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Encodings subsection</span> </button> <ul id="toc-Encodings-sublist" class="vector-toc-list"> <li id="toc-Typing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Typing"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Typing</span> </div> </a> <ul id="toc-Typing-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Similar_characters" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Similar_characters"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Similar characters</span> </div> </a> <ul id="toc-Similar_characters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Plus–minus sign</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 32 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-32" 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">32 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AF%E0%A7%8B%E0%A6%97-%E0%A6%AC%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A7%8B%E0%A6%97_%E0%A6%9A%E0%A6%BF%E0%A6%B9%E0%A7%8D%E0%A6%A8" title="যোগ-বিয়োগ চিহ্ন – Bangla" lang="bn" hreflang="bn" data-title="যোগ-বিয়োগ চিহ্ন" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%97%D0%BD%D0%B0%D0%BA_%D0%BF%D0%BB%D1%8E%D1%81-%D0%BC%D1%96%D0%BD%D1%83%D1%81" title="Знак плюс-мінус – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Знак плюс-мінус" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Signe_de_m%C3%A9s_o_menys" title="Signe de més o menys – Catalan" lang="ca" hreflang="ca" data-title="Signe de més o menys" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C2%B1" title="± – Czech" lang="cs" hreflang="cs" data-title="±" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Plusminuszeichen" title="Plusminuszeichen – German" lang="de" hreflang="de" data-title="Plusminuszeichen" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%8D%CE%BC%CE%B2%CE%BF%CE%BB%CE%BF_%CF%83%CF%85%CE%BD-%CF%80%CE%BB%CE%B7%CE%BD" title="Σύμβολο συν-πλην – Greek" lang="el" hreflang="el" data-title="Σύμβολο συν-πλην" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C2%B1" title="± – Spanish" lang="es" hreflang="es" data-title="±" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Plusminuso" title="Plusminuso – Esperanto" lang="eo" hreflang="eo" data-title="Plusminuso" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D9%84%D8%A7%D9%85%D8%AA_%D9%85%D8%AB%D8%A8%D8%AA%E2%80%93%D9%85%D9%86%D9%81%DB%8C" title="علامت مثبت–منفی – Persian" lang="fa" hreflang="fa" data-title="علامت مثبت–منفی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Signe_plus_ou_moins" title="Signe plus ou moins – French" lang="fr" hreflang="fr" data-title="Signe plus ou moins" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/M%C3%A1is-menos" title="Máis-menos – Galician" lang="gl" hreflang="gl" data-title="Máis-menos" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%8C%EB%9F%AC%EC%8A%A4%EB%A7%88%EC%9D%B4%EB%84%88%EC%8A%A4" title="플러스마이너스 – Korean" lang="ko" hreflang="ko" data-title="플러스마이너스" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D5%AC%D5%B5%D5%B8%D6%82%D5%BD-%D5%B4%D5%AB%D5%B6%D5%B8%D6%82%D5%BD_%D5%B6%D5%B7%D5%A1%D5%B6" title="Պլյուս-մինուս նշան – Armenian" lang="hy" hreflang="hy" data-title="Պլյուս-մինուս նշան" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Pi%C3%B9_o_meno" title="Più o meno – Italian" lang="it" hreflang="it" data-title="Più o meno" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%8D%E0%B4%B2%E0%B4%B8%E0%B5%8D-%E0%B4%AE%E0%B5%88%E0%B4%A8%E0%B4%B8%E0%B5%8D_%E0%B4%9A%E0%B4%BF%E0%B4%B9%E0%B5%8D%E0%B4%A8%E0%B4%82" title="പ്ലസ്-മൈനസ് ചിഹ്നം – Malayalam" lang="ml" hreflang="ml" data-title="പ്ലസ്-മൈനസ് ചിഹ്നം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Plusminus" title="Plusminus – Dutch" lang="nl" hreflang="nl" data-title="Plusminus" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%97%E3%83%A9%E3%82%B9%E3%83%9E%E3%82%A4%E3%83%8A%E3%82%B9%E8%A8%98%E5%8F%B7" title="プラスマイナス記号 – Japanese" lang="ja" hreflang="ja" data-title="プラスマイナス記号" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/%C2%B1" title="± – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="±" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Znak_plus-minus" title="Znak plus-minus – Polish" lang="pl" hreflang="pl" data-title="Znak plus-minus" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Sinal_de_mais_ou_menos" title="Sinal de mais ou menos – Portuguese" lang="pt" hreflang="pt" data-title="Sinal de mais ou menos" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Semn_plus-minus" title="Semn plus-minus – Romanian" lang="ro" hreflang="ro" data-title="Semn plus-minus" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%97%D0%BD%D0%B0%D0%BA_%D0%BF%D0%BB%D1%8E%D1%81-%D0%BC%D0%B8%D0%BD%D1%83%D1%81" title="Знак плюс-минус – Russian" lang="ru" hreflang="ru" data-title="Знак плюс-минус" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shenja_plus-minus_%C2%B1" title="Shenja plus-minus ± – Albanian" lang="sq" hreflang="sq" data-title="Shenja plus-minus ±" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Plus-miinusmerkki" title="Plus-miinusmerkki – Finnish" lang="fi" hreflang="fi" data-title="Plus-miinusmerkki" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Plus%E2%80%93minustecken" title="Plus–minustecken – Swedish" lang="sv" hreflang="sv" data-title="Plus–minustecken" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%82%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%B2%E0%AF%8D-%E0%AE%95%E0%AE%B4%E0%AE%BF%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%B2%E0%AF%8D_%E0%AE%95%E0%AF%81%E0%AE%B1%E0%AE%BF" title="கூட்டல்-கழித்தல் குறி – Tamil" lang="ta" hreflang="ta" data-title="கூட்டல்-கழித்தல் குறி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%84%E0%B8%A3%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%AB%E0%B8%A1%E0%B8%B2%E0%B8%A2%E0%B8%9A%E0%B8%A7%E0%B8%81-%E0%B8%A5%E0%B8%9A" title="เครื่องหมายบวก-ลบ – Thai" lang="th" hreflang="th" data-title="เครื่องหมายบวก-ลบ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Art%C4%B1%E2%80%93eksi_i%C5%9Fareti" title="Artı–eksi işareti – Turkish" lang="tr" hreflang="tr" data-title="Artı–eksi işareti" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%BD%D0%B0%D0%BA_%D0%BF%D0%BB%D1%8E%D1%81-%D0%BC%D1%96%D0%BD%D1%83%D1%81" title="Знак плюс-мінус – Ukrainian" lang="uk" hreflang="uk" data-title="Знак плюс-мінус" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/D%E1%BA%A5u_c%E1%BB%99ng-tr%E1%BB%AB" title="Dấu cộng-trừ – Vietnamese" lang="vi" hreflang="vi" data-title="Dấu cộng-trừ" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%AD%A3%E8%B2%A0%E8%99%9F" title="正負號 – Cantonese" lang="yue" hreflang="yue" data-title="正負號" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%AD%A3%E8%B2%A0%E8%99%9F" title="正負號 – Chinese" lang="zh" hreflang="zh" data-title="正負號" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q260387#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> 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searchaux" style="display:none">Symbol combining both + and - signs</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Plus%E2%80%93minus_(disambiguation)" class="mw-redirect mw-disambig" title="Plus–minus (disambiguation)">Plus–minus (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox" style="max-width:20em;"><tbody><tr><th colspan="2" class="infobox-above" style="background: #ccc; font-size: 500%; line-height:1.3; font-weight:normal; font-family:'times new roman', times, georgia, serif, sans-serif;">±</th></tr><tr><th colspan="2" class="infobox-header" style="background: #ccc;"><div style="background: #ccc; font-size: 125%; font-weight: bold; padding: 0.1em 0.25em 0.2em; line-height: 1.2em;">Plus–minus sign</div></th></tr><tr><th scope="row" class="infobox-label">In <a href="/wiki/Unicode" title="Unicode">Unicode</a></th><td class="infobox-data"><span class="nowrap"><style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">U+00B1</span> </span><span style="font-size:125%;line-height:1em">±</span> <span style="font-variant: small-caps; text-transform: lowercase;">PLUS-MINUS SIGN</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">&plusmn;, &PlusMinus;, &pm;</span>)</td></tr><tr><th colspan="2" class="infobox-header" style="background: #ccc;">Related</th></tr><tr><th scope="row" class="infobox-label">See also</th><td class="infobox-data"><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">U+2213</span> </span><span style="font-size:125%;line-height:1em">∓</span> <span style="font-variant: small-caps; text-transform: lowercase;">MINUS-OR-PLUS SIGN</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">&MinusPlus;, &mnplus;, &mp;</span>)</td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Mas_menos.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Mas_menos.jpg/220px-Mas_menos.jpg" decoding="async" width="220" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Mas_menos.jpg/330px-Mas_menos.