมบัติการเรียงลำดับ</span> </div> </a> <ul id="toc-สมบัติการเรียงลำดับ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-จำนวนเต็มในการคำนวณ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#จำนวนเต็มในการคำนวณ"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>จำนวนเต็มในการคำนวณ</span> </div> </a> <ul id="toc-จำนวนเต็มในการคำนวณ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-อ้างอิง" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#อ้างอิง"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>อ้างอิง</span> </div> </a> <ul id="toc-อ้างอิง-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-แหล่งข้อมูลอื่น" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#แหล่งข้อมูลอื่น"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>แหล่งข้อมูลอื่น</span> </div> </a> <ul id="toc-แหล่งข้อมูลอื่น-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="สารบัญ" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">จำนวนเต็ม</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="ไปที่บทความในภาษาอื่น ซึ่งมีใน 131 ภาษา" > <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-131" 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">131 ภาษา</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Heelgetal" title="Heelgetal – แอฟริกานส์" lang="af" hreflang="af" data-title="Heelgetal" data-language-autonym="Afrikaans" data-language-local-name="แอฟริกานส์" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Ganze_Zahl" title="Ganze Zahl – เยอรมันสวิส" lang="gsw" hreflang="gsw" data-title="Ganze Zahl" data-language-autonym="Alemannisch" data-language-local-name="เยอรมันสวิส" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Numero_entero" title="Numero entero – อารากอน" lang="an" hreflang="an" data-title="Numero entero" data-language-autonym="Aragonés" data-language-local-name="อารากอน" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%AA%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="पूर्ण संख्या – อังคิกา" lang="anp" hreflang="anp" data-title="पूर्ण संख्या" data-language-autonym="अंगिका" data-language-local-name="อังคิกา" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%B5%D8%AD%D9%8A%D8%AD" title="عدد صحيح – อาหรับ" lang="ar" hreflang="ar" data-title="عدد صحيح" data-language-autonym="العربية" data-language-local-name="อาหรับ" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%85%E0%A6%96%E0%A6%A3%E0%A7%8D%E0%A6%A1_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="অখণ্ড সংখ্যা – อัสสัม" lang="as" hreflang="as" data-title="অখণ্ড সংখ্যা" data-language-autonym="অসমীয়া" data-language-local-name="อัสสัม" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/N%C3%BAmberu_enteru" title="Númberu enteru – อัสตูเรียส" lang="ast" hreflang="ast" data-title="Númberu enteru" data-language-autonym="Asturianu" data-language-local-name="อัสตูเรียส" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Tam_%C9%99d%C9%99dl%C9%99r" title="Tam ədədlər – อาเซอร์ไบจาน" lang="az" hreflang="az" data-title="Tam ədədlər" data-language-autonym="Azərbaycanca" data-language-local-name="อาเซอร์ไบจาน" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AA%D8%A7%D9%85_%D8%B3%D8%A7%DB%8C%DB%8C%D9%84%D8%A7%D8%B1" title="تام ساییلار – South Azerbaijani" lang="azb" hreflang="azb" data-title="تام ساییلار" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%91%D3%A9%D1%82%D3%A9%D0%BD_%D2%BB%D0%B0%D0%BD" title="Бөтөн һан – บัชคีร์" lang="ba" hreflang="ba" data-title="Бөтөн һан" data-language-autonym="Башҡортса" data-language-local-name="บัชคีร์" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Sv%C4%93kas%C4%97s_skaitlios" title="Svēkasės skaitlios – ซาโมจิเตียน" lang="sgs" hreflang="sgs" data-title="Svēkasės skaitlios" data-language-autonym="Žemaitėška" data-language-local-name="ซาโมจิเตียน" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Integer" title="Integer – Central Bikol" lang="bcl" hreflang="bcl" data-title="Integer" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A6%D1%8D%D0%BB%D1%8B_%D0%BB%D1%96%D0%BA" title="Цэлы лік – เบลารุส" lang="be" hreflang="be" data-title="Цэлы лік" data-language-autonym="Беларуская" data-language-local-name="เบลารุส" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A6%D1%8D%D0%BB%D1%8B_%D0%BB%D1%96%D0%BA" title="Цэлы лік – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Цэлы лік" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A6%D1%8F%D0%BB%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Цяло число – บัลแกเรีย" lang="bg" hreflang="bg" data-title="Цяло число" data-language-autonym="Български" data-language-local-name="บัลแกเรีย" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%82%E0%A6%B0%E0%A7%8D%E0%A6%A3_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="পূর্ণ সংখ্যা – บังกลา" lang="bn" hreflang="bn" data-title="পূর্ণ সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="บังกลา" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Kevan_daveel" title="Kevan daveel – เบรตัน" lang="br" hreflang="br" data-title="Kevan daveel" data-language-autonym="Brezhoneg" data-language-local-name="เบรตัน" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Cijeli_broj" title="Cijeli broj – บอสเนีย" lang="bs" hreflang="bs" data-title="Cijeli broj" data-language-autonym="Bosanski" data-language-local-name="บอสเนีย" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_enter" title="Nombre enter – คาตาลัน" lang="ca" hreflang="ca" data-title="Nombre enter" data-language-autonym="Català" data-language-local-name="คาตาลัน" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95%DB%8C_%D8%AA%DB%95%D9%88%D8%A7%D9%88" title="ژمارەی تەواو – เคิร์ดตอนกลาง" lang="ckb" hreflang="ckb" data-title="ژمارەی تەواو" data-language-autonym="کوردی" data-language-local-name="เคิร์ดตอนกลาง" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Cel%C3%A9_%C4%8D%C3%ADslo" title="Celé číslo – เช็ก" lang="cs" hreflang="cs" data-title="Celé číslo" data-language-autonym="Čeština" data-language-local-name="เช็ก" 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%A2%D1%83%D0%BB%D0%BB%D0%B8_%D1%85%D0%B8%D1%81%D0%B5%D0%BF" title="Тулли хисеп – ชูวัช" lang="cv" hreflang="cv" data-title="Тулли хисеп" data-language-autonym="Чӑвашла" data-language-local-name="ชูวัช" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cyfanrif" title="Cyfanrif – เวลส์" lang="cy" hreflang="cy" data-title="Cyfanrif" data-language-autonym="Cymraeg" data-language-local-name="เวลส์" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Heltal" title="Heltal – เดนมาร์ก" lang="da" hreflang="da" data-title="Heltal" data-language-autonym="Dansk" data-language-local-name="เดนมาร์ก" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Ganze_Zahl" title="Ganze Zahl – เยอรมัน" lang="de" hreflang="de" data-title="Ganze Zahl" data-language-autonym="Deutsch" data-language-local-name="เยอรมัน" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BA%CE%AD%CF%81%CE%B1%CE%B9%CE%BF%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82" title="Ακέραιος αριθμός – กรีก" lang="el" hreflang="el" data-title="Ακέραιος αριθμός" data-language-autonym="Ελληνικά" data-language-local-name="กรีก" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Integer" title="Integer – อังกฤษ" lang="en" hreflang="en" data-title="Integer" data-language-autonym="English" data-language-local-name="อังกฤษ" 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/Entjero" title="Entjero – เอสเปรันโต" lang="eo" hreflang="eo" data-title="Entjero" data-language-autonym="Esperanto" data-language-local-name="เอสเปรันโต" 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/N%C3%BAmero_entero" title="Número entero – สเปน" lang="es" hreflang="es" data-title="Número entero" data-language-autonym="Español" data-language-local-name="สเปน" 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/T%C3%A4isarv" title="Täisarv – เอสโตเนีย" lang="et" hreflang="et" data-title="Täisarv" data-language-autonym="Eesti" data-language-local-name="เอสโตเนีย" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki_oso" title="Zenbaki oso – บาสก์" lang="eu" hreflang="eu" data-title="Zenbaki oso" data-language-autonym="Euskara" data-language-local-name="บาสก์" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%B5%D8%AD%DB%8C%D8%AD" title="عدد صحیح – เปอร์เซีย" lang="fa" hreflang="fa" data-title="عدد صحیح" data-language-autonym="فارسی" data-language-local-name="เปอร์เซีย" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kokonaisluku" title="Kokonaisluku – ฟินแลนด์" lang="fi" hreflang="fi" data-title="Kokonaisluku" data-language-autonym="Suomi" data-language-local-name="ฟินแลนด์" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Terveharv" title="Terveharv – โวโร" lang="vro" hreflang="vro" data-title="Terveharv" data-language-autonym="Võro" data-language-local-name="โวโร" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Integer" title="Integer – ฟิจิ" lang="fj" hreflang="fj" data-title="Integer" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="ฟิจิ" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Heiltal" title="Heiltal – แฟโร" lang="fo" hreflang="fo" data-title="Heiltal" data-language-autonym="Føroyskt" data-language-local-name="แฟโร" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Entier_relatif" title="Entier relatif – ฝรั่งเศส" lang="fr" hreflang="fr" data-title="Entier relatif" data-language-autonym="Français" data-language-local-name="ฝรั่งเศส" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Hial_taal" title="Hial taal – ฟริเซียนเหนือ" lang="frr" hreflang="frr" data-title="Hial taal" data-language-autonym="Nordfriisk" data-language-local-name="ฟริเซียนเหนือ" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Sl%C3%A1nuimhir" title="Slánuimhir – ไอริช" lang="ga" hreflang="ga" data-title="Slánuimhir" data-language-autonym="Gaeilge" data-language-local-name="ไอริช" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%95%B4%E6%95%B8" title="整數 – จีนกั้น" lang="gan" hreflang="gan" data-title="整數" data-language-autonym="贛語" data-language-local-name="จีนกั้น" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Anty%C3%A9_r%C3%A9latif" title="Antyé rélatif – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Antyé rélatif" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%BAmero_enteiro" title="Número enteiro – กาลิเซีย" lang="gl" hreflang="gl" data-title="Número enteiro" data-language-autonym="Galego" data-language-local-name="กาลิเซีย" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AA%E0%AB%82%E0%AA%B0%E0%AB%8D%E0%AA%A3%E0%AA%BE%E0%AA%82%E0%AA%95_%E0%AA%B8%E0%AA%82%E0%AA%96%E0%AB%8D%E0%AA%AF%E0%AA%BE%E0%AA%93" title="પૂર્ણાંક સંખ્યાઓ – คุชราต" lang="gu" hreflang="gu" data-title="પૂર્ણાંક સંખ્યાઓ" data-language-autonym="ગુજરાતી" data-language-local-name="คุชราต" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/Helu_piha" title="Helu piha – ฮาวาย" lang="haw" hreflang="haw" data-title="Helu piha" data-language-autonym="Hawaiʻi" data-language-local-name="ฮาวาย" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%A9%D7%9C%D7%9D" title="מספר שלם – ฮิบรู" lang="he" hreflang="he" data-title="מספר שלם" data-language-autonym="עברית" data-language-local-name="ฮิบรู" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3%E0%A4%BE%E0%A4%82%E0%A4%95" title="पूर्णांक – ฮินดี" lang="hi" hreflang="hi" data-title="पूर्णांक" data-language-autonym="हिन्दी" data-language-local-name="ฮินดี" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Cijeli_broj" title="Cijeli broj – โครเอเชีย" lang="hr" hreflang="hr" data-title="Cijeli broj" data-language-autonym="Hrvatski" data-language-local-name="โครเอเชีย" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Cy%C5%82a_li%C4%8Dba" title="Cyła ličba – ซอร์เบียตอนบน" lang="hsb" hreflang="hsb" data-title="Cyła ličba" data-language-autonym="Hornjoserbsce" data-language-local-name="ซอร์เบียตอนบน" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Eg%C3%A9sz_sz%C3%A1mok" title="Egész számok – ฮังการี" lang="hu" hreflang="hu" data-title="Egész számok" data-language-autonym="Magyar" data-language-local-name="ฮังการี" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B4%D5%A2%D5%B8%D5%B2%D5%BB_%D5%A9%D5%AB%D5%BE" title="Ամբողջ թիվ – อาร์เมเนีย" lang="hy" hreflang="hy" data-title="Ամբողջ թիվ" data-language-autonym="Հայերեն" data-language-local-name="อาร์เมเนีย" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B1%D5%B4%D5%A2%D5%B8%D5%B2%D5%BB_%D5%A9%D5%AB%D6%82" title="Ամբողջ թիւ – Western Armenian" lang="hyw" hreflang="hyw" data-title="Ամբողջ թիւ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Numero_integre" title="Numero integre – อินเตอร์ลิงกัว" lang="ia" hreflang="ia" data-title="Numero integre" data-language-autonym="Interlingua" data-language-local-name="อินเตอร์ลิงกัว" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Integer" title="Integer – อิบาน" lang="iba" hreflang="iba" data-title="Integer" data-language-autonym="Jaku Iban" data-language-local-name="อิบาน" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan_bulat" title="Bilangan bulat – อินโดนีเซีย" lang="id" hreflang="id" data-title="Bilangan bulat" data-language-autonym="Bahasa Indonesia" data-language-local-name="อินโดนีเซีย" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%91%D3%80%D0%B0%D1%80%D1%87%D1%87%D0%B0_%D1%82%D0%B0%D1%8C%D1%80%D0%B0%D1%85%D1%8C" title="БӀарчча таьрахь – อินกุช" lang="inh" hreflang="inh" data-title="БӀарчча таьрахь" data-language-autonym="ГӀалгӀай" data-language-local-name="อินกุช" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Integro" title="Integro – อีโด" lang="io" hreflang="io" data-title="Integro" data-language-autonym="Ido" data-language-local-name="อีโด" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Heilt%C3%B6lur" title="Heiltölur – ไอซ์แลนด์" lang="is" hreflang="is" data-title="Heiltölur" data-language-autonym="Íslenska" data-language-local-name="ไอซ์แลนด์" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_intero" title="Numero intero – อิตาลี" lang="it" hreflang="it" data-title="Numero intero" data-language-autonym="Italiano" data-language-local-name="อิตาลี" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%95%B4%E6%95%B0" title="整数 – ญี่ปุ่น" lang="ja" hreflang="ja" data-title="整数" data-language-autonym="日本語" data-language-local-name="ญี่ปุ่น" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Intiga" title="Intiga – อังกฤษคลีโอลจาเมกา" lang="jam" hreflang="jam" data-title="Intiga" data-language-autonym="Patois" data-language-local-name="อังกฤษคลีโอลจาเมกา" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/mulna%27u" title="mulna'u – โลชบัน" lang="jbo" hreflang="jbo" data-title="mulna'u" data-language-autonym="La .lojban." data-language-local-name="โลชบัน" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Wilangan_bulat" title="Wilangan bulat – ชวา" lang="jv" hreflang="jv" data-title="Wilangan bulat" data-language-autonym="Jawa" data-language-local-name="ชวา" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%97%E1%83%94%E1%83%9A%E1%83%98_%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%98" title="მთელი რიცხვი – จอร์เจีย" lang="ka" hreflang="ka" data-title="მთელი რიცხვი" data-language-autonym="ქართული" data-language-local-name="จอร์เจีย" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D2%AF%D1%82%D1%96%D0%BD_%D1%81%D0%B0%D0%BD" title="Бүтін сан – คาซัค" lang="kk" hreflang="kk" data-title="Бүтін сан" data-language-autonym="Қазақша" data-language-local-name="คาซัค" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%95%EC%88%98" title="정수 – เกาหลี" lang="ko" hreflang="ko" data-title="정수" data-language-autonym="한국어" data-language-local-name="เกาหลี" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Tamhejmar" title="Tamhejmar – เคิร์ด" lang="ku" hreflang="ku" data-title="Tamhejmar" data-language-autonym="Kurdî" data-language-local-name="เคิร์ด" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D2%AF%D1%82%D2%AF%D0%BD_%D1%81%D0%B0%D0%BD%D0%B4%D0%B0%D1%80" title="Бүтүн сандар – คีร์กีซ" lang="ky" hreflang="ky" data-title="Бүтүн сандар" data-language-autonym="Кыргызча" data-language-local-name="คีร์กีซ" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numerus_integer" title="Numerus integer – ละติน" lang="la" hreflang="la" data-title="Numerus integer" data-language-autonym="Latina" data-language-local-name="ละติน" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Ganz_Zuel" title="Ganz Zuel – ลักเซมเบิร์ก" lang="lb" hreflang="lb" data-title="Ganz Zuel" data-language-autonym="Lëtzebuergesch" data-language-local-name="ลักเซมเบิร์ก" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Numero_intera" title="Numero intera – ลิงกัวฟรังกาโนวา" lang="lfn" hreflang="lfn" data-title="Numero intera" data-language-autonym="Lingua Franca Nova" data-language-local-name="ลิงกัวฟรังกาโนวา" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Gans_getal" title="Gans getal – ลิมเบิร์ก" lang="li" hreflang="li" data-title="Gans