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-disabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-not-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>View source for Approximation - Wikipedia</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-disabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-not-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);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":true,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat": "dmy","wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"dd0b8ab5-3301-41bd-a9a7-3568d41c7e3d","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Approximation","wgTitle":"Approximation","wgCurRevisionId":1250919141,"wgRevisionId":0,"wgArticleId":336271,"wgIsArticle":false,"wgIsRedirect":false,"wgAction":"edit","wgUserName":null,"wgUserGroups":["*"],"wgCategories":[],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Approximation","wgRelevantArticleId":336271,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor": {"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":10000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","skins.vector.search.codex.styles": "ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.charinsert.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["mediawiki.action.edit.collapsibleFooter","site","mediawiki.page.ready","jquery.makeCollapsible","skins.vector.js","ext.centralNotice.geoIP","ext.charinsert","ext.gadget.ReferenceTooltips","ext.gadget.charinsert","ext.gadget.extra-toolbar-buttons","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.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=en&modules=ext.charinsert.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="noindex,nofollow,max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="View source for Approximation - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Approximation"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Approximation&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="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Approximation"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <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-Approximation rootpage-Approximation skin-vector-2022 action-edit"><a class="mw-jump-link" href="#bodyContent">Jump to content</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="Site"> <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="Main menu" > <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">Main menu</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">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" 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="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </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/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</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="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <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="Appearance"> <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="Appearance" > <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">Appearance</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="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class=""><span>Donate</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=Special:CreateAccount&returnto=Approximation&returntoquery=action%3Dedit" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</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=Special:UserLogin&returnto=Approximation&returntoquery=action%3Dedit" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</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="Log in and more options" > <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="Personal tools" > <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">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <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="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Approximation&returntoquery=action%3Dedit" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Approximation&returntoquery=action%3Dedit" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</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"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</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/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</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="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading">View source for Approximation</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="This article exist only in this language. Add the article for other languages" > <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-0" 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">Add languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> <div class="after-portlet after-portlet-lang"><span class="uls-after-portlet-link"></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <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/Approximation" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Approximation" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</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="Change language variant" > <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">English</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="Views"> <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="vector-tab-noicon mw-list-item"><a href="/wiki/Approximation"><span>Read</span></a></li><li id="ca-edit" class="selected vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Approximation&action=edit" title="Edit this page"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Approximation&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <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="Tools" > <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">Tools</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">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="vector-more-collapsible-item mw-list-item"><a href="/wiki/Approximation"><span>Read</span></a></li><li id="ca-more-edit" class="selected vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Approximation&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Approximation&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Approximation" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Approximation" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Approximation&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DApproximation%26action%3Dedit"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DApproximation%26action%3Dedit"><span>Download QR code</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"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q27058" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <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">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</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> <div id="contentSub"><div id="mw-content-subtitle">← <a href="/wiki/Approximation" title="Approximation">Approximation</a></div></div> <div id="mw-content-text" class="mw-body-content"><p>You do not have permission to edit this page, for the following reasons: </p> <ul class="permissions-errors"><li class="mw-permissionerror-blockedtext"> <div id="mw-blocked-text" style="border: 1px solid #AAA; background-color: var(--background-color-warning-subtle, ivory); color: inherit; padding: 1.5em; width: 100%; box-sizing: border-box;"> <div style="text-align: center;"><span style="font-size: 26px;"><span typeof="mw:File"><a href="/wiki/File:Stop_hand_nuvola.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/f/f1/Stop_hand_nuvola.svg/50px-Stop_hand_nuvola.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f1/Stop_hand_nuvola.svg/75px-Stop_hand_nuvola.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f1/Stop_hand_nuvola.svg/100px-Stop_hand_nuvola.svg.png 2x" data-file-width="240" data-file-height="240" /></a></span><b> This IP address has been <a href="/wiki/Wikipedia:Blocking_policy" title="Wikipedia:Blocking policy">blocked</a> from <i>editing</i> Wikipedia.</b></span><br /><span style="font-size: 18px;">This does not affect your ability to <i>read</i> Wikipedia pages.</span></div><div class="paragraphbreak" style="margin-top:0.5em"></div><b>Most people who see this message have done nothing wrong.</b> Some kinds of blocks restrict editing from specific service providers or telecom companies in response to recent abuse or vandalism, and can sometimes affect other users who are unrelated to that abuse. Review the information below for assistance if you do not believe that you have done anything wrong.