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Mas_menos.jpg/440px-Mas_menos.jpg 2x" data-file-width="817" data-file-height="824" /></a><figcaption> Plus or minus sign</figcaption></figure> <p>The <b>plus–minus sign</b> or <b>plus-or-minus sign</b>, <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">±</span>, is a symbol with multiple meanings. </p> <ul><li>In <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, it generally indicates a choice of exactly two possible values, one of which is obtained through <a href="/wiki/Addition" title="Addition">addition</a> and the other through <a href="/wiki/Subtraction" title="Subtraction">subtraction</a>.</li> <li>In <a href="/wiki/Statistics" title="Statistics">statistics</a> and <a href="/wiki/Experimental_science" class="mw-redirect" title="Experimental science">experimental sciences</a>, the sign commonly indicates the <a href="/wiki/Confidence_interval" title="Confidence interval">confidence interval</a> or <a href="/wiki/Measurement_uncertainty" title="Measurement uncertainty">uncertainty</a> bounding a range of possible <a href="/wiki/Errors_and_residuals_in_statistics" class="mw-redirect" title="Errors and residuals in statistics">errors</a> in a measurement, often the <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a> or <a href="/wiki/Standard_error" title="Standard error">standard error</a>. The sign may also represent an inclusive range of values that a reading might have.</li> <li>In <a href="/wiki/Chess" title="Chess">chess</a>, the sign indicates a clear advantage for the white player; the complementary <a href="/wiki/Minus-plus_sign" class="mw-redirect" title="Minus-plus sign">minus-plus sign</a>, <b><span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">∓</span></b> indicates the same advantage for the black player.</li></ul> <p>Other meanings occur in other fields, including medicine, engineering, chemistry, electronics, linguistics, and philosophy. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A version of the sign, including also the French word <i>ou</i> ("or"), was used in its mathematical meaning by <a href="/wiki/Albert_Girard" title="Albert Girard">Albert Girard</a> in 1626, and the sign in its modern form was used as early as 1631, in <a href="/wiki/William_Oughtred" title="William Oughtred">William Oughtred</a>'s <i>Clavis Mathematicae</i>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Usage">Usage</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=2" title="Edit section: Usage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="In_mathematics">In mathematics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=3" title="Edit section: In mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Mathematical_formula" class="mw-redirect" title="Mathematical formula">mathematical formulas</a>, the <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">±</span> symbol may be used to indicate a symbol that may be replaced by either of the <a href="/wiki/Plus_and_minus_signs" title="Plus and minus signs">plus and minus signs</a>, <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">+</span> or <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">−</span>, allowing the formula to represent two values or two equations.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>If <span class="texhtml"><i>x</i><sup>2</sup> = 9</span>, one may give the solution as <span class="texhtml"><i>x</i> = ±3</span>. This indicates that the equation has two solutions: <span class="texhtml"><i>x</i> = +3</span> and <span class="texhtml"><i>x</i> = −3</span>. A common use of this notation is found in the <a href="/wiki/Quadratic_formula" title="Quadratic formula">quadratic formula</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>b</mi> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mi>a</mi> <mi>c</mi> </msqrt> </mrow> </mrow> <mrow> <mn>2</mn> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca3ce631f83b33ad881aed5f6e12e2f6c3afbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:22.172ex; height:6.176ex;" alt="{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}},}"></span></dd></dl> <p>which describes the two solutions to the <a href="/wiki/Quadratic_equation" title="Quadratic equation">quadratic equation</a> <span class="texhtml"><i>ax</i><sup>2</sup> + <i>bx</i> + <i>c</i> = 0.