getal" data-language-autonym="Limburgs" data-language-local-name="ลิมเบิร์ก" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Numer_intreg" title="Numer intreg – ลอมบาร์ด" lang="lmo" hreflang="lmo" data-title="Numer intreg" data-language-autonym="Lombard" data-language-local-name="ลอมบาร์ด" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%88%E0%BA%B3%E0%BA%99%E0%BA%A7%E0%BA%99%E0%BA%96%E0%BB%89%E0%BA%A7%E0%BA%99" title="ຈຳນວນຖ້ວນ – ลาว" lang="lo" hreflang="lo" data-title="ຈຳນວນຖ້ວນ" data-language-autonym="ລາວ" data-language-local-name="ลาว" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Sveikasis_skai%C4%8Dius" title="Sveikasis skaičius – ลิทัวเนีย" lang="lt" hreflang="lt" data-title="Sveikasis skaičius" data-language-autonym="Lietuvių" data-language-local-name="ลิทัวเนีย" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Vesels_skaitlis" title="Vesels skaitlis – ลัตเวีย" lang="lv" hreflang="lv" data-title="Vesels skaitlis" data-language-autonym="Latviešu" data-language-local-name="ลัตเวีย" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Isa_tsimivaky" title="Isa tsimivaky – มาลากาซี" lang="mg" hreflang="mg" data-title="Isa tsimivaky" data-language-autonym="Malagasy" data-language-local-name="มาลากาซี" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BB_%D0%B1%D1%80%D0%BE%D1%98" title="Цел број – มาซิโดเนีย" lang="mk" hreflang="mk" data-title="Цел број" data-language-autonym="Македонски" data-language-local-name="มาซิโดเนีย" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%82%E0%B5%BC%E0%B4%A3%E0%B5%8D%E0%B4%A3%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF" title="പൂർണ്ണസംഖ്യ – มาลายาลัม" lang="ml" hreflang="ml" data-title="പൂർണ്ണസംഖ്യ" data-language-autonym="മലയാളം" data-language-local-name="มาลายาลัม" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%91%D2%AF%D1%85%D1%8D%D0%BB_%D1%82%D0%BE%D0%BE" title="Бүхэл тоо – มองโกเลีย" lang="mn" hreflang="mn" data-title="Бүхэл тоо" data-language-autonym="Монгол" data-language-local-name="มองโกเลีย" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="पूर्ण संख्या – มราฐี" lang="mr" hreflang="mr" data-title="पूर्ण संख्या" data-language-autonym="मराठी" data-language-local-name="มราฐี" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Integer" title="Integer – มาเลย์" lang="ms" hreflang="ms" data-title="Integer" data-language-autonym="Bahasa Melayu" data-language-local-name="มาเลย์" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Integer" title="Integer – มอลตา" lang="mt" hreflang="mt" data-title="Integer" data-language-autonym="Malti" data-language-local-name="มอลตา" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/N%C3%BAmaro_anteiro" title="Númaro anteiro – มีรันดา" lang="mwl" hreflang="mwl" data-title="Númaro anteiro" data-language-autonym="Mirandés" data-language-local-name="มีรันดา" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Hele_Tall" title="Hele Tall – เยอรมันต่ำ" lang="nds" hreflang="nds" data-title="Hele Tall" data-language-autonym="Plattdüütsch" data-language-local-name="เยอรมันต่ำ" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Geheel_getal" title="Geheel getal – ดัตช์" lang="nl" hreflang="nl" data-title="Geheel getal" data-language-autonym="Nederlands" data-language-local-name="ดัตช์" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Heiltal" title="Heiltal – นอร์เวย์นีนอสก์" lang="nn" hreflang="nn" data-title="Heiltal" data-language-autonym="Norsk nynorsk" data-language-local-name="นอร์เวย์นีนอสก์" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Heltall" title="Heltall – นอร์เวย์บุคมอล" lang="nb" hreflang="nb" data-title="Heltall" data-language-autonym="Norsk bokmål" data-language-local-name="นอร์เวย์บุคมอล" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nso mw-list-item"><a href="https://nso.wikipedia.org/wiki/Integer" title="Integer – โซโทเหนือ" lang="nso" hreflang="nso" data-title="Integer" data-language-autonym="Sesotho sa Leboa" data-language-local-name="โซโทเหนือ" class="interlanguage-link-target"><span>Sesotho sa Leboa</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Nombre_enti%C3%A8r" title="Nombre entièr – อ็อกซิตัน" lang="oc" hreflang="oc" data-title="Nombre entièr" data-language-autonym="Occitan" data-language-local-name="อ็อกซิตัน" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Lakkoofsa_Intiijarii" title="Lakkoofsa Intiijarii – โอโรโม" lang="om" hreflang="om" data-title="Lakkoofsa Intiijarii" data-language-autonym="Oromoo" data-language-local-name="โอโรโม" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A9%82%E0%A8%B0%E0%A8%A8_%E0%A8%B8%E0%A9%B0%E0%A8%96%E0%A8%BF%E0%A8%86" title="ਪੂਰਨ ਸੰਖਿਆ – ปัญจาบ" lang="pa" hreflang="pa" data-title="ਪੂਰਨ ਸੰਖਿਆ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="ปัญจาบ" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczby_ca%C5%82kowite" title="Liczby całkowite – โปแลนด์" lang="pl" hreflang="pl" data-title="Liczby całkowite" data-language-autonym="Polski" data-language-local-name="โปแลนด์" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/N%C3%B9mer_antregh" title="Nùmer antregh – พีดมอนต์" lang="pms" hreflang="pms" data-title="Nùmer antregh" data-language-autonym="Piemontèis" data-language-local-name="พีดมอนต์" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%86%D9%B9%DB%8C%D8%AC%D8%B1" title="انٹیجر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انٹیجر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero_inteiro" title="Número inteiro – โปรตุเกส" lang="pt" hreflang="pt" data-title="Número inteiro" data-language-autonym="Português" data-language-local-name="โปรตุเกส" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_%C3%AEntreg" title="Număr întreg – โรมาเนีย" lang="ro" hreflang="ro" data-title="Număr întreg" data-language-autonym="Română" data-language-local-name="โรมาเนีย" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437798 badge-goodarticle mw-list-item" title="บทความคุณภาพ"><a href="https://ru.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BB%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Целое число – รัสเซีย" lang="ru" hreflang="ru" data-title="Целое число" data-language-autonym="Русский" data-language-local-name="รัสเซีย" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/N%C3%B9mmuru_rilativu" title="Nùmmuru rilativu – ซิซิลี" lang="scn" hreflang="scn" data-title="Nùmmuru rilativu" data-language-autonym="Sicilianu" data-language-local-name="ซิซิลี" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Cijeli_broj" title="Cijeli broj – เซอร์โบ-โครเอเชีย" lang="sh" hreflang="sh" data-title="Cijeli broj" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="เซอร์โบ-โครเอเชีย" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B1%E0%B7%92%E0%B6%9B%E0%B7%92%E0%B6%BD" title="නිඛිල – สิงหล" lang="si" hreflang="si" data-title="නිඛිල" data-language-autonym="සිංහල" data-language-local-name="สิงหล" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Integer" title="Integer – Simple English" lang="en-simple" hreflang="en-simple" data-title="Integer" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Cel%C3%A9_%C4%8D%C3%ADslo" title="Celé číslo – สโลวัก" lang="sk" hreflang="sk" data-title="Celé číslo" data-language-autonym="Slovenčina" data-language-local-name="สโลวัก" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Celo_%C5%A1tevilo" title="Celo število – สโลวีเนีย" lang="sl" hreflang="sl" data-title="Celo število" data-language-autonym="Slovenščina" data-language-local-name="สโลวีเนีย" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Nhamba_mhumburu" title="Nhamba mhumburu – โชนา" lang="sn" hreflang="sn" data-title="Nhamba mhumburu" data-language-autonym="ChiShona" data-language-local-name="โชนา" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Abyoone" title="Abyoone – โซมาลี" lang="so" hreflang="so" data-title="Abyoone" data-language-autonym="Soomaaliga" data-language-local-name="โซมาลี" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Numrat_e_plot%C3%AB" title="Numrat e plotë – แอลเบเนีย" lang="sq" hreflang="sq" data-title="Numrat e plotë" data-language-autonym="Shqip" data-language-local-name="แอลเบเนีย" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BE_%D0%B1%D1%80%D0%BE%D1%98" title="Цео број – เซอร์เบีย" lang="sr" hreflang="sr" data-title="Цео број" data-language-autonym="Српски / srpski" data-language-local-name="เซอร์เบีย" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Heltal" title="Heltal – สวีเดน" lang="sv" hreflang="sv" data-title="Heltal" data-language-autonym="Svenska" data-language-local-name="สวีเดน" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Nambakamili" title="Nambakamili – สวาฮีลี" lang="sw" hreflang="sw" data-title="Nambakamili" data-language-autonym="Kiswahili" data-language-local-name="สวาฮีลี" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Co%C5%82kowito_n%C5%AFmera" title="Cołkowito nůmera – ไซลีเซีย" lang="szl" hreflang="szl" data-title="Cołkowito nůmera" data-language-autonym="Ślůnski" data-language-local-name="ไซลีเซีย" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%B4%E0%AF%81_%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="முழு எண் – ทมิฬ" lang="ta" hreflang="ta" data-title="முழு எண்" data-language-autonym="தமிழ்" data-language-local-name="ทมิฬ" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AA%E0%B1%82%E0%B0%B0%E0%B1%8D%E0%B0%A3_%E0%B0%B8%E0%B0%82%E0%B0%96%E0%B1%8D%E0%B0%AF" title="పూర్ణ సంఖ్య – เตลูกู" lang="te" hreflang="te" data-title="పూర్ణ సంఖ్య" data-language-autonym="తెలుగు" data-language-local-name="เตลูกู" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%B4%D0%B0%D0%B4%D2%B3%D0%BE%D0%B8_%D0%B1%D1%83%D1%82%D1%83%D0%BD" title="Ададҳои бутун – ทาจิก" lang="tg" hreflang="tg" data-title="Ададҳои бутун" data-language-autonym="Тоҷикӣ" data-language-local-name="ทาจิก" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Bitin_sanlar" title="Bitin sanlar – เติร์กเมน" lang="tk" hreflang="tk" data-title="Bitin sanlar" data-language-autonym="Türkmençe" data-language-local-name="เติร์กเมน" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Buumbilang" title="Buumbilang – ตากาล็อก" lang="tl" hreflang="tl" data-title="Buumbilang" data-language-autonym="Tagalog" data-language-local-name="ตากาล็อก" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Tam_say%C4%B1" title="Tam sayı – ตุรกี" lang="tr" hreflang="tr" data-title="Tam sayı" data-language-autonym="Türkçe" data-language-local-name="ตุรกี" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A6%D1%96%D0%BB%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Ціле число – ยูเครน" lang="uk" hreflang="uk" data-title="Ціле число" data-language-autonym="Українська" data-language-local-name="ยูเครน" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B5%D8%AD%DB%8C%D8%AD_%D8%B9%D8%AF%D8%AF" title="صحیح عدد – อูรดู" lang="ur" hreflang="ur" data-title="صحیح عدد" data-language-autonym="اردو" data-language-local-name="อูรดู" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Butun_sonlar" title="Butun sonlar – อุซเบก" lang="uz" hreflang="uz" data-title="Butun sonlar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="อุซเบก" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91_nguy%C3%AAn" title="Số nguyên – เวียดนาม" lang="vi" hreflang="vi" data-title="Số nguyên" data-language-autonym="Tiếng Việt" data-language-local-name="เวียดนาม" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Geh%C3%AAel_getal" title="Gehêel getal – เฟลมิชตะวันตก" lang="vls" hreflang="vls" data-title="Gehêel getal" data-language-autonym="West-Vlams" data-language-local-name="เฟลมิชตะวันตก" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Buok" title="Buok – วาเรย์" lang="war" hreflang="war" data-title="Buok" data-language-autonym="Winaray" data-language-local-name="วาเรย์" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%95%B4%E6%95%B0" title="整数 – จีนอู๋" lang="wuu" hreflang="wuu" data-title="整数" data-language-autonym="吴语" data-language-local-name="จีนอู๋" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%91%D2%AF%D0%BA%D0%BB_%D1%82%D0%BE%D0%B9%D0%B3" title="Бүкл тойг – คัลมืยค์" lang="xal" hreflang="xal" data-title="Бүкл тойг" data-language-autonym="Хальмг" data-language-local-name="คัลมืยค์" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-integer" title="I-integer – คะห์โอซา" lang="xh" hreflang="xh" data-title="I-integer" data-language-autonym="IsiXhosa" data-language-local-name="คะห์โอซา" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%92%D7%90%D7%A0%D7%A6%D7%A2_%D7%A6%D7%90%D7%9C" title="גאנצע צאל – ยิดดิช" lang="yi" hreflang="yi" data-title="גאנצע צאל" data-language-autonym="ייִדיש" data-language-local-name="ยิดดิช" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/N%E1%BB%8D%CC%81mb%C3%A0_odidi" title="Nọ́mbà odidi – โยรูบา" lang="yo" hreflang="yo" data-title="Nọ́mbà odidi" data-language-autonym="Yorùbá" data-language-local-name="โยรูบา" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%B4%E6%95%B0" title="整数 – จีน" lang="zh" hreflang="zh" data-title="整数" data-language-autonym="中文" data-language-local-name="จีน" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%95%B4%E6%95%B8" title="整數 – จีนคลาสสิก" lang="lzh" hreflang="lzh" data-title="整數" data-language-autonym="文言" data-language-local-name="จีนคลาสสิก" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ch%C3%A9ng-s%C3%B2%CD%98" title="Chéng-sò͘ – จีนมินหนาน" lang="nan" hreflang="nan" data-title="Chéng-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="จีนมินหนาน" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%95%B4%E6%95%B8" title="整數 – กวางตุ้ง" lang="yue" hreflang="yue" data-title="整數" data-language-autonym="粵語" data-language-local-name="กวางตุ้ง" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12503#sitelinks-wikipedia" title="แก้ไขลิงก์ข้ามภาษา" class="wbc-editpage">แก้ไขลิงก์</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="เนมสเปซ"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="ดูหน้าเนื้อหา [c]" accesskey="c"><span>บทความ</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B9%E0%B8%94%E0%B8%84%E0%B8%B8%E0%B8%A2:%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" rel="discussion" title="อภิปรายเกี่ยวกับหน้าเนื้อหา [t]" accesskey="t"><span>อภิปราย</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="เปลี่ยนรูปแบบภาษา" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">ไทย</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="ดู"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1"><span>อ่าน</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit" title="แก้ไขรหัสต้นฉบับของหน้านี้ [e]" accesskey="e"><span>แก้ไข</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=history" title="แก้ไขเก่าของหน้านี้ [h]" accesskey="h"><span>ดูประวัติ</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="หน้าเครื่องมือ"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="เครื่องมือ" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">เครื่องมือ</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">เครื่องมือ</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ซ่อน</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="ตัวเลือกเพิ่มเติม" > <div class="vector-menu-heading"> การกระทำ </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1"><span>อ่าน</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit" title="แก้ไขรหัสต้นฉบับของหน้านี้ [e]" accesskey="e"><span>แก้ไข</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=history"><span>ดูประวัติ</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> ทั่วไป </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B9%82%E0%B8%A2%E0%B8%87%E0%B8%A1%E0%B8%B2/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="รายการหน้าวิกิทุกหน้าที่ลิงก์มาที่นี่ [j]" accesskey="j"><span>หน้าที่ลิงก์มา</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9B%E0%B8%A3%E0%B8%B1%E0%B8%9A%E0%B8%9B%E0%B8%A3%E0%B8%B8%E0%B8%87%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B9%82%E0%B8%A2%E0%B8%87%E0%B8%A1%E0%B8%B2/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" rel="nofollow" title="รายการเปลี่ยนแปลงล่าสุดในหน้าที่ลิงก์จากหน้านี้ [k]" accesskey="k"><span>การเปลี่ยนแปลงที่เกี่ยวโยง</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%AD%E0%B8%B1%E0%B8%9B%E0%B9%82%E0%B8%AB%E0%B8%A5%E0%B8%94" title="อัปโหลดไฟล์ [u]" accesskey="u"><span>อัปโหลดไฟล์</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9" title="รายการหน้าพิเศษทั้งหมด [q]" accesskey="q"><span>หน้าพิเศษ</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&oldid=11888802" title="ลิงก์ถาวรมารุ่นนี้ของหน้านี้"><span>ลิงก์ถาวร</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=info" title="ข้อมูลเพิ่มเติมเกี่ยวกับหน้านี้"><span>สารสนเทศหน้า</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AD%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%AD%E0%B8%B4%E0%B8%87&page=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&id=11888802&wpFormIdentifier=titleform" title="สารสนเทศเกี่ยวกับวิธีการอ้างอิงหน้านี้"><span>อ้างอิงบทความนี้</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:UrlShortener&url=https%3A%2F%2Fth.wikipedia.org%2Fwiki%2F%25E0%25B8%2588%25E0%25B8%25B3%25E0%25B8%2599%25E0%25B8%25A7%25E0%25B8%2599%25E0%25B9%2580%25E0%25B8%2595%25E0%25B9%2587%25E0%25B8%25A1"><span>รับยูอาร์แอลแบบสั้น</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:QrCode&url=https%3A%2F%2Fth.wikipedia.org%2Fwiki%2F%25E0%25B8%2588%25E0%25B8%25B3%25E0%25B8%2599%25E0%25B8%25A7%25E0%25B8%2599%25E0%25B9%2580%25E0%25B8%2595%25E0%25B9%2587%25E0%25B8%25A1"><span>ดาวน์โหลดคิวอาร์โค้ด</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> พิมพ์/ส่งออก </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%99%E0%B8%B1%E0%B8%87%E0%B8%AA%E0%B8%B7%E0%B8%AD&bookcmd=book_creator&referer=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1"><span>สร้างหนังสือ</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:DownloadAsPdf&page=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=show-download-screen"><span>ดาวน์โหลดเป็น PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&printable=yes" title="รุ่นที่พร้อมพิมพ์ของหน้านี้ [p]" accesskey="p"><span>รุ่นพร้อมพิมพ์</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"> ในโครงการอื่น </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Integers" hreflang="en"><span>วิกิมีเดียคอมมอนส์</span></a></li><li class="wb-otherproject-link wb-otherproject-wikifunctions mw-list-item"><a href="https://www.wikifunctions.org/wiki/Z16683" hreflang="en"><span>วิกิฟังก์ชัน</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12503" title="ลิงก์ไปยังสิ่งนี้ในคลังซึ่งเชื่อมโยงข้อมูลต่าง ๆ เข้าด้วยกัน [g]" accesskey="g"><span>สิ่งนี้ในวิกิสนเทศ</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="หน้าเครื่องมือ"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="หน้าตา"> <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">หน้าตา</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ซ่อน</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">จากวิกิพีเดีย สารานุกรมเสรี</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="th" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r10224066">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}</style><table class="box-ต้องการอ้างอิง plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">บทความนี้<b>ไม่มี<a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AD%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%AD%E0%B8%B4%E0%B8%87%E0%B9%81%E0%B8%AB%E0%B8%A5%E0%B9%88%E0%B8%87%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%A1%E0%B8%B2" title="วิกิพีเดีย:การอ้างอิงแหล่งที่มา">การอ้างอิง</a>จาก<a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9E%E0%B8%B4%E0%B8%AA%E0%B8%B9%E0%B8%88%E0%B8%99%E0%B9%8C%E0%B8%A2%E0%B8%B7%E0%B8%99%E0%B8%A2%E0%B8%B1%E0%B8%99%E0%B9%84%E0%B8%94%E0%B9%89" title="วิกิพีเดีย:การพิสูจน์ยืนยันได้">แหล่งที่มาใด</a></b><span class="hide-when-compact"> กรุณาช่วย<a class="external text" href="https://th.wikipedia.org/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit">ปรับปรุงบทความนี้</a> โดยเพิ่มการอ้างอิงแหล่งที่มาที่น่าเชื่อถือ เนื้อความที่ไม่มีแหล่งที่มาอาจถูกคัดค้านหรือลบออก</span><span class="hide-when-compact"><i> (<small><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%98%E0%B8%B5%E0%B9%83%E0%B8%8A%E0%B9%89:%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%99%E0%B8%B3%E0%B9%81%E0%B8%A1%E0%B9%88%E0%B9%81%E0%B8%9A%E0%B8%9A%E0%B8%9A%E0%B8%B3%E0%B8%A3%E0%B8%B8%E0%B8%87%E0%B8%A3%E0%B8%B1%E0%B8%81%E0%B8%A9%E0%B8%B2%E0%B8%AD%E0%B8%AD%E0%B8%81" title="วิธีใช้:การนำแม่แบบบำรุงรักษาออก">เรียนรู้ว่าจะนำสารแม่แบบนี้ออกได้อย่างไรและเมื่อไร</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Latex_integers.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Latex_integers.svg/220px-Latex_integers.svg.png" decoding="async" width="220" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Latex_integers.svg/330px-Latex_integers.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Latex_integers.svg/440px-Latex_integers.svg.png 2x" data-file-width="420" data-file-height="473" /></a><figcaption>เครื่องหมาย<a href="/wiki/%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%AB%E0%B8%99%E0%B8%B2%E0%B8%81%E0%B8%A3%E0%B8%B0%E0%B8%94%E0%B8%B2%E0%B8%99%E0%B8%94%E0%B8%B3" class="mw-redirect" title="ตัวหนากระดานดำ">ตัวหนากระดานดำ</a> ℤ มักใช้เพื่อแสดงเซตของจำนวนเต็มทั้งหมด (ดูเพิ่มที่ <a href="/wiki/%E0%B8%A3%E0%B8%B2%E0%B8%A2%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AA%E0%B8%B1%E0%B8%8D%E0%B8%A5%E0%B8%B1%E0%B8%81%E0%B8%A9%E0%B8%93%E0%B9%8C%E0%B8%97%E0%B8%B2%E0%B8%87%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C#ℤ" title="รายการสัญลักษณ์ทางคณิตศาสตร์">รายการสัญลักษณ์ทางคณิตศาสตร์</a>)</figcaption></figure> <p><i><b>จำนวนเต็ม</b></i> (<a href="/wiki/%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B8%AD%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B8%A4%E0%B8%A9" title="ภาษาอังกฤษ">อังกฤษ</a>: <span lang="en">Integer</span>, <a href="/wiki/%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B9%80%E0%B8%A2%E0%B8%AD%E0%B8%A3%E0%B8%A1%E0%B8%B1%E0%B8%99" title="ภาษาเยอรมัน">เยอรมัน</a>: <i lang="de">Ganze Zahl</i>, <a href="/wiki/%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B8%9D%E0%B8%A3%E0%B8%B1%E0%B9%88%E0%B8%87%E0%B9%80%E0%B8%A8%E0%B8%AA" title="ภาษาฝรั่งเศส">ฝรั่งเศส</a>: <i lang="fr">nombre entier</i>) คือ<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%9F%E0%B8%B5%E0%B9%82%E0%B8%9A%E0%B8%99%E0%B8%B1%E0%B8%8A%E0%B8%8A%E0%B8%B5" title="จำนวนฟีโบนัชชี">จำนวน</a>ที่สามารถเขียนได้โดยปราศจากองค์ประกอบทางเศษส่วนหรือทศนิยม ตัวอย่างเช่น 21, 4, −2048 เหล่านี้คือจำนวนเต็ม แต่ 9.75, 5<span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center; text-indent:0;"><span style="display:block; line-height:1em; padding:0 0.1em;">1</span><span style="display:none;">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">2</span></span>, √2 เหล่านี้ไม่ใช่จำนวนเต็ม เศษของจำนวนเต็มเป็นเศษย่อยของ<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%88%E0%B8%A3%E0%B8%B4%E0%B8%87" title="จำนวนจริง">จำนวนจริง</a> และประกอบด้วย<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%98%E0%B8%A3%E0%B8%A3%E0%B8%A1%E0%B8%8A%E0%B8%B2%E0%B8%95%E0%B8%B4" title="จำนวนธรรมชาติ">จำนวนธรรมชาติ</a> (1, 2, 3, ...) <a href="/wiki/%E0%B8%A8%E0%B8%B9%E0%B8%99%E0%B8%A2%E0%B9%8C" class="mw-redirect" title="ศูนย์">ศูนย์</a> (0) และ<a href="/wiki/%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%9C%E0%B8%81%E0%B8%9C%E0%B8%B1%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9A%E0%B8%A7%E0%B8%81" title="ตัวผกผันการบวก">ตัวผกผันการบวก</a>ของจำนวนธรรมชาติ (−1, −2, −3, ...)<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>เซตของจำนวนเต็มทั้งหมดมักแสดงด้วย <b>Z</b> ตัวหนา (หรือ <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 \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle \mathbb {Z} }"></span> <a href="/w/index.php?title=%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%AB%E0%B8%99%E0%B8%B2%E0%B8%9A%E0%B8%99%E0%B8%81%E0%B8%A3%E0%B8%B0%E0%B8%94%E0%B8%B2%E0%B8%99%E0%B8%94%E0%B8%B3&action=edit&redlink=1" class="new" title="ตัวหนาบนกระดานดำ (ไม่มีหน้านี้)">ตัวหนาบนกระดานดำ</a>, <span class="Unicode">ℤ</span> <a href="/wiki/%E0%B8%A2%E0%B8%B9%E0%B8%99%E0%B8%B4%E0%B9%82%E0%B8%84%E0%B8%94" title="ยูนิโคด">U+2124</a>) มาจากคำใน<a href="/wiki/%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B9%80%E0%B8%A2%E0%B8%AD%E0%B8%A3%E0%B8%A1%E0%B8%B1%E0%B8%99" title="ภาษาเยอรมัน">ภาษาเยอรมัน</a>ว่า <a href="https://en.wiktionary.org/wiki/Zahlen" class="extiw" title="wiktionary:Zahlen">Zahlen</a> <small></small><span title="เสียงอ่านในสัทอักษรสากล" class="IPA">[ˈtsaːlən]</span> แปลว่าจำนวน<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>จำนวนเต็ม (พร้อมด้วยการดำเนินการการบวก) ก่อร่างเป็น<a href="/wiki/%E0%B8%81%E0%B8%A3%E0%B8%B8%E0%B8%9B_(%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="กรุป (คณิตศาสตร์)">กรุป</a>เล็กที่สุดอันประกอบด้วย<a href="/w/index.php?title=%E0%B9%82%E0%B8%A1%E0%B8%99%E0%B8%AD%E0%B8%A2%E0%B8%94%E0%B9%8C&action=edit&redlink=1" class="new" title="โมนอยด์ (ไม่มีหน้านี้)">โมนอยด์</a>เชิงการบวกของจำนวนธรรมชาติ จำนวนเต็มก่อให้เกิด<a href="/wiki/%E0%B9%80%E0%B8%8B%E0%B8%95%E0%B8%AD%E0%B8%99%E0%B8%B1%E0%B8%99%E0%B8%95%E0%B9%8C%E0%B8%99%E0%B8%B1%E0%B8%9A%E0%B9%84%E0%B8%94%E0%B9%89" class="mw-redirect" title="เซตอนันต์นับได้">เซตอนันต์นับได้</a>เช่นเดียวกับจำนวนธรรมชาติ สิ่งเหล่านี้ใน<a