<div class="paragraphbreak" style="margin-top:0.5em"></div> <p>The IP address or range 8.222.128.0/17 has been <a href="/wiki/Wikipedia:Blocking_policy" title="Wikipedia:Blocking policy">blocked</a> by <a href="/wiki/User:L235" title="User:L235">‪L235‬</a> for the following reason(s): </p> <div style="padding:10px; background:var(--background-color-base, white); color:inherit; border:1px #666 solid;"> <div class="user-block colocation-webhost" style="margin-bottom: 0.5em; background-color: #ffefd5; border: 1px solid #AAA; padding: 0.7em;"> <figure class="mw-halign-left" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Server-multiple.svg/40px-Server-multiple.svg.png" decoding="async" width="40" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Server-multiple.svg/60px-Server-multiple.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Server-multiple.svg/80px-Server-multiple.svg.png 2x" data-file-width="744" data-file-height="1052" /></span><figcaption></figcaption></figure><b>The <a href="/wiki/IP_address" title="IP address">IP address</a> that you are currently using has been blocked because it is believed to be a <a href="/wiki/Web_hosting_service" title="Web hosting service">web host provider</a> or <a href="/wiki/Colocation_centre" title="Colocation centre">colocation provider</a>.</b> To prevent abuse, <a href="/wiki/Wikipedia:Open_proxies" title="Wikipedia:Open proxies">web hosts and colocation providers may be blocked</a> from editing Wikipedia. <div style="border-top: 1px solid #AAA; clear: both">You will not be able to edit Wikipedia using a web host or colocation provider because it hides your IP address, much like a <a href="/wiki/Wikipedia:Open_proxies" title="Wikipedia:Open proxies">proxy</a> or <a href="/wiki/Virtual_private_network" title="Virtual private network">VPN</a>. <p><b>We recommend that you attempt to use another connection to edit.</b> For example, if you use a proxy or VPN to connect to the internet, turn it off when editing Wikipedia. If you edit using a mobile connection, try using a Wi-Fi connection, and vice versa. If you are using a corporate internet connection, switch to a different Wi-Fi network. If you have a Wikipedia account, please log in. </p><p>If you do not have any other way to edit Wikipedia, you will need to <a href="/wiki/Wikipedia:IP_block_exemption#Requesting_and_granting_exemption" title="Wikipedia:IP block exemption">request an IP block exemption</a>. </p> <style data-mw-deduplicate="TemplateStyles:r1214851843">.mw-parser-output .hidden-begin{box-sizing:border-box;width:100%;padding:5px;border:none;font-size:95%}.mw-parser-output .hidden-title{font-weight:bold;line-height:1.6;text-align:left}.mw-parser-output .hidden-content{text-align:left}@media all and (max-width:500px){.mw-parser-output .hidden-begin{width:auto!important;clear:none!important;float:none!important}}</style><div class="hidden-begin mw-collapsible mw-collapsed" style=""><div class="hidden-title skin-nightmode-reset-color" style="text-align:center;">How to appeal if you are confident that your connection does not use a colocation provider's IP address:</div><div class="hidden-content mw-collapsible-content" style=""> If you are confident that you are not using a web host, you may <a href="/wiki/Wikipedia:Appealing_a_block" title="Wikipedia:Appealing a block">appeal this block</a> by adding the following text on your <a href="/wiki/Help:Talk_pages" title="Help:Talk pages">talk page</a>: <code>{{<a href="/wiki/Template:Unblock" title="Template:Unblock">unblock</a>|reason=Caught by a colocation web host block but this host or IP is not a web host. My IP address is _______. <i>Place any further information here.</i> ~~~~}}</code>. <b>You must fill in the blank with your IP address for this block to be investigated.</b> Your IP address can be determined <span class="plainlinks"><b><a class="external text" href="https://en.wikipedia.org/wiki/Wikipedia:Get_my_IP_address?withJS=MediaWiki:Get-my-ip.js">here</a></b></span>. Alternatively, if you wish to keep your IP address private you can use the <a href="/wiki/Wikipedia:Unblock_Ticket_Request_System" title="Wikipedia:Unblock Ticket Request System">unblock ticket request system</a>. There are several reasons you might be editing using the IP address of a web host or colocation provider (such as if you are using VPN software or a business network); please use this method of appeal only if you think your IP address is in fact not a web host or colocation provider.</div></div> <p><span class="sysop-show" style="font-size: 85%;"><span style="border:#707070 solid 1px;background-color:#ffe0e0;padding:2px"><b>Administrators:</b></span> The <a href="/wiki/Wikipedia:IP_block_exemption" title="Wikipedia:IP block exemption">IP block exemption</a> user right should only be applied to allow users to edit using web host in exceptional circumstances, and requests should usually be directed to the functionaries team via email. If you intend to give the IPBE user right, a <a href="/wiki/Wikipedia:CheckUser" title="Wikipedia:CheckUser">CheckUser</a> needs to take a look at the account. This can be requested most easily at <a href="/wiki/Wikipedia:SPI#Quick_CheckUser_requests" class="mw-redirect" title="Wikipedia:SPI">SPI Quick Checkuser Requests</a>. <b>Unblocking</b> an IP or IP range with this template <b>is highly discouraged</b> without at least contacting the blocking administrator.</span> </p> </div></div> </div> <p>This block will expire on 18:23, 24 August 2026. Your current IP address is 8.222.208.146. </p> <div class="paragraphbreak" style="margin-top:0.5em"></div><div style="font-size: 16px;"> <p>Even when blocked, you will <i>usually</i> still be able to edit your <a href="/wiki/Special:MyTalk" title="Special:MyTalk">user talk page</a>, as well as <a href="/wiki/Wikipedia:Emailing_users" title="Wikipedia:Emailing users">email</a> administrators and other editors. </p> </div> <div class="paragraphbreak" style="margin-top:0.5em"></div><div style="font-size: 16px;"> <p>For information on how to proceed, please read the <b><a href="/wiki/Wikipedia:Appealing_a_block#Common_questions" title="Wikipedia:Appealing a block">FAQ for blocked users</a></b> and the <a href="/wiki/Wikipedia:Appealing_a_block" title="Wikipedia:Appealing a block">guideline on block appeals</a>. The <a href="/wiki/Wikipedia:Guide_to_appealing_blocks" title="Wikipedia:Guide to appealing blocks">guide to appealing blocks</a> may also be helpful. </p> </div> <p>Other useful links: <a href="/wiki/Wikipedia:Blocking_policy" title="Wikipedia:Blocking policy">Blocking policy</a> · <a href="/wiki/Help:I_have_been_blocked" title="Help:I have been blocked">Help:I have been blocked</a> </p> </div></li><li class="mw-permissionerror-globalblocking-blockedtext-range"> <div id="mw-blocked-text" style="border: 1px solid #AAA; background-color: var(--background-color-warning-subtle, ivory); color: inherit; padding: 1.5em; width: 100%; box-sizing: border-box;"> <div style="text-align: center;"><span style="font-size: 26px;"><span typeof="mw:File"><a href="/wiki/File:Stop_hand_nuvola.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/f/f1/Stop_hand_nuvola.svg/50px-Stop_hand_nuvola.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f1/Stop_hand_nuvola.svg/75px-Stop_hand_nuvola.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f1/Stop_hand_nuvola.svg/100px-Stop_hand_nuvola.svg.png 2x" data-file-width="240" data-file-height="240" /></a></span><b> This IP address range has been <a href="https://meta.wikimedia.org/wiki/Global_blocks" class="extiw" title="m:Global blocks">globally blocked</a>.</b></span><br /><span style="font-size: 18px;">This does not affect your ability to <i>read</i> Wikipedia pages.</span></div><div class="paragraphbreak" style="margin-top:0.5em"></div><b>Most people who see this message have done nothing wrong.</b> Some kinds of blocks restrict editing from specific service providers or telecom companies in response to recent abuse or vandalism, and can sometimes affect other users who are unrelated to that abuse. Review the information below for assistance if you do not believe that you have done anything wrong.