</span> </p><p>Similarly, the <a href="/wiki/Trigonometric_identity" class="mw-redirect" title="Trigonometric identity">trigonometric identity</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(A\pm B)=\sin(A)\cos(B)\pm \cos(A)\sin(B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>±</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>±</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(A\pm B)=\sin(A)\cos(B)\pm \cos(A)\sin(B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00d9081ccef9d9b5d6d4ea54f4bf8a34949db38b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.91ex; height:2.843ex;" alt="{\displaystyle \sin(A\pm B)=\sin(A)\cos(B)\pm \cos(A)\sin(B)}"></span></dd></dl> <p>can be interpreted as a shorthand for two equations: one with <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">+</span> on both sides of the equation, and one with <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">−</span> on both sides. </p><p><span class="anchor" id="Minus_plus_sign"></span> The <b>minus–plus sign</b>, <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">∓</span>, is generally used in conjunction with the <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">±</span> sign, in such expressions as <span class="texhtml"><i>x</i> ± <i>y</i> ∓ <i>z</i></span>, which can be interpreted as meaning <span class="texhtml"><i>x</i> + <i>y</i> − <i>z</i></span> or <span class="texhtml"><i>x</i> − <i>y</i> + <i>z</i></span> (but <em>not</em> <span class="texhtml"><i>x</i> + <i>y</i> + <i>z</i></span> or <span class="texhtml"><i>x</i> − <i>y</i> − <i>z</i></span>). The <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">∓</span> always has the opposite sign to <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">±</span>. </p><p>The above expression can be rewritten as <span class="texhtml"><i>x</i> ± (<i>y</i> − <i>z</i>)</span> to avoid use of <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">∓</span>, but cases such as the trigonometric identity are most neatly written using the "∓" sign: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos(A\pm B)=\cos(A)\cos(B)\mp \sin(A)\sin(B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>±</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>∓</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(A\pm B)=\cos(A)\cos(B)\mp \sin(A)\sin(B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7cb8a2106ac9a46d4b4fc62799e6db8166b27be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.166ex; height:2.843ex;" alt="{\displaystyle \cos(A\pm B)=\cos(A)\cos(B)\mp \sin(A)\sin(B)}"></span></dd></dl> <p>which represents the two equations: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\cos(A+B)&=\cos(A)\cos(B)-\sin(A)\sin(B)\\\cos(A-B)&=\cos(A)\cos(B)+\sin(A)\sin(B)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>−</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\cos(A+B)&=\cos(A)\cos(B)-\sin(A)\sin(B)\\\cos(A-B)&=\cos(A)\cos(B)+\sin(A)\sin(B)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5eb4221e9f940996938d37d6f6203b4b833b5c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:44.917ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}\cos(A+B)&=\cos(A)\cos(B)-\sin(A)\sin(B)\\\cos(A-B)&=\cos(A)\cos(B)+\sin(A)\sin(B)\end{aligned}}}"></span></dd></dl> <p>Another example is the <a href="/wiki/Conjugate_(square_roots)" title="Conjugate (square roots)">conjugate</a> of the <a href="/wiki/Square_number" title="Square number">perfect squares</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{3}\pm y^{3}=(x\pm y)\left((x\mp y)^{2}\pm xy\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>±</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>±</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mrow> <mo>(</mo> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>∓</mo> <mi>y</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>±</mo> <mi>x</mi> <mi>y</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}\pm y^{3}=(x\pm y)\left((x\mp y)^{2}\pm xy\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3da8955bccb7cb63560a0aeec4eb9f94f6f44679" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:33.704ex; height:3.343ex;" alt="{\displaystyle x^{3}\pm y^{3}=(x\pm y)\left((x\mp y)^{2}\pm xy\right)}"></span></dd></dl> <p>which represents the two equations: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}x^{3}+y^{3}&=(x+y)\left((x-y)^{2}+xy\right)\\x^{3}-y^{3}&=(x-y)\left((x+y)^{2}-xy\right)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mrow> <mo>(</mo> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>x</mi> <mi>y</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mrow> <mo>(</mo> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>x</mi> <mi>y</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x^{3}+y^{3}&=(x+y)\left((x-y)^{2}+xy\right)\\x^{3}-y^{3}&=(x-y)\left((x+y)^{2}-xy\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/840c10b4315211a34546ba15e4098453d78902c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:34.455ex; height:6.843ex;" alt="{\displaystyle {\begin{aligned}x^{3}+y^{3}&=(x+y)\left((x-y)^{2}+xy\right)\\x^{3}-y^{3}&=(x-y)\left((x+y)^{2}-xy\right)\end{aligned}}}"></span></dd></dl> <p>A related usage is found in this presentation of the formula for the <a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a> of the sine function: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \left(x\right)=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \pm {\frac {1}{(2n+1)!