href="/w/index.php?title=%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%9E%E0%B8%B5%E0%B8%8A%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95&action=edit&redlink=1" class="new" title="ทฤษฎีจำนวนเชิงพีชคณิต (ไม่มีหน้านี้)">ทฤษฎีจำนวนเชิงพีชคณิต</a>ทำให้เข้าใจได้โดยสามัญว่า จำนวนเต็มซึ่งฝังตัวอยู่ใน<a href="/wiki/%E0%B8%9F%E0%B8%B5%E0%B8%A5%E0%B8%94%E0%B9%8C" title="ฟีลด์">ฟีลด์</a>ของ<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%95%E0%B8%A3%E0%B8%A3%E0%B8%81%E0%B8%A2%E0%B8%B0" title="จำนวนตรรกยะ">จำนวนตรรกยะ</a> หมายถึง <b>จำนวนเต็มตรรกยะ</b> เพื่อแยกแยะออกจาก<a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%9E%E0%B8%B5%E0%B8%8A%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95&action=edit&redlink=1" class="new" title="จำนวนเต็มเชิงพีชคณิต (ไม่มีหน้านี้)">จำนวนเต็มเชิงพีชคณิต</a>ที่ได้นิยามไว้กว้างกว่าจำนวนเต็มเป็นจำนวนนับ </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="สมบัติทางพีชคณิต"><span id=".E0.B8.AA.E0.B8.A1.E0.B8.9A.E0.B8.B1.E0.B8.95.E0.B8.B4.E0.B8.97.E0.B8.B2.E0.B8.87.E0.B8.9E.E0.B8.B5.E0.B8.8A.E0.B8.84.E0.B8.93.E0.B8.B4.E0.B8.95"></span>สมบัติทางพีชคณิต</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit&section=1" title="แก้ไขส่วน: สมบัติทางพีชคณิต"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Z</b> เป็น<a href="/w/index.php?title=%E0%B9%80%E0%B8%8B%E0%B8%95%E0%B8%9B%E0%B8%B4%E0%B8%94&action=edit&redlink=1" class="new" title="เซตปิด (ไม่มีหน้านี้)">เซตปิด</a>สำหรับการดำเนินการ<a href="/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9A%E0%B8%A7%E0%B8%81" title="การบวก">การบวก</a>และ<a href="/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%84%E0%B8%B9%E0%B8%93" title="การคูณ">การคูณ</a> เช่นเดียวกับจำนวนธรรมชาติ นั่นคือ ผลบวกและผลคูณของจำนวนเต็มสองจำนวนใด ๆ เป็นจำนวนเต็ม แต่ <b>Z</b> ยังเป็นเซตปิด เมื่อรวมจำนวนธรรมชาติลบและ 0 ด้วย แต่ <b>Z</b> ไม่เป็นเซตปิดสำหรับการหาร เนื่องจากผลหารของจำนวนเต็มสองจำนวน (เช่น 1 หารด้วย 2) ไม่จำเป็นต้องเป็นจำนวนเต็ม จำนวนเต็มไม่เปิดเซตปิดภายใต้การยกกำลัง ซึ่งต่างจากจำนวนธรรมชาติ (เพราะเมื่อยกกำลังด้วยเลขชี้กำลังเป็นบวกจะได้เศษส่วน) </p><p>ตารางด้านล่างแสดงสมบัติพื้นฐานของการบวกและการคูณของจำนวนเต็ม <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/181523deba732fda302fd176275a0739121d3bc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.261ex; height:2.509ex;" alt="{\displaystyle a,b}"></span> และ <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> ใด ๆ </p><p>กรณีการคูณ นิยมเขียน <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\times b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>×</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\times b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b420244850c1a22be4c326f91e146db8b037f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.068ex; height:2.176ex;" alt="{\displaystyle a\times b}"></span> ด้วย <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 ab}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49337c5cf256196e2292f7047cb5da68c24ca95d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.227ex; height:2.176ex;" alt="{\displaystyle ab}"></span> </p> <table class="wikitable"> <caption>สมบัติการบวกและการคูณจำนวนเต็ม </caption> <tbody><tr> <td> </td> <th scope="col">การบวก </th> <th scope="col">การคูณ </th></tr> <tr> <th scope="row"><a href="/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%9A%E0%B8%B1%E0%B8%95%E0%B8%B4%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9B%E0%B8%B4%E0%B8%94" title="สมบัติการปิด">ปิด</a>: </th> <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 a+b\in \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a+b\in \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d39d32649d4f48f8b2efea91dd67653a760b977" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.459ex; height:2.343ex;" alt="{\displaystyle a+b\in \mathbb {Z} }"></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 ab\in \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab\in \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae1a6acd3952f205add6520972a1907b27bb5bc3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.618ex; height:2.176ex;" alt="{\displaystyle ab\in \mathbb {Z} }"></span> </td></tr> <tr> <th scope="row"><a href="/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%9A%E0%B8%B1%E0%B8%95%E0%B8%B4%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%80%E0%B8%9B%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%99%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88" title="สมบัติการเปลี่ยนหมู่">การเปลี่ยนหมู่</a>: </th> <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 (a+b)+c=a+(b+c)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a+b)+c=a+(b+c)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46b7b8d31d5845966e6abdbb030c73f343c17d4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.547ex; height:2.843ex;" alt="{\displaystyle (a+b)+c=a+(b+c)}"></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 (ab)c=a(bc)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mi>b</mi> <mo stretchy="false">)</mo> <mi>c</mi> <mo>=</mo> <mi>a</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (ab)c=a(bc)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe39cd5b70c1c6b7e467d25b61554b02b1bd122" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.185ex; height:2.843ex;" alt="{\displaystyle (ab)c=a(bc)}"></span> </td></tr> <tr> <th scope="row"><a href="/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%9A%E0%B8%B1%E0%B8%95%E0%B8%B4%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AA%E0%B8%A5%E0%B8%B1%E0%B8%9A%E0%B8%97%E0%B8%B5%E0%B9%88" title="สมบัติการสลับที่">การสลับที่</a>: </th> <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 a+b=b+a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>=</mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a+b=b+a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/684f43b5094501674e8314be5e24a80ee64682e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.234ex; height:2.343ex;" alt="{\displaystyle a+b=b+a}"></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 ab=ba}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> <mo>=</mo> <mi>b</mi> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab=ba}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/794f6c310259e816eed4a00262d91bf4f53e37c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.553ex; height:2.176ex;" alt="{\displaystyle ab=ba}"></span> </td></tr> <tr> <th scope="row">การมี<a href="/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%B2%E0%B8%8A%E0%B8%B4%E0%B8%81%E0%B9%80%E0%B8%AD%E0%B8%81%E0%B8%A5%E0%B8%B1%E0%B8%81%E0%B8%A9%E0%B8%93%E0%B9%8C" title="สมาชิกเอกลักษณ์">สมาชิกเอกลักษณ์</a>: </th> <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 a+0=a=0+a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>+</mo> <mn>0</mn> <mo>=</mo> <mi>a</mi> <mo>=</mo> <mn>0</mn> <mo>+</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a+0=a=0+a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18238cbafc891aac0a2710826bf7dc8b12a80e89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:17.892ex; height:2.343ex;" alt="{\displaystyle a+0=a=0+a}"></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 a1=a=1a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mn>1</mn> <mo>=</mo> <mi>a</mi> <mo>=</mo> <mn>1</mn> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a1=a=1a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a25e26f1fe9ba622ff1df1a065f04d509e9152eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.211ex; height:2.176ex;" alt="{\displaystyle a1=a=1a}"></span> </td></tr> <tr> <th scope="row">การมี<a href="/w/index.php?title=%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%9C%E0%B8%81%E0%B8%9C%E0%B8%B1%E0%B8%99&action=edit&redlink=1" class="new" title="ตัวผกผัน (ไม่มีหน้านี้)">ตัวผกผัน</a>: </th> <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 a+(-a)=0=-a+a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mo>−</mo> <mi>a</mi> <mo>+</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a+(-a)=0=-a+a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10d309839e9e47346a832b3a44bc96f3a4edacf2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.385ex; height:2.843ex;" alt="{\displaystyle a+(-a)=0=-a+a}"></span> </td> <td>ไม่มีตัวผกผันสำหรับการคูณ </td></tr> <tr> <th scope="row"><a href="/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%9A%E0%B8%B1%E0%B8%95%E0%B8%B4%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%81%E0%B8%88%E0%B8%81%E0%B9%81%E0%B8%88%E0%B8%87" title="สมบัติการแจกแจง">การแจกแจง</a>: </th> <td colspan="2" align="center"><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+c)=ab+ac}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mi>b</mi> <mo>+</mo> <mi>a</mi> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a(b+c)=ab+ac}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5aad41bae613e8522d4d598bcf9f52772f472c55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.287ex; height:2.843ex;" alt="{\displaystyle a(b+c)=ab+ac}"></span> และ <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)c=ac+bc}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mi>c</mi> <mo>=</mo> <mi>a</mi> <mi>c</mi> <mo>+</mo> <mi>b</mi> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a+b)c=ac+bc}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21bac1470710402d1e4dcefa2a0623be84f66735" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.064ex; height:2.843ex;" alt="{\displaystyle (a+b)c=ac+bc}"></span> </td></tr> <tr> <th scope="row">ไม่มี<a href="/w/index.php?title=%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%AB%E0%B8%B2%E0%B8%A3%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A8%E0%B8%B9%E0%B8%99%E0%B8%A2%E0%B9%8C&action=edit&redlink=1" class="new" title="ตัวหารของศูนย์ (ไม่มีหน้านี้)">ตัวหารของศูนย์</a>: (*) </th> <td></td> <td>ถ้า <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 ab=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a59b821cbfde052e05d53bf5f013cbb97a6bbd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.488ex; height:2.176ex;" alt="{\displaystyle ab=0}"></span> แล้ว <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=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90d476e5e765a5d77bbcff32e4584579207ec7d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.491ex; height:2.176ex;" alt="{\displaystyle a=0}"></span> หรือ <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=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19206e7d4dab695ccb34c502eff0741e98dbdfc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.258ex; height:2.176ex;" alt="{\displaystyle b=0}"></span> </td></tr></tbody></table> <p>ตามศัพท์ของพีชคณิตนามธรรม คุณสมบัติห้าข้อแรกข้างบนสามารถบอกได้ว่าเซต <b>Z</b> กับการบวกเป็น กรุปสลับที่ หรือ อาบิเลียนกรุป </p> <div class="mw-heading mw-heading2"><h2 id="สมบัติการเรียงลำดับ"><span id=".E0.B8.AA.E0.B8.A1.E0.B8.9A.E0.B8.B1.E0.B8.95.E0.B8.B4.E0.B8.81.E0.B8.B2.E0.B8.A3.E0.B9.80.E0.B8.A3.E0.B8.B5.E0.B8.A2.E0.B8.87.E0.B8.A5.E0.B8.B3.E0.B8.94.E0.B8.B1.E0.B8.9A"></span>สมบัติการเรียงลำดับ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit&section=2" title="แก้ไขส่วน: สมบัติการเรียงลำดับ"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Z</b> เป็น <a href="/w/index.php?title=%E0%B9%80%E0%B8%8B%E0%B8%95%E0%B9%80%E0%B8%A3%E0%B8%B5%E0%B8%A2%E0%B8%87%E0%B8%A5%E0%B8%B3%E0%B8%94%E0%B8%B1%E0%B8%9A&action=edit&redlink=1" class="new" title="เซตเรียงลำดับ (ไม่มีหน้านี้)">เซตเรียงลำดับ</a>ที่ไม่มีขอบเขตบนหรือขอบเขตล่าง. การเรียงลำดับของ <b>Z</b> อยู่ในรูป </p><p>... < −2 < −1 < 0 < 1 < 2 < ... </p><p>จำนวนเต็มใด ๆ จะเป็น<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%A5%E0%B8%9A%E0%B9%81%E0%B8%A5%E0%B8%B0%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%84%E0%B8%A1%E0%B9%88%E0%B9%80%E0%B8%9B%E0%B9%87%E0%B8%99%E0%B8%A5%E0%B8%9A" title="จำนวนลบและจำนวนไม่เป็นลบ">จำนวนบวก</a> เมื่อมีค่ามากกว่าศูนย์ และเป็น<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%A5%E0%B8%9A%E0%B9%81%E0%B8%A5%E0%B8%B0%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%84%E0%B8%A1%E0%B9%88%E0%B9%80%E0%B8%9B%E0%B9%87%E0%B8%99%E0%B8%A5%E0%B8%9A" title="จำนวนลบและจำนวนไม่เป็นลบ">จำนวนลบ</a> เมื่อมีค่าน้อยกว่าศูนย์ สำหรับศูนย์ ไม่ได้จัดอยู่ในจำนวนบวกหรือจำนวนลบแต่อย่างใด </p><p>การเรียงลำดับจำนวนเต็มโดยใช้การดำเนินการทาง<a href="/wiki/%E0%B8%9E%E0%B8%B5%E0%B8%8A%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="พีชคณิต">พีชคณิต</a> ดังนี้ </p> <ol><li>ถ้า <i>a</i> < <i>b</i> และ <i>c</i> < <i>d</i> แล้ว <i>a</i> + <i>c</i> < <i>b</i> + <i>d</i></li> <li>ถ้า <i>a</i> < <i>b</i> และ 0 < <i>c</i> แล้ว <i>ac</i> < <i>bc</i></li> <li>ถ้า <i>a</i> < <i>b</i> และ <i>c</i> < 0 แล้ว <i>ac</i> > <i>bc</i>.</li></ol> <div class="mw-heading mw-heading2"><h2 id="จำนวนเต็มในการคำนวณ"><span id=".E0.B8.88.E0.B8.B3.E0.B8.99.E0.B8.A7.E0.B8.99.E0.B9.80.E0.B8.95.E0.B9.87.E0.B8.A1.E0.B9.83.E0.B8.99.E0.B8.81.E0.B8.B2.E0.B8.A3.E0.B8.84.E0.B8.B3.E0.B8.99.E0.B8.A7.E0.B8.93"></span>จำนวนเต็มในการคำนวณ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit&section=3" title="แก้ไขส่วน: จำนวนเต็มในการคำนวณ"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>จำนวนเต็มมักเป็นชนิดข้อมูลพื้นฐานใน<a href="/wiki/%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B9%82%E0%B8%9B%E0%B8%A3%E0%B9%81%E0%B8%81%E0%B8%A3%E0%B8%A1" title="ภาษาโปรแกรม">ภาษาโปรแกรม</a> แต่จำนวนเต็มในภาษาโปรแกรมมีความจุจำกัด และมักมีจำนวนบิตที่ตายตัว ทำให้สามารถเก็บค่าได้แค่บางส่วนจากจำนวนเต็มทั้งหมดทางคณิตศาสตร์ แต่ในอีกด้านหนึ่ง แบบจำลองทางทฤษฎีทางคำนวณ เช่น <a href="/wiki/%E0%B9%80%E0%B8%84%E0%B8%A3%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%88%E0%B8%B1%E0%B8%81%E0%B8%A3%E0%B8%97%E0%B8%B1%E0%B8%A7%E0%B8%A3%E0%B8%B4%E0%B8%87" class="mw-redirect" title="เครื่องจักรทัวริง">เครื่องจักรทัวริง</a> สมมุติให้เครื่องคำนวณมีความจุไม่มีที่สิ้นสุด (a+)-b </p> <div class="mw-heading mw-heading2"><h2 id="อ้างอิง"><span id=".E0.B8.AD.E0.B9.89.E0.B8.B2.E0.B8.87.E0.B8.AD.E0.B8.B4.E0.B8.87"></span>อ้างอิง</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit&section=4" title="แก้ไขส่วน: อ้างอิง"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.techtarget.com/whatis/definition/integer#:~:text=An%20integer%20(pronounced%20IN%2Dtuh,%2C%20.09%2C%20and%205%2C643.1.">https://www.techtarget.com/whatis/definition/integer#:~:text=An%20integer%20(pronounced%20IN%2Dtuh,%2C%20.09%2C%20and%205%2C643.1.</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r10205087">.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:#d33}.mw-parser-output .cs1-visible-error{color:#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="CITEREFMiller2010" class="citation web cs1">Miller, Jeff (2010-08-29). <a rel="nofollow" class="external text" href="http://jeff560.tripod.com/nth.html">"Earliest Uses of Symbols of Number Theory"</a><span class="reference-accessdate">. สืบค้นเมื่อ <span class="nowrap">2010-09-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Earliest+Uses+of+Symbols+of+Number+Theory&rft.date=2010-08-29&rft.aulast=Miller&rft.aufirst=Jeff&rft_id=http%3A%2F%2Fjeff560.tripod.com%2Fnth.html&rfr_id=info%3Asid%2Fth.wikipedia.org%3A%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="แหล่งข้อมูลอื่น"><span id=".E0.B9.81.E0.B8.AB.E0.B8.A5.E0.B9.88.E0.B8.87.E0.B8.82.E0.B9.89.E0.B8.AD.E0.B8.A1.E0.B8.B9.E0.B8.A5.E0.B8.AD.E0.B8.B7.E0.B9.88.E0.B8.99"></span>แหล่งข้อมูลอื่น</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit&section=5" title="แก้ไขส่วน: แหล่งข้อมูลอื่น"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.positiveintegers.org">The Positive Integers - divisor tables and numeral representation tools</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r9895811">.