<div class="paragraphbreak" style="margin-top:0.5em"></div><div class="paragraphbreak" style="margin-top:0.5em"></div> <p>This block affects editing on all Wikimedia wikis. </p><p>The IP address or range 8.222.128.0/17 has been globally <a href="/wiki/Wikipedia:Blocking_policy" title="Wikipedia:Blocking policy">blocked</a> by <a href="/wiki/User:Jon_Kolbert" title="User:Jon Kolbert">‪Jon Kolbert‬</a> for the following reason(s): </p> <div style="padding:10px; background:var(--background-color-base, white); color:inherit; border:1px #666 solid;"> <p><a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/NOP" class="extiw" title="m:Special:MyLanguage/NOP">Open proxy/Webhost</a>: See the <a href="https://meta.wikimedia.org/wiki/WM:OP/H" class="extiw" title="m:WM:OP/H">help page</a> if you are affected </p> </div> <p>This block will expire on 15:12, 27 August 2028. Your current IP address is 8.222.208.146. </p> <div class="paragraphbreak" style="margin-top:0.5em"></div><div style="font-size: 16px;"> <p>Even while globally blocked, you will <i>usually</i> still be able to edit pages on <a href="https://meta.wikimedia.org/wiki/" class="extiw" title="m:">Meta-Wiki</a>. </p> </div> <div class="paragraphbreak" style="margin-top:0.5em"></div><div style="font-size: 16px;"> <p>If you believe you were blocked by mistake, you can find additional information and instructions in the <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/No_open_proxies" class="extiw" title="m:Special:MyLanguage/No open proxies">No open proxies</a> global policy. Otherwise, to discuss the block please <a href="https://meta.wikimedia.org/wiki/Steward_requests/Global" class="extiw" title="m:Steward requests/Global">post a request for review on Meta-Wiki</a>. You could also send an email to the <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/Stewards" class="extiw" title="m:Special:MyLanguage/Stewards">stewards</a> <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/VRT" class="extiw" title="m:Special:MyLanguage/VRT">VRT</a> queue at <kbd>stewards@wikimedia.org</kbd> including all above details. </p> </div> <p>Other useful links: <a href="https://meta.wikimedia.org/wiki/Global_blocks" class="extiw" title="m:Global blocks">Global blocks</a> · <a href="/wiki/Help:I_have_been_blocked" title="Help:I have been blocked">Help:I have been blocked</a> </p> </div></li></ul><hr /> <div id="viewsourcetext">You can view and copy the source of this page:</div><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" class="mw-editfont-monospace" lang="en" dir="ltr" name="wpTextbox1">{{short description|Something roughly the same as something else}} {{for|the sound change|Lenition}} {{Redirect-distinguish|Approximate|Approximant}} {{Refimprove|date=April 2013}} An '''approximation''' is anything that is intentionally similar but not exactly [[equality (mathematics)|equal]] to something else. ==Etymology and usage== The word ''approximation'' is derived from [[Latin]] ''approximatus'', from ''proximus'' meaning ''very near'' and the [[prefix]] ''ad-'' (''ad-'' before ''p'' becomes ap- by [[assimilation (phonology)|assimilation]]) meaning ''to''.<ref>The Concise Oxford Dictionary, ''Eighth edition 1990, {{ISBN|0-19-861243-5}}''</ref> Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning.<ref>Longman Dictionary of Contemporary English, ''Pearson Education Ltd 2009, {{ISBN|978 1 4082 1532 6}}''</ref> It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to [[number]]s, it is also frequently applied to such things as [[Function (mathematics)|mathematical functions]], [[shape]]s, and [[physical law]]s. In science, approximation can refer to using a simpler process or model when the correct model is difficult to use. An approximate model is used to make calculations easier. Approximations might also be used if incomplete [[information]] prevents use of exact representations. The type of approximation used depends on the available [[information]], [[Order of approximation|the degree of accuracy required]], the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation. == Mathematics == [[Approximation theory]] is a branch of mathematics, and a quantitative part of [[functional analysis]]. [[Diophantine approximation]] deals with approximations of [[real number]]s by [[rational number]]s. Approximation usually occurs when an exact form or an exact numerical number is unknown or difficult to obtain. However some known form may exist and may be able to represent the real form so that no significant deviation can be found. For example, 1.5 × 10<sup>6</sup> means that the true value of something being measured is 1,500,000 to the nearest hundred thousand (so the actual value is somewhere between 1,450,000 and 1,550,000); this is in contrast to the notation 1.500 × 10<sup>6</sup>, which means that the true value is 1,500,000 to the nearest thousand (implying that the true value is somewhere between 1,499,500 and 1,500,500). [[Numerical approximation]]s sometimes result from using a small number of [[Significant figures|significant digits]]. Calculations are likely to involve [[Round-off error|rounding errors]] and other [[approximation error]]s. [[Logarithm|Log tables]], slide rules and calculators produce approximate answers to all but the simplest calculations. The results of computer calculations are normally an approximation expressed in a limited number of significant digits, although they can be programmed to produce more precise results.<ref>{{Cite web |url=http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html |title=Numerical Computation Guide |access-date=2013-06-16 |archive-url=https://web.archive.org/web/20160406101256/http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html |archive-date=2016-04-06 |url-status=dead }}</ref> Approximation can occur when a decimal number cannot be expressed in a finite number of binary digits. Related to approximation of functions is the [[Asymptotic analysis|asymptotic]] value of a function, i.e. the value as one or more of a function's parameters becomes arbitrarily large. For example, the sum {{tmath|k/2+k/4+k/8+ \cdots +k/2^n}} is asymptotically equal to ''k''. No consistent notation is used throughout mathematics and some texts use ≈ to mean approximately equal and ~ to mean asymptotically equal whereas other texts use the symbols the other way around. ===Typography <span class="anchor" id="approximately equals sign"></span><span class="anchor" id="approximately equal to"></span><span class="anchor" id="almost equal to"></span>=== {{Infobox symbol |name=Approximately equal to<br/>Almost equal to |mark= ≅&nbsp;≈   |unicode = {{unichar|2245|Approximately equal to|html=}}<br />{{unichar|2248|Almost equal to |html=}} |see also = {{unichar|2249|Not almost equal to|nlink=Approximation#Unicode}}<br />{{unichar|3D|nlink=Equals sign}}<br />{{unichar|2243|Asymptotically equal to}} |different from={{unichar|2242|Minus tilde}} }} {{See also|Glossary of mathematical symbols#Equality, equivalence and similarity}} The '''approximately equals sign''', '''≈''', was introduced by British mathematician [[Alfred Greenhill]].{{Citation needed | reason=The citation that was provided did not mention Alfred Greenhill | date=October 2024}} ====LaTeX symbols==== Symbols used in [[LaTeX]] markup. * <math> \approx </math> (<code>\approx</code>), usually to indicate approximation between numbers, like <math> \pi \approx 3.14</math>. * <math> \not\approx </math> (<code>\not\approx</code>), usually to indicate that numbers are not approximately equal (<math>1 \not\approx 2</math>). * <math> \simeq </math> (<code>\simeq</code>), usually to indicate asymptotic equivalence between functions, like <math> f(n) \simeq 3n^2 </math>. ** So writing <math> \pi \simeq 3.14 </math> would be wrong under this definition, despite wide use. * <math> \sim </math> (<code>\sim</code>), usually to indicate proportionality between functions, the same <math> f(n) </math> of the line above will be <math> f(n) \sim n^2 </math>. * <math> \cong </math> (<code>\cong</code>), usually to indicate congruence between figures, like <math> \Delta ABC \cong \Delta A'B'C' </math>. * <math> \eqsim </math> (<code>\eqsim</code>), usually to indicate that two quantities are equal up to constants. * <math>\lessapprox</math> (<code>\lessapprox</code>) and <math>\gtrapprox</math> (<code>\gtrapprox</code>), usually to indicate that either the inequality holds or the two values are approximately equal. ====Unicode==== {{See also|Unicode mathematical operators}} Symbols used to denote items that are approximately equal are wavy or dotted equals signs.<ref>{{cite web| title =Mathematical Operators – Unicode| url =https://www.unicode.org/charts/PDF/U2200.pdf| access-date =2013-04-20}}</ref> {{aligned table |cols=2|class=wikitable | {{Unichar|223C|TILDE OPERATOR}} | Which is also sometimes used to indicate [[proportionality (mathematics)|proportionality.]] | {{Unichar|223D|REVERSED TILDE}} | Which is also sometimes used to indicate proportionality. | {{Unichar|2243|ASYMPTOTICALLY EQUAL TO}} | A combination of "≈" and "{{=}}", which is used to indicate [[Asymptotic analysis|asymptotic equality]]. | {{Unichar|2245|APPROXIMATELY EQUAL TO}} | Another combination of "≈" and "{{=}}", which is used to indicate [[isomorphism]] or [[congruence relation|congruence]]. | {{unichar|2246|approximately but not actually equal to}} | | {{unichar|2247|neither approximately nor actually equal to}} | | {{Unichar|2248|ALMOST EQUAL TO}} | | {{Unichar|2249|NOT ALMOST EQUAL TO}} | | {{Unichar|224A|ALMOST EQUAL OR EQUAL TO}} | Another combination of "≈" and "{{=}}", used to indicate equivalence or approximate equivalence. | {{Unichar|2250|APPROACHES THE LIMIT}} | Which can be used to represent the approach of a variable, {{mvar|y}}, to a [[limit (mathematics)|limit]]; like the common syntax, <math>\lim_{x \to \infty} y(x) \doteq 0</math>.