}}x^{2n+1}+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>x</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>3</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mn>5</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mrow> <mn>7</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \left(x\right)=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \pm {\frac {1}{(2n+1)!}}x^{2n+1}+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d45d636447a5dcbceeedb0ad9ffdc82bff0230b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:57.895ex; height:6.509ex;" alt="{\displaystyle \sin \left(x\right)=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \pm {\frac {1}{(2n+1)!}}x^{2n+1}+\cdots }"></span></dd></dl> <p>Here, the plus-or-minus sign indicates that the term may be added or subtracted depending on whether <span class="texhtml mvar" style="font-style:italic;">n</span> is odd or even; a rule which can be deduced from the first few terms. A more rigorous presentation would multiply each term by a factor of <span class="texhtml">(−1)<sup><i>n</i></sup></span>, which gives +1 when <span class="texhtml mvar" style="font-style:italic;">n</span> is even, and −1 when <span class="texhtml mvar" style="font-style:italic;">n</span> is odd. In older texts one occasionally finds <span class="texhtml">(−)<sup><i>n</i></sup></span>, which means the same. </p><p>When the standard presumption that the plus-or-minus signs all take on the same value of +1 or all −1 is not true, then the line of text that immediately follows the equation must contain a brief description of the actual connection, if any, most often of the form <i>"where the ‘±’ signs are independent"</i> or similar. If a brief, simple description is not possible, the equation must be re-written to provide clarity; e.g. by introducing variables such as <span class="texhtml"><i>s</i><sub>1</sub></span>, <span class="texhtml"><i>s</i><sub>2</sub></span>, ... and specifying a value of +1 or −1 separately for each, or some appropriate relation, like <span class="texhtml"><i>s</i><sub>3</sub> = <i>s</i><sub>1</sub> · (<i>s</i><sub>2</sub>)<sup><i>n</i></sup></span> or similar. </p> <div class="mw-heading mw-heading3"><h3 id="In_statistics">In statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=4" title="Edit section: In statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The use of <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">±</span> for an approximation is most commonly encountered in presenting the numerical value of a quantity, together with its <a href="/wiki/Engineering_tolerance" title="Engineering tolerance">tolerance</a> or its statistical <a href="/wiki/Margin_of_error" title="Margin of error">margin of error</a>.<sup id="cite_ref-stderror_3-0" class="reference"><a href="#cite_note-stderror-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> For example, <span class="nowrap">5.7 ± 0.2</span> may be anywhere in the range from 5.5 to 5.9 inclusive. In scientific usage, it sometimes refers to a probability of being within the stated interval, usually corresponding to either 1 or 2 <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviations</a> (a probability of 68.3% or 95.4% in a <a href="/wiki/Normal_distribution" title="Normal distribution">normal distribution</a>). </p><p>Operations involving uncertain values should always try to preserve the uncertainty, in order to avoid <a href="/wiki/Propagation_of_uncertainty" title="Propagation of uncertainty">propagation of error</a>. If <span class="texhtml"><i>n</i> = <i>a</i> ± <i>b</i></span>, any operation of the form <span class="texhtml"><i>m</i> = <i>f</i>(<i>n</i>)</span> must return a value of the form <span class="texhtml"><i>m</i> = <i>c</i> ± <i>d</i></span>, where <span class="texhtml mvar" style="font-style:italic;">c</span> is <span class="texhtml"><i>f</i>(<i>a</i>)</span> and <span class="texhtml mvar" style="font-style:italic;">d</span> is