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .asbox table{background:transparent}.mw-parser-output .asbox p{margin:0}.mw-parser-output .asbox p+p{margin-top:0.25em}.mw-parser-output .asbox-body{font-style:italic}.mw-parser-output .asbox-note{font-size:smaller}.mw-parser-output .asbox .navbar{position:absolute;top:-0.75em;right:1em;display:none}</style><div role="note" class="metadata plainlinks asbox stub"><table role="presentation"><tbody><tr class="noresize"><td><span typeof="mw:File"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Nuvola_apps_edu_mathematics-p.svg" class="mw-file-description"><img alt="Stub icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/35px-Nuvola_apps_edu_mathematics-p.svg.png" decoding="async" width="35" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/53px-Nuvola_apps_edu_mathematics-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/70px-Nuvola_apps_edu_mathematics-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></td><td><p class="asbox-body"> บทความ<a href="/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="คณิตศาสตร์">คณิตศาสตร์</a>นี้ยังเป็น<a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B9%82%E0%B8%84%E0%B8%A3%E0%B8%87" title="วิกิพีเดีย:โครง">โครง</a> คุณสามารถช่วยวิกิพีเดียได้โดยการ<a class="external text" href="https://th.wikipedia.org/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&action=edit">เพิ่มเติมข้อมูล</a></p></td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r10552737">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r10552732">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-ดู"><a href="/wiki/%E0%B9%81%E0%B8%A1%E0%B9%88%E0%B9%81%E0%B8%9A%E0%B8%9A:%E0%B9%82%E0%B8%84%E0%B8%A3%E0%B8%87%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="แม่แบบ:โครงคณิตศาสตร์"><abbr title="ดูแม่แบบนี้">ด</abbr></a></li><li class="nv-คุย"><a href="/wiki/%E0%B8%84%E0%B8%B8%E0%B8%A2%E0%B9%80%E0%B8%A3%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B9%81%E0%B8%A1%E0%B9%88%E0%B9%81%E0%B8%9A%E0%B8%9A:%E0%B9%82%E0%B8%84%E0%B8%A3%E0%B8%87%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="คุยเรื่องแม่แบบ:โครงคณิตศาสตร์"><abbr title="อภิปรายแม่แบบนี้">ค</abbr></a></li><li class="nv-แก้"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:EditPage/%E0%B9%81%E0%B8%A1%E0%B9%88%E0%B9%81%E0%B8%9A%E0%B8%9A:%E0%B9%82%E0%B8%84%E0%B8%A3%E0%B8%87%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="พิเศษ:EditPage/แม่แบบ:โครงคณิตศาสตร์"><abbr title="แก้ไขแม่แบบนี้">ก</abbr></a></li></ul></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">เข้าถึงจาก "<a dir="ltr" href="https://th.wikipedia.org/w/index.php?title=จำนวนเต็ม&oldid=11888802">https://th.wikipedia.org/w/index.php?title=จำนวนเต็ม&oldid=11888802</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88" title="พิเศษ:หมวดหมู่">หมวดหมู่</a>: <ul><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%81%E0%B8%A3%E0%B8%B8%E0%B8%9B" title="หมวดหมู่:ทฤษฎีกรุป">ทฤษฎีกรุป</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99" title="หมวดหมู่:จำนวน">จำนวน</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99" title="หมวดหมู่:ทฤษฎีจำนวน">ทฤษฎีจำนวน</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B9%80%E0%B8%8B%E0%B8%95" title="หมวดหมู่:ทฤษฎีเซต">ทฤษฎีเซต</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B8%A1%E0%B8%B9%E0%B8%A5%E0%B8%90%E0%B8%B2%E0%B8%99" title="หมวดหมู่:คณิตศาสตร์มูลฐาน">คณิตศาสตร์มูลฐาน</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="หมวดหมู่:จำนวนเต็ม">จำนวนเต็ม</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%81%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A7%E0%B8%81%E0%B8%B1%E0%B8%9A_%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C_%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%B1%E0%B8%87%E0%B9%84%E0%B8%A1%E0%B9%88%E0%B8%AA%E0%B8%A1%E0%B8%9A%E0%B8%B9%E0%B8%A3%E0%B8%93%E0%B9%8C" title="หมวดหมู่:บทความเกี่ยวกับ คณิตศาสตร์ ที่ยังไม่สมบูรณ์">บทความเกี่ยวกับ คณิตศาสตร์ ที่ยังไม่สมบูรณ์</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">หมวดหมู่ที่ซ่อนอยู่: <ul><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%82%E0%B8%B2%E0%B8%94%E0%B9%81%E0%B8%AB%E0%B8%A5%E0%B9%88%E0%B8%87%E0%B8%AD%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%AD%E0%B8%B4%E0%B8%87" title="หมวดหมู่:บทความที่ขาดแหล่งอ้างอิง">บทความที่ขาดแหล่งอ้างอิง</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B1%E0%B9%89%E0%B8%87%E0%B8%AB%E0%B8%A1%E0%B8%94%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%82%E0%B8%B2%E0%B8%94%E0%B9%81%E0%B8%AB%E0%B8%A5%E0%B9%88%E0%B8%87%E0%B8%AD%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%AD%E0%B8%B4%E0%B8%87" title="หมวดหมู่:บทความทั้งหมดที่ขาดแหล่งอ้างอิง">บทความทั้งหมดที่ขาดแหล่งอ้างอิง</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%A1%E0%B8%B5%E0%B8%82%E0%B9%89%E0%B8%AD%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B8%AD%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B8%A4%E0%B8%A9" title="หมวดหมู่:บทความที่มีข้อความภาษาอังกฤษ">บทความที่มีข้อความภาษาอังกฤษ</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%A1%E0%B8%B5%E0%B8%82%E0%B9%89%E0%B8%AD%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B9%80%E0%B8%A2%E0%B8%AD%E0%B8%A3%E0%B8%A1%E0%B8%B1%E0%B8%99" title="หมวดหมู่:บทความที่มีข้อความภาษาเยอรมัน">บทความที่มีข้อความภาษาเยอรมัน</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%A1%E0%B8%B5%E0%B8%82%E0%B9%89%E0%B8%AD%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B8%9D%E0%B8%A3%E0%B8%B1%E0%B9%88%E0%B8%87%E0%B9%80%E0%B8%A8%E0%B8%AA" title="หมวดหมู่:บทความที่มีข้อความภาษาฝรั่งเศส">บทความที่มีข้อความภาษาฝรั่งเศส</a></li><li><a href="/wiki/%E0%B8%AB%E0%B8%A1%E0%B8%A7%E0%B8%94%E0%B8%AB%E0%B8%A1%E0%B8%B9%E0%B9%88:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B1%E0%B9%89%E0%B8%87%E0%B8%AB%E0%B8%A1%E0%B8%94%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%B1%E0%B8%87%E0%B9%84%E0%B8%A1%E0%B9%88%E0%B8%AA%E0%B8%A1%E0%B8%9A%E0%B8%B9%E0%B8%A3%E0%B8%93%E0%B9%8C" title="หมวดหมู่:บทความทั้งหมดที่ยังไม่สมบูรณ์">บทความทั้งหมดที่ยังไม่สมบูรณ์</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> หน้านี้แก้ไขล่าสุดเมื่อวันที่ 7 พฤศจิกายน 2567 เวลา 07:05 น.</li> <li id="footer-info-copyright"><div>อนุญาตให้เผยแพร่ภายใต้<a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">สัญญาอนุญาตครีเอทีฟคอมมอนส์ แบบแสดงที่มา-อนุญาตแบบเดียวกัน</a> และอาจมีเงื่อนไขเพิ่มเติม ดูรายละเอียดที่ <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use/th">ข้อกำหนดการใช้งาน</a><br /> Wikipedia® เป็นเครื่องหมายการค้าจดทะเบียนของ<a rel="nofollow" class="external text" href="https://www.wikimediafoundation.org">มูลนิธิวิกิมีเดีย</a> องค์กรไม่แสวงผลกำไร</div> <div class="noprint"><br /><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%95%E0%B8%B4%E0%B8%94%E0%B8%95%E0%B9%88%E0%B8%AD" title="วิกิพีเดีย:ติดต่อ">ติดต่อเรา</a></div></li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">นโยบายความเป็นส่วนตัว</a></li> <li id="footer-places-about"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B9%80%E0%B8%81%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A7%E0%B8%81%E0%B8%B1%E0%B8%9A">เกี่ยวกับวิกิพีเดีย</a></li> <li id="footer-places-disclaimers"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%82%E0%B9%89%E0%B8%AD%E0%B8%9B%E0%B8%8F%E0%B8%B4%E0%B9%80%E0%B8%AA%E0%B8%98%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A3%E0%B8%B1%E0%B8%9A%E0%B8%9C%E0%B8%B4%E0%B8%94%E0%B8%8A%E0%B8%AD%E0%B8%9A">ข้อปฏิเสธความรับผิดชอบ</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">จรรยาบรรณ</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">ผู้พัฒนา</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/th.wikipedia.org">สถิติ</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">นโยบายการใช้คุกกี้</a></li> <li id="footer-places-mobileview"><a href="//th.m.wikipedia.org/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">มุมมองสำหรับอุปกรณ์เคลื่อนที่</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-78f4c97c5d-crm7d","wgBackendResponseTime":172,"wgPageParseReport":{"limitreport":{"cputime":"0.293","walltime":"0.499","ppvisitednodes":{"value":429,"limit":1000000},"postexpandincludesize":{"value":15606,"limit":2097152},"templateargumentsize":{"value":108,"limit":2097152},"expansiondepth":{"value":8,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":9714,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 382.872 1 -total"," 33.93% 129.910 1 แม่แบบ:โครงคณิตศาสตร์"," 33.25% 127.297 1 แม่แบบ:Asbox"," 24.07% 92.169 3 แม่แบบ:Langx"," 21.94% 84.001 1 แม่แบบ:รายการอ้างอิง"," 18.86% 72.206 1 แม่แบบ:Cite_web"," 16.81% 64.352 1 แม่แบบ:ต้องการอ้างอิง"," 12.87% 49.273 1 แม่แบบ:Ambox"," 0.80% 3.076 1 แม่แบบ:Unicode"," 0.69% 2.628 1 แม่แบบ:เศษ"]},"scribunto":{"limitreport-timeusage":{"value":"0.213","limit":"10.000"},"limitreport-memusage":{"value":16906686,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-78f4c97c5d-6ldbz","timestamp":"20241129033102","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"\u0e08\u0e33\u0e19\u0e27\u0e19\u0e40\u0e15\u0e47\u0e21","url":"https:\/\/th.wikipedia.org\/wiki\/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1","sameAs":"http:\/\/www.wikidata.org\/entity\/Q12503","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q12503","author":{"@type":"Organization","name":"\u0e1c\u0e39\u0e49\u0e21\u0e35\u0e2a\u0e48\u0e27\u0e19\u0e23\u0e48\u0e27\u0e21\u0e01\u0e31\u0e1a\u0e42\u0e04\u0e23\u0e07\u0e01\u0e32\u0e23\u0e27\u0e34\u0e01\u0e34\u0e21\u0e35\u0e40\u0e14\u0e35\u0e22"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2005-03-24T09:24:06Z","dateModified":"2024-11-07T00:05:38Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/c\/c1\/Latex_integers.svg"}</script> </body> </html>