<ref>{{cite book |title=D & D Standard Oil & Gas Abbreviator |year=2006 |publisher=PennWell |url=https://books.google.com/books?id=7FPtZp8abSAC&dq=%22%E2%89%90%22+approach+limit&pg=PA366 |access-date=May 21, 2020 |quote=≐ approaches a limit |page=366|isbn=9781593701086 }}</ref> | {{Unichar|2252|APPROXIMATELY EQUAL TO OR THE IMAGE OF}} | Which is used like "<big>≈</big>" or "<big>≃</big>" in [[Japanese language|Japan]], [[Taiwanese Mandarin|Taiwan]], and [[Korean language|Korea]]. | {{Unichar|2253|IMAGE OF OR APPROXIMATELY EQUAL TO}} | A reversed variation of {{Unichar|2252}}. | {{Unichar|225F|QUESTIONED EQUAL TO|nlink=≟}} | | {{unichar|2A85|LESS-THAN OR APPROXIMATE}} | | {{unichar|2A86|GREATER-THAN OR APPROXIMATE}} | }} == Science == Approximation arises naturally in [[scientific experiment]]s. The predictions of a scientific theory can differ from actual measurements. This can be because there are factors in the real situation that are not included in the theory. For example, simple calculations may not include the effect of air resistance. Under these circumstances, the theory is an approximation to reality. Differences may also arise because of limitations in the measuring technique. In this case, the measurement is an approximation to the actual value. The [[history of science]] shows that earlier theories and laws can be ''approximations'' to some deeper set of laws. Under the [[correspondence principle]], a new scientific theory should reproduce the results of older, well-established, theories in those domains where the old theories work.<ref>[https://www.britannica.com/EBchecked/topic/138678/correspondence-principle Correspondence principle] – ''[[Encyclopædia Britannica]]''</ref> The old theory becomes an approximation to the new theory. Some problems in physics are too complex to solve by direct analysis, or progress could be limited by available analytical tools. Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly. [[Physicists]] often approximate the [[shape of the Earth]] as a [[sphere]] even though more accurate representations are possible, because many physical characteristics (e.g., [[gravity]]) are much easier to calculate for a sphere than for other shapes. Approximation is also used to analyze the motion of several planets orbiting a star. This is extremely difficult due to the complex interactions of the planets' gravitational effects on each other.<ref>[http://plus.maths.org/content/mathematical-mysteries-three-body-problem The three body problem]</ref> An approximate solution is effected by performing [[iteration]]s. In the first iteration, the planets' gravitational interactions are ignored, and the star is assumed to be fixed. If a more precise solution is desired, another iteration is then performed, using the positions and motions of the planets as identified in the first iteration, but adding a first-order gravity interaction from each planet on the others. This process may be repeated until a satisfactorily precise solution is obtained. The use of [[Perturbation theory|perturbations]] to correct for the errors can yield more accurate solutions. Simulations of the motions of the planets and the star also yields more accurate solutions. The most common versions of [[philosophy of science]] accept that empirical [[measurement]]s are always ''approximations'' — they do not perfectly represent what is being measured. ==Law== Within the [[European Union]] (EU), "approximation" refers to a process through which EU legislation is implemented and incorporated within [[Member state of the European Union|Member States]]' national laws, despite variations in the existing legal framework in each country. Approximation is required as part of the [[EU accession|pre-accession process]] for new member states,<ref name=env>European Commission, [https://ec.europa.eu/environment/archives/guide/part1.htm Guide to the Approximation of European Union Environmental Legislation], last updated 2 August 2019, accessed 15 November 2022</ref> and as a continuing process when required by an [[Directive (European Union)|EU Directive]]. ''Approximation'' is a key word generally employed within the title of a directive, for example the Trade Marks Directive of 16 December 2015 serves "to approximate the laws of the Member States relating to trade marks".<ref>EUR-Lex, [https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A32015L2436&qid=1668514262360 Directive (EU) 2015/2436 of the European Parliament and of the Council of 16 December 2015 to approximate the laws of the Member States relating to trade marks (recast) (Text with EEA relevance)], published 23 December 2015, accessed 15 November 2022</ref> The [[European Commission]] describes approximation of law as "a unique obligation of membership in the European Union".<ref name=env /> == See also == {{div col}} * {{Annotated link |Approximation algorithm}} * {{Annotated link |Approximate computing}} * {{Annotated link |Approximations of π}} * {{Annotated link |Binomial approximation}} * {{Annotated link |Congruence relation}} * [[Double tilde (disambiguation)]]{{snd}}Various meanings of ~~ or ≈ * {{Annotated link |Estimation}} * {{Annotated link |Fermi problem}} * {{Annotated link |Idealization (philosophy of science)}} * {{Annotated link |Least squares}} * {{Annotated link |Linear approximation}} * {{Annotated link |Newton's method}} * {{Annotated link |Order of approximation}} * {{Annotated link |Rough set}} * {{Annotated link |Runge–Kutta methods}} * {{Annotated link |Significant figures}} * {{Annotated link |Small-angle approximation}} * {{Annotated link |Successive-approximation ADC}} * {{Annotated link |Taylor series}} * {{Annotated link |Tolerance relation}} * {{Annotated link |Intuition}} {{div col end}} == References == {{Reflist}} == External links == {{Wiktionary|approximation}} * {{Commons category-inline}} {{Authority control}} [[Category:Approximations| ]] [[Category:Numerical analysis]] [[Category:Equivalence (mathematics)]] [[Category:Comparison (mathematical)]]  </textarea><div class="templatesUsed"><div class="mw-templatesUsedExplanation"><p><span id="templatesused">Pages transcluded onto the current version of this page<span class="posteditwindowhelplinks"> (<a href="/wiki/Help:Transclusion" title="Help:Transclusion">help</a>)</span>:</span> </p></div><ul> <li><a href="/wiki/Approximate_computing" title="Approximate computing">Approximate computing</a> (<a href="/w/index.php?title=Approximate_computing&action=edit" title="Approximate computing">edit</a>) </li><li><a href="/wiki/Approximation_algorithm" title="Approximation algorithm">Approximation algorithm</a> (<a href="/w/index.php?title=Approximation_algorithm&action=edit" title="Approximation algorithm">edit</a>) </li><li><a href="/wiki/Approximations_of_%CF%80" title="Approximations of π">Approximations of π</a> (<a href="/w/index.php?title=Approximations_of_%CF%80&action=edit" title="Approximations of π">edit</a>) </li><li><a href="/wiki/Binomial_approximation" title="Binomial approximation">Binomial approximation</a> (<a href="/w/index.php?title=Binomial_approximation&action=edit" title="Binomial approximation">edit</a>) </li><li><a href="/wiki/Congruence_relation" title="Congruence relation">Congruence relation</a> (<a href="/w/index.php?title=Congruence_relation&action=edit" title="Congruence relation">edit</a>) </li><li><a href="/wiki/Estimation" title="Estimation">Estimation</a> (<a href="/w/index.php?title=Estimation&action=edit" title="Estimation">edit</a>) </li><li><a href="/wiki/Fermi_problem" title="Fermi problem">Fermi problem</a> (<a href="/w/index.php?title=Fermi_problem&action=edit" title="Fermi problem">edit</a>) </li><li><a href="/wiki/Idealization_(philosophy_of_science)" title="Idealization (philosophy of science)">Idealization (philosophy of science)</a> (<a href="/w/index.php?title=Idealization_(philosophy_of_science)&action=edit" title="Idealization (philosophy of science)">edit</a>) </li><li><a href="/wiki/Intuition" title="Intuition">Intuition</a> (<a href="/w/index.php?title=Intuition&action=edit" title="Intuition">edit</a>) </li><li><a href="/wiki/Least_squares" title="Least squares">Least squares</a> (<a href="/w/index.php?title=Least_squares&action=edit" title="Least squares">edit</a>) </li><li><a href="/wiki/Linear_approximation" title="Linear approximation">Linear approximation</a> (<a href="/w/index.php?title=Linear_approximation&action=edit" title="Linear approximation">edit</a>) </li><li><a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a> (<a href="/w/index.php?title=Newton%27s_method&action=edit" title="Newton's method">edit</a>) </li><li><a href="/wiki/Order_of_approximation" title="Order of approximation">Order of approximation</a> (<a href="/w/index.php?title=Order_of_approximation&action=edit" title="Order of approximation">edit</a>) </li><li><a href="/wiki/Rough_set" title="Rough set">Rough set</a> (<a href="/w/index.php?title=Rough_set&action=edit" title="Rough set">edit</a>) </li><li><a href="/wiki/Runge%E2%80%93Kutta_methods" title="Runge–Kutta methods">Runge–Kutta methods</a> (<a href="/w/index.php?title=Runge%E2%80%93Kutta_methods&action=edit" title="Runge–Kutta methods">edit</a>) </li><li><a href="/wiki/Significant_figures" title="Significant figures">Significant figures</a> (<a href="/w/index.php?title=Significant_figures&action=edit" title="Significant figures">edit</a>) </li><li><a href="/wiki/Small-angle_approximation" title="Small-angle approximation">Small-angle approximation</a> (<a href="/w/index.php?title=Small-angle_approximation&action=edit" title="Small-angle approximation">edit</a>) </li><li><a href="/wiki/Successive-approximation_ADC" title="Successive-approximation ADC">Successive-approximation ADC</a> (<a href="/w/index.php?title=Successive-approximation_ADC&action=edit" title="Successive-approximation ADC">edit</a>) </li><li><a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a> (<a href="/w/index.php?title=Taylor_series&action=edit" title="Taylor series">edit</a>) </li><li><a href="/wiki/Tolerance_relation" title="Tolerance relation">Tolerance relation</a> (<a href="/w/index.php?title=Tolerance_relation&action=edit" title="Tolerance relation">edit</a>) </li><li><a href="/wiki/Template:Aligned_table" title="Template:Aligned table">Template:Aligned table</a> (<a href="/w/index.php?title=Template:Aligned_table&action=edit" title="Template:Aligned table">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Ambox" title="Template:Ambox">Template:Ambox</a> (<a href="/w/index.php?title=Template:Ambox&action=edit" title="Template:Ambox">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Annotated_link" title="Template:Annotated link">Template:Annotated link</a> (<a href="/w/index.php?title=Template:Annotated_link&action=edit" title="Template:Annotated link">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Authority_control" title="Template:Authority control">Template:Authority control</a> (<a href="/w/index.php?title=Template:Authority_control&action=edit" title="Template:Authority control">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Catalog_lookup_link" title="Template:Catalog lookup link">Template:Catalog lookup link</a> (<a href="/w/index.php?title=Template:Catalog_lookup_link&action=edit" title="Template:Catalog lookup link">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Category_handler" title="Template:Category handler">Template:Category handler</a> (<a href="/w/index.php?title=Template:Category_handler&action=edit" title="Template:Category handler">view source</a>) (protected)</li><li><a href="/wiki/Template:Citation_needed" title="Template:Citation needed">Template:Citation needed</a> (<a href="/w/index.php?title=Template:Citation_needed&action=edit" title="Template:Citation needed">view source</a>) (protected)</li><li><a href="/wiki/Template:Cite_book" title="Template:Cite book">Template:Cite book</a> (<a href="/w/index.php?title=Template:Cite_book&action=edit" title="Template:Cite book">view source</a>) (protected)</li><li><a href="/wiki/Template:Cite_web" title="Template:Cite web">Template:Cite web</a> (<a href="/w/index.php?title=Template:Cite_web&action=edit" title="Template:Cite web">view source</a>) (protected)</li><li><a href="/wiki/Template:Commons_category-inline" title="Template:Commons category-inline">Template:Commons category-inline</a> (<a href="/w/index.php?title=Template:Commons_category-inline&action=edit" title="Template:Commons category-inline">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Delink" title="Template:Delink">Template:Delink</a> (<a href="/w/index.php?title=Template:Delink&action=edit" title="Template:Delink">view source</a>) (protected)</li><li><a href="/wiki/Template:Div_col" title="Template:Div col">Template:Div col</a> (<a href="/w/index.php?title=Template:Div_col&action=edit" title="Template:Div col">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Div_col/styles.css" title="Template:Div col/styles.css">Template:Div col/styles.css</a> (<a href="/w/index.php?title=Template:Div_col/styles.css&action=edit" title="Template:Div col/styles.css">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Div_col_end" title="Template:Div col end">Template:Div col end</a> (<a href="/w/index.php?title=Template:Div_col_end&action=edit" title="Template:Div col end">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Find_sources_mainspace" title="Template:Find sources mainspace">Template:Find sources mainspace</a> (<a href="/w/index.php?title=Template:Find_sources_mainspace&action=edit" title="Template:Find sources mainspace">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Fix" title="Template:Fix">Template:Fix</a> (<a href="/w/index.php?title=Template:Fix&action=edit" title="Template:Fix">view source</a>) (protected)</li><li><a href="/wiki/Template:Fix/category" title="Template:Fix/category">Template:Fix/category</a> (<a href="/w/index.php?title=Template:Fix/category&action=edit" title="Template:Fix/category">view source</a>) (protected)</li><li><a href="/wiki/Template:For" title="Template:For">Template:For</a> (<a href="/w/index.php?title=Template:For&action=edit" title="Template:For">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Hex2dec" title="Template:Hex2dec">Template:Hex2dec</a> (<a href="/w/index.php?title=Template:Hex2dec&action=edit" title="Template:Hex2dec">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Hlist/styles.css" title="Template:Hlist/styles.css">Template:Hlist/styles.css</a> (<a href="/w/index.php?title=Template:Hlist/styles.css&action=edit" title="Template:Hlist/styles.css">view source</a>) (protected)</li><li><a href="/wiki/Template:ISBN" title="Template:ISBN">Template:ISBN</a> (<a href="/w/index.php?title=Template:ISBN&action=edit" title="Template:ISBN">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:If_empty" title="Template:If empty">Template:If empty</a> (<a href="/w/index.php?title=Template:If_empty&action=edit" title="Template:If empty">view source</a>) (protected)</li><li><a href="/wiki/Template:Ifsubst" title="Template:Ifsubst">Template:Ifsubst</a> (<a href="/w/index.php?title=Template:Ifsubst&action=edit" title="Template:Ifsubst">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Infobox" title="Template:Infobox">Template:Infobox</a> (<a href="/w/index.php?title=Template:Infobox&action=edit" title="Template:Infobox">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Infobox_symbol" title="Template:Infobox symbol">Template:Infobox symbol</a> (<a href="/w/index.php?title=Template:Infobox_symbol&action=edit" title="Template:Infobox symbol">edit</a>) </li><li><a href="/wiki/Template:Main_other" title="Template:Main other">Template:Main other</a> (<a href="/w/index.php?title=Template:Main_other&action=edit" title="Template:Main other">view source</a>) (protected)</li><li><a href="/wiki/Template:Mono" title="Template:Mono">Template:Mono</a> (<a href="/w/index.php?title=Template:Mono&action=edit" title="Template:Mono">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Mono/styles.css" title="Template:Mono/styles.css">Template:Mono/styles.css</a> (<a href="/w/index.php?title=Template:Mono/styles.css&action=edit" title="Template:Mono/styles.css">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:More_citations_needed" title="Template:More citations needed">Template:More citations needed</a> (<a href="/w/index.php?title=Template:More_citations_needed&action=edit" title="Template:More citations needed">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Mvar" title="Template:Mvar">Template:Mvar</a> (<a href="/w/index.php?title=Template:Mvar&action=edit" title="Template:Mvar">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Nowrap" title="Template:Nowrap">Template:Nowrap</a> (<a href="/w/index.php?title=Template:Nowrap&action=edit" title="Template:Nowrap">view source</a>) (protected)</li><li><a href="/wiki/Template:Pagetype" title="Template:Pagetype">Template:Pagetype</a> (<a href="/w/index.php?title=Template:Pagetype&action=edit" title="Template:Pagetype">view source</a>) (protected)</li><li><a href="/wiki/Template:Plainlist/styles.css" title="Template:Plainlist/styles.css">Template:Plainlist/styles.css</a> (<a href="/w/index.php?title=Template:Plainlist/styles.css&action=edit" title="Template:Plainlist/styles.css">view source</a>) (protected)</li><li><a href="/wiki/Template:Redirect-distinguish" title="Template:Redirect-distinguish">Template:Redirect-distinguish</a> (<a href="/w/index.php?title=Template:Redirect-distinguish&action=edit" title="Template:Redirect-distinguish">view source</a>) (extended confirmed protected)</li><li><a href="/wiki/Template:Refimprove" class="mw-redirect" title="Template:Refimprove">Template:Refimprove</a> (<a href="/w/index.php?title=Template:Refimprove&action=edit" class="mw-redirect" title="Template:Refimprove">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Reflist" title="Template:Reflist">Template:Reflist</a> (<a href="/w/index.php?title=Template:Reflist&action=edit" title="Template:Reflist">view source</a>) (protected)</li><li><a href="/wiki/Template:Reflist/styles.css" title="Template:Reflist/styles.css">Template:Reflist/styles.css</a> (<a href="/w/index.php?title=Template:Reflist/styles.css&action=edit" title="Template:Reflist/styles.css">view source</a>) (protected)</li><li><a href="/wiki/Template:SDcat" title="Template:SDcat">Template:SDcat</a> (<a href="/w/index.php?title=Template:SDcat&action=edit" title="Template:SDcat">view source</a>) (protected)</li><li><a href="/wiki/Template:See_also" title="Template:See also">Template:See also</a> (<a href="/w/index.php?title=Template:See_also&action=edit" title="Template:See also">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Short_description" title="Template:Short description">Template:Short description</a> (<a href="/w/index.php?title=Template:Short_description&action=edit" title="Template:Short description">view source</a>) (protected)</li><li><a href="/wiki/Template:Short_description/lowercasecheck" title="Template:Short description/lowercasecheck">Template:Short description/lowercasecheck</a> (<a href="/w/index.php?title=Template:Short_description/lowercasecheck&action=edit" title="Template:Short description/lowercasecheck">view source</a>) (protected)</li><li><a href="/wiki/Template:Side_box" title="Template:Side box">Template:Side box</a> (<a href="/w/index.php?title=Template:Side_box&action=edit" title="Template:Side box">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Sister-inline" title="Template:Sister-inline">Template:Sister-inline</a> (<a href="/w/index.php?title=Template:Sister-inline&action=edit" title="Template:Sister-inline">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Sister_project" title="Template:Sister project">Template:Sister project</a> (<a href="/w/index.php?title=Template:Sister_project&action=edit" title="Template:Sister project">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Sister_project/styles.css" title="Template:Sister project/styles.css">Template:Sister project/styles.css</a> (<a href="/w/index.php?title=Template:Sister_project/styles.css&action=edit" title="Template:Sister project/styles.css">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Snd" class="mw-redirect" title="Template:Snd">Template:Snd</a> (<a href="/w/index.php?title=Template:Snd&action=edit" class="mw-redirect" title="Template:Snd">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Spaced_en_dash" title="Template:Spaced en dash">Template:Spaced en dash</a> (<a href="/w/index.php?title=Template:Spaced_en_dash&action=edit" title="Template:Spaced en dash">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Template_other" title="Template:Template other">Template:Template other</a> (<a href="/w/index.php?title=Template:Template_other&action=edit" title="Template:Template other">view source</a>) (protected)</li><li><a href="/wiki/Template:Tmath" title="Template:Tmath">Template:Tmath</a> (<a href="/w/index.php?title=Template:Tmath&action=edit" title="Template:Tmath">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Trim" title="Template:Trim">Template:Trim</a> (<a href="/w/index.php?title=Template:Trim&action=edit" title="Template:Trim">view source</a>) (protected)</li><li><a href="/wiki/Template:Unichar" title="Template:Unichar">Template:Unichar</a> (<a href="/w/index.php?title=Template:Unichar&action=edit" title="Template:Unichar">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Unichar/gc" title="Template:Unichar/gc">Template:Unichar/gc</a> (<a href="/w/index.php?title=Template:Unichar/gc&action=edit" title="Template:Unichar/gc">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Unichar/glyph" title="Template:Unichar/glyph">Template:Unichar/glyph</a> (<a href="/w/index.php?title=Template:Unichar/glyph&action=edit" title="Template:Unichar/glyph">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Unichar/hexformat" title="Template:Unichar/hexformat">Template:Unichar/hexformat</a> (<a href="/w/index.php?title=Template:Unichar/hexformat&action=edit" title="Template:Unichar/hexformat">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Unichar/main" title="Template:Unichar/main">Template:Unichar/main</a> (<a href="/w/index.php?title=Template:Unichar/main&action=edit" title="Template:Unichar/main">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Unichar/name" title="Template:Unichar/name">Template:Unichar/name</a> (<a href="/w/index.php?title=Template:Unichar/name&action=edit" title="Template:Unichar/name">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Unichar/notes" title="Template:Unichar/notes">Template:Unichar/notes</a> (<a href="/w/index.php?title=Template:Unichar/notes&action=edit" title="Template:Unichar/notes">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Unichar/ulink" title="Template:Unichar/ulink">Template:Unichar/ulink</a> (<a href="/w/index.php?title=Template:Unichar/ulink&action=edit" title="Template:Unichar/ulink">view source</a>) (semi-protected)</li><li><a href="/wiki/Template:Wiktionary" title="Template:Wiktionary">Template:Wiktionary</a> (<a href="/w/index.php?title=Template:Wiktionary&action=edit" title="Template:Wiktionary">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Yesno" title="Template:Yesno">Template:Yesno</a> (<a href="/w/index.php?title=Template:Yesno&action=edit" title="Template:Yesno">view source</a>) (protected)</li><li><a href="/wiki/Template:Yesno-no" title="Template:Yesno-no">Template:Yesno-no</a> (<a href="/w/index.php?title=Template:Yesno-no&action=edit" title="Template:Yesno-no">view source</a>) (template editor protected)</li><li><a href="/wiki/Template:Yesno-yes" title="Template:Yesno-yes">Template:Yesno-yes</a> (<a href="/w/index.php?title=Template:Yesno-yes&action=edit" title="Template:Yesno-yes">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Aligned_table" title="Module:Aligned table">Module:Aligned table</a> (<a href="/w/index.php?title=Module:Aligned_table&action=edit" title="Module:Aligned table">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Annotated_link" title="Module:Annotated link">Module:Annotated link</a> (<a href="/w/index.php?title=Module:Annotated_link&action=edit" title="Module:Annotated link">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Arguments" title="Module:Arguments">Module:Arguments</a> (<a href="/w/index.php?title=Module:Arguments&action=edit" title="Module:Arguments">view source</a>) (protected)</li><li><a href="/wiki/Module:Authority_control" title="Module:Authority control">Module:Authority control</a> (<a href="/w/index.php?title=Module:Authority_control&action=edit" title="Module:Authority control">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Authority_control/config" title="Module:Authority control/config">Module:Authority control/config</a> (<a href="/w/index.php?title=Module:Authority_control/config&action=edit" title="Module:Authority control/config">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:BaseConvert" title="Module:BaseConvert">Module:BaseConvert</a> (<a href="/w/index.php?title=Module:BaseConvert&action=edit" title="Module:BaseConvert">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Catalog_lookup_link" title="Module:Catalog lookup link">Module:Catalog lookup link</a> (<a href="/w/index.php?title=Module:Catalog_lookup_link&action=edit" title="Module:Catalog lookup link">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Category_handler" title="Module:Category handler">Module:Category handler</a> (<a href="/w/index.php?title=Module:Category_handler&action=edit" title="Module:Category handler">view source</a>) (protected)</li><li><a href="/wiki/Module:Category_handler/blacklist" title="Module:Category handler/blacklist">Module:Category handler/blacklist</a> (<a href="/w/index.php?title=Module:Category_handler/blacklist&action=edit" title="Module:Category handler/blacklist">view source</a>) (protected)</li><li><a href="/wiki/Module:Category_handler/config" title="Module:Category handler/config">Module:Category handler/config</a> (<a href="/w/index.php?title=Module:Category_handler/config&action=edit" title="Module:Category handler/config">view source</a>) (protected)</li><li><a href="/wiki/Module:Category_handler/data" title="Module:Category handler/data">Module:Category handler/data</a> (<a href="/w/index.php?title=Module:Category_handler/data&action=edit" title="Module:Category handler/data">view source</a>) (protected)</li><li><a href="/wiki/Module:Category_handler/shared" title="Module:Category handler/shared">Module:Category handler/shared</a> (<a href="/w/index.php?title=Module:Category_handler/shared&action=edit" title="Module:Category handler/shared">view source</a>) (protected)</li><li><a href="/wiki/Module:Check_for_unknown_parameters" title="Module:Check for unknown parameters">Module:Check for unknown parameters</a> (<a href="/w/index.php?title=Module:Check_for_unknown_parameters&action=edit" title="Module:Check for unknown parameters">view source</a>) (protected)</li><li><a href="/wiki/Module:Check_isxn" title="Module:Check isxn">Module:Check isxn</a> (<a href="/w/index.php?title=Module:Check_isxn&action=edit" title="Module:Check isxn">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Citation/CS1" title="Module:Citation/CS1">Module:Citation/CS1</a> (<a href="/w/index.php?title=Module:Citation/CS1&action=edit" title="Module:Citation/CS1">view source</a>) (protected)</li><li><a href="/wiki/Module:Citation/CS1/COinS" title="Module:Citation/CS1/COinS">Module:Citation/CS1/COinS</a> (<a href="/w/index.php?title=Module:Citation/CS1/COinS&action=edit" title="Module:Citation/CS1/COinS">view source</a>) (protected)</li><li><a href="/wiki/Module:Citation/CS1/Configuration" title="Module:Citation/CS1/Configuration">Module:Citation/CS1/Configuration</a> (<a href="/w/index.php?title=Module:Citation/CS1/Configuration&action=edit" title="Module:Citation/CS1/Configuration">view source</a>) (protected)</li><li><a href="/wiki/Module:Citation/CS1/Date_validation" title="Module:Citation/CS1/Date validation">Module:Citation/CS1/Date validation</a> (<a href="/w/index.php?title=Module:Citation/CS1/Date_validation&action=edit" title="Module:Citation/CS1/Date validation">view source</a>) (protected)</li><li><a href="/wiki/Module:Citation/CS1/Identifiers" title="Module:Citation/CS1/Identifiers">Module:Citation/CS1/Identifiers</a> (<a href="/w/index.php?title=Module:Citation/CS1/Identifiers&action=edit" title="Module:Citation/CS1/Identifiers">view source</a>) (protected)</li><li><a href="/wiki/Module:Citation/CS1/Utilities" title="Module:Citation/CS1/Utilities">Module:Citation/CS1/Utilities</a> (<a href="/w/index.php?title=Module:Citation/CS1/Utilities&action=edit" title="Module:Citation/CS1/Utilities">view source</a>) (protected)</li><li><a href="/wiki/Module:Citation/CS1/Whitelist" title="Module:Citation/CS1/Whitelist">Module:Citation/CS1/Whitelist</a> (<a href="/w/index.php?title=Module:Citation/CS1/Whitelist&action=edit" title="Module:Citation/CS1/Whitelist">view source</a>) (protected)</li><li><a href="/wiki/Module:Citation/CS1/styles.css" title="Module:Citation/CS1/styles.css">Module:Citation/CS1/styles.css</a> (<a href="/w/index.php?title=Module:Citation/CS1/styles.css&action=edit" title="Module:Citation/CS1/styles.css">view source</a>) (protected)</li><li><a href="/wiki/Module:Commons_link" title="Module:Commons link">Module:Commons link</a> (<a href="/w/index.php?title=Module:Commons_link&action=edit" title="Module:Commons link">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Delink" title="Module:Delink">Module:Delink</a> (<a href="/w/index.php?title=Module:Delink&action=edit" title="Module:Delink">view source</a>) (protected)</li><li><a href="/wiki/Module:Disambiguation/templates" title="Module:Disambiguation/templates">Module:Disambiguation/templates</a> (<a href="/w/index.php?title=Module:Disambiguation/templates&action=edit" title="Module:Disambiguation/templates">view source</a>) (protected)</li><li><a href="/wiki/Module:EditAtWikidata" title="Module:EditAtWikidata">Module:EditAtWikidata</a> (<a href="/w/index.php?title=Module:EditAtWikidata&action=edit" title="Module:EditAtWikidata">view source</a>) (protected)</li><li><a href="/wiki/Module:Find_sources" title="Module:Find sources">Module:Find sources</a> (<a href="/w/index.php?title=Module:Find_sources&action=edit" title="Module:Find sources">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Find_sources/config" title="Module:Find sources/config">Module:Find sources/config</a> (<a href="/w/index.php?title=Module:Find_sources/config&action=edit" title="Module:Find sources/config">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Find_sources/links" title="Module:Find sources/links">Module:Find sources/links</a> (<a href="/w/index.php?title=Module:Find_sources/links&action=edit" title="Module:Find sources/links">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Find_sources/templates/Find_sources_mainspace" title="Module:Find sources/templates/Find sources mainspace">Module:Find sources/templates/Find sources mainspace</a> (<a href="/w/index.php?title=Module:Find_sources/templates/Find_sources_mainspace&action=edit" title="Module:Find sources/templates/Find sources mainspace">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:For" title="Module:For">Module:For</a> (<a href="/w/index.php?title=Module:For&action=edit" title="Module:For">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Format_link" title="Module:Format link">Module:Format link</a> (<a href="/w/index.php?title=Module:Format_link&action=edit" title="Module:Format link">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:GetShortDescription" title="Module:GetShortDescription">Module:GetShortDescription</a> (<a href="/w/index.php?title=Module:GetShortDescription&action=edit" title="Module:GetShortDescription">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Hatnote" title="Module:Hatnote">Module:Hatnote</a> (<a href="/w/index.php?title=Module:Hatnote&action=edit" title="Module:Hatnote">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Hatnote/styles.css" title="Module:Hatnote/styles.css">Module:Hatnote/styles.css</a> (<a href="/w/index.php?title=Module:Hatnote/styles.css&action=edit" title="Module:Hatnote/styles.css">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Hatnote_list" title="Module:Hatnote list">Module:Hatnote list</a> (<a href="/w/index.php?title=Module:Hatnote_list&action=edit" title="Module:Hatnote list">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:If_empty" title="Module:If empty">Module:If empty</a> (<a href="/w/index.php?title=Module:If_empty&action=edit" title="Module:If empty">view source</a>) (protected)</li><li><a href="/wiki/Module:Infobox" title="Module:Infobox">Module:Infobox</a> (<a href="/w/index.php?title=Module:Infobox&action=edit" title="Module:Infobox">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Infobox/styles.css" title="Module:Infobox/styles.css">Module:Infobox/styles.css</a> (<a href="/w/index.php?title=Module:Infobox/styles.css&action=edit" title="Module:Infobox/styles.css">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:InfoboxImage" title="Module:InfoboxImage">Module:InfoboxImage</a> (<a href="/w/index.php?title=Module:InfoboxImage&action=edit" title="Module:InfoboxImage">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Labelled_list_hatnote" title="Module:Labelled list hatnote">Module:Labelled list hatnote</a> (<a href="/w/index.php?title=Module:Labelled_list_hatnote&action=edit" title="Module:Labelled list hatnote">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Lang" title="Module:Lang">Module:Lang</a> (<a href="/w/index.php?title=Module:Lang&action=edit" title="Module:Lang">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Lang/ISO_639_synonyms" title="Module:Lang/ISO 639 synonyms">Module:Lang/ISO 639 synonyms</a> (<a href="/w/index.php?title=Module:Lang/ISO_639_synonyms&action=edit" title="Module:Lang/ISO 639 synonyms">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Lang/data" title="Module:Lang/data">Module:Lang/data</a> (<a href="/w/index.php?title=Module:Lang/data&action=edit" title="Module:Lang/data">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Lang/data/iana_languages" title="Module:Lang/data/iana languages">Module:Lang/data/iana languages</a> (<a href="/w/index.php?title=Module:Lang/data/iana_languages&action=edit" title="Module:Lang/data/iana languages">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Lang/data/iana_regions" title="Module:Lang/data/iana regions">Module:Lang/data/iana regions</a> (<a href="/w/index.php?title=Module:Lang/data/iana_regions&action=edit" title="Module:Lang/data/iana regions">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Lang/data/iana_scripts" title="Module:Lang/data/iana scripts">Module:Lang/data/iana scripts</a> (<a href="/w/index.php?title=Module:Lang/data/iana_scripts&action=edit" title="Module:Lang/data/iana scripts">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Lang/data/iana_suppressed_scripts" title="Module:Lang/data/iana suppressed scripts">Module:Lang/data/iana suppressed scripts</a> (<a href="/w/index.php?title=Module:Lang/data/iana_suppressed_scripts&action=edit" title="Module:Lang/data/iana suppressed scripts">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Lang/data/iana_variants" title="Module:Lang/data/iana variants">Module:Lang/data/iana variants</a> (<a href="/w/index.php?title=Module:Lang/data/iana_variants&action=edit" title="Module:Lang/data/iana variants">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:LoadData" title="Module:LoadData">Module:LoadData</a> (<a href="/w/index.php?title=Module:LoadData&action=edit" title="Module:LoadData">view source</a>) (semi-protected)</li><li><a href="/wiki/Module:Message_box" title="Module:Message box">Module:Message box</a> (<a href="/w/index.php?title=Module:Message_box&action=edit" title="Module:Message box">view source</a>) (protected)</li><li><a href="/wiki/Module:Message_box/ambox.css" title="Module:Message box/ambox.css">Module:Message box/ambox.css</a> (<a href="/w/index.php?title=Module:Message_box/ambox.css&action=edit" title="Module:Message box/ambox.css">view source</a>) (protected)</li><li><a href="/wiki/Module:Message_box/configuration" title="Module:Message box/configuration">Module:Message box/configuration</a> (<a href="/w/index.php?title=Module:Message_box/configuration&action=edit" title="Module:Message box/configuration">view source</a>) (protected)</li><li><a href="/wiki/Module:Namespace_detect/config" title="Module:Namespace detect/config">Module:Namespace detect/config</a> (<a href="/w/index.php?title=Module:Namespace_detect/config&action=edit" title="Module:Namespace detect/config">view source</a>) (protected)</li><li><a href="/wiki/Module:Namespace_detect/data" title="Module:Namespace detect/data">Module:Namespace detect/data</a> (<a href="/w/index.php?title=Module:Namespace_detect/data&action=edit" title="Module:Namespace detect/data">view source</a>) (protected)</li><li><a href="/wiki/Module:Navbox" title="Module:Navbox">Module:Navbox</a> (<a href="/w/index.php?title=Module:Navbox&action=edit" title="Module:Navbox">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Navbox/configuration" title="Module:Navbox/configuration">Module:Navbox/configuration</a> (<a href="/w/index.php?title=Module:Navbox/configuration&action=edit" title="Module:Navbox/configuration">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Navbox/styles.css" title="Module:Navbox/styles.css">Module:Navbox/styles.css</a> (<a href="/w/index.php?title=Module:Navbox/styles.css&action=edit" title="Module:Navbox/styles.css">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Numcr2namecr" title="Module:Numcr2namecr">Module:Numcr2namecr</a> (<a href="/w/index.php?title=Module:Numcr2namecr&action=edit" title="Module:Numcr2namecr">view source</a>) (semi-protected)</li><li><a href="/wiki/Module:Pagetype" title="Module:Pagetype">Module:Pagetype</a> (<a href="/w/index.php?title=Module:Pagetype&action=edit" title="Module:Pagetype">view source</a>) (protected)</li><li><a href="/wiki/Module:Pagetype/config" title="Module:Pagetype/config">Module:Pagetype/config</a> (<a href="/w/index.php?title=Module:Pagetype/config&action=edit" title="Module:Pagetype/config">view source</a>) (protected)</li><li><a href="/wiki/Module:Pagetype/disambiguation" class="mw-redirect" title="Module:Pagetype/disambiguation">Module:Pagetype/disambiguation</a> (<a href="/w/index.php?title=Module:Pagetype/disambiguation&action=edit" class="mw-redirect" title="Module:Pagetype/disambiguation">view source</a>) (protected)</li><li><a href="/wiki/Module:Pagetype/rfd" title="Module:Pagetype/rfd">Module:Pagetype/rfd</a> (<a href="/w/index.php?title=Module:Pagetype/rfd&action=edit" title="Module:Pagetype/rfd">view source</a>) (protected)</li><li><a href="/wiki/Module:Pagetype/setindex" title="Module:Pagetype/setindex">Module:Pagetype/setindex</a> (<a href="/w/index.php?title=Module:Pagetype/setindex&action=edit" title="Module:Pagetype/setindex">view source</a>) (protected)</li><li><a href="/wiki/Module:Pagetype/softredirect" title="Module:Pagetype/softredirect">Module:Pagetype/softredirect</a> (<a href="/w/index.php?title=Module:Pagetype/softredirect&action=edit" title="Module:Pagetype/softredirect">view source</a>) (protected)</li><li><a href="/wiki/Module:Redirect-distinguish" title="Module:Redirect-distinguish">Module:Redirect-distinguish</a> (<a href="/w/index.php?title=Module:Redirect-distinguish&action=edit" title="Module:Redirect-distinguish">view source</a>) (extended confirmed protected)</li><li><a href="/wiki/Module:SDcat" title="Module:SDcat">Module:SDcat</a> (<a href="/w/index.php?title=Module:SDcat&action=edit" title="Module:SDcat">view source</a>) (protected)</li><li><a href="/wiki/Module:Side_box" title="Module:Side box">Module:Side box</a> (<a href="/w/index.php?title=Module:Side_box&action=edit" title="Module:Side box">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Side_box/styles.css" title="Module:Side box/styles.css">Module:Side box/styles.css</a> (<a href="/w/index.php?title=Module:Side_box/styles.css&action=edit" title="Module:Side box/styles.css">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:String" title="Module:String">Module:String</a> (<a href="/w/index.php?title=Module:String&action=edit" title="Module:String">view source</a>) (protected)</li><li><a href="/wiki/Module:TableTools" title="Module:TableTools">Module:TableTools</a> (<a href="/w/index.php?title=Module:TableTools&action=edit" title="Module:TableTools">view source</a>) (protected)</li><li><a href="/wiki/Module:Unicode_data" title="Module:Unicode data">Module:Unicode data</a> (<a href="/w/index.php?title=Module:Unicode_data&action=edit" title="Module:Unicode data">view source</a>) (template editor protected)</li><li><a href="/wiki/Module:Unicode_data/names/000" title="Module:Unicode data/names/000">Module:Unicode data/names/000</a> (<a href="/w/index.php?title=Module:Unicode_data/names/000&action=edit" title="Module:Unicode data/names/000">view source</a>) (semi-protected)</li><li><a href="/wiki/Module:Unicode_data/names/002" title="Module:Unicode data/names/002">Module:Unicode data/names/002</a> (<a href="/w/index.php?title=Module:Unicode_data/names/002&action=edit" title="Module:Unicode data/names/002">view source</a>) (semi-protected)</li><li><a href="/wiki/Module:Unsubst" title="Module:Unsubst">Module:Unsubst</a> (<a href="/w/index.php?title=Module:Unsubst&action=edit" title="Module:Unsubst">view source</a>) (protected)</li><li><a href="/wiki/Module:Wikitext_Parsing" title="Module:Wikitext Parsing">Module:Wikitext Parsing</a> (<a href="/w/index.php?title=Module:Wikitext_Parsing&action=edit" title="Module:Wikitext Parsing">view source</a>) (protected)</li><li><a href="/wiki/Module:Yesno" title="Module:Yesno">Module:Yesno</a> (<a href="/w/index.php?title=Module:Yesno&action=edit" title="Module:Yesno">view source</a>) (protected)</li></ul></div><p id="mw-returnto">Return to <a href="/wiki/Approximation" title="Approximation">Approximation</a>.</p> <noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/wiki/Approximation">https://en.wikipedia.org/wiki/Approximation</a>"</div></div> <div id="catlinks" class="catlinks catlinks-allhidden" data-mw="interface"></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Approximation&action=edit&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</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-f69cdc8f6-jl9dk","wgBackendResponseTime":491,"wgPageParseReport":{"limitreport":{"cputime":"0.071","walltime":"0.093","ppvisitednodes":{"value":418,"limit":1000000},"postexpandincludesize":{"value":17740,"limit":2097152},"templateargumentsize":{"value":6556,"limit":2097152},"expansiondepth":{"value":9,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":469,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 65.824 1 -total"," 99.88% 65.744 2 Template:Blocked_text"," 45.99% 30.275 2 Template:Replace"," 36.37% 23.940 1 Template:Colocationwebhost"," 31.47% 20.712 1 Template:Hidden"," 13.72% 9.030 1 Template:Hidden_begin"," 12.43% 8.181 1 Template:Tlx"," 2.16% 1.425 1 MediaWiki:Wikimedia-globalblocking-blockedtext-mistake"," 1.96% 1.288 1 Template:Hidden_end"," 1.60% 1.051 1 MediaWiki:Wikimedia-globalblocking-blockedtext-mistake-email-steward"]},"scribunto":{"limitreport-timeusage":{"value":"0.013","limit":"10.000"},"limitreport-memusage":{"value":1043257,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-f69cdc8f6-jl9dk","timestamp":"20241125043450","ttl":2592000,"transientcontent":false}}});});</script> </body> </html>