the range <span class="texhtml mvar" style="font-style:italic;">b</span> updated using <a href="/wiki/Interval_arithmetic" title="Interval arithmetic">interval arithmetic</a>. </p> <div class="mw-heading mw-heading3"><h3 id="In_chess">In chess</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=5" title="Edit section: In chess"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The symbols <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">±</span> and <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">∓</span> are used in <a href="/wiki/Chess_annotation_symbols" title="Chess annotation symbols">chess annotation</a> to denote a moderate but significant advantage for White and Black, respectively.<sup id="cite_ref-chess_4-0" class="reference"><a href="#cite_note-chess-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Weaker and stronger advantages are denoted by <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">⩲</span> and <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">⩱</span> for only a slight advantage, and <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">+–</span> and <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">–+</span> for a strong, potentially winning advantage, again for White and Black respectively.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other_meanings">Other meanings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=6" title="Edit section: Other meanings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>In <a href="/wiki/Medicine" title="Medicine">medicine</a>, it may mean "with or without" in some cases.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li> <li>In <a href="/wiki/Engineering" title="Engineering">engineering</a>, the sign indicates the <a href="/wiki/Engineering_tolerance" title="Engineering tolerance">tolerance</a>, which is the range of values that are considered to be acceptable or safe, or which comply with some standard or with a contract.</li> <li>In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, the sign is used to indicate a <a href="/wiki/Racemic_mixture" title="Racemic mixture">racemic mixture</a>.</li> <li>In <a href="/wiki/Electronics" title="Electronics">electronics</a>, this sign may indicate a dual voltage power supply, such as ±5 volts means +5 volts and −5 volts, when used with audio circuits and <a href="/wiki/Operational_amplifier" title="Operational amplifier">operational amplifiers</a>.</li> <li>In <a href="/wiki/Linguistics" title="Linguistics">linguistics</a>, it may indicate a <a href="/wiki/Distinctive_feature" title="Distinctive feature">distinctive feature</a>, such as [±voiced].<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Encodings">Encodings</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=7" title="Edit section: Encodings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>In <a href="/wiki/Unicode" title="Unicode">Unicode</a>: <span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">U+00B1</span> </span><span style="font-size:125%;line-height:1em">±</span> <span style="font-variant: small-caps; text-transform: lowercase;">PLUS-MINUS SIGN</span></li> <li>In <a href="/wiki/ISO_8859-1" class="mw-redirect" title="ISO 8859-1">ISO 8859-1</a>, <a href="/wiki/ISO_8859-7" class="mw-redirect" title="ISO 8859-7">-7</a>, <a href="/wiki/ISO_8859-8" class="mw-redirect" title="ISO 8859-8">-8</a>, <a href="/wiki/ISO_8859-9" class="mw-redirect" title="ISO 8859-9">-9</a>, <a href="/wiki/ISO_8859-13" class="mw-redirect" title="ISO 8859-13">-13</a>, <a href="/wiki/ISO_8859-15" class="mw-redirect" title="ISO 8859-15">-15</a>, and <a href="/wiki/ISO_8859-16" class="mw-redirect" title="ISO 8859-16">-16</a>, the plus–minus symbol is code 0xB1<sub><a href="/wiki/Hexadecimal" title="Hexadecimal">hex</a></sub>. This location was copied to Unicode.</li> <li>The symbol also has a <a href="/wiki/Character_entity_reference" class="mw-redirect" title="Character entity reference">HTML entity</a> representations of <code>&pm;</code>, <code>&plusmn;</code>, and <code>&#177;</code>.</li> <li>The rarer minus–plus sign is not generally found in legacy encodings, but is available in Unicode as <span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734"><span class="monospaced">U+2213</span> </span><span style="font-size:125%;line-height:1em">∓</span> <span style="font-variant: small-caps; text-transform: lowercase;">MINUS-OR-PLUS SIGN</span> so can be used in HTML using <code>&#x2213;</code> or <code>&#8723;</code>.</li> <li>In <a href="/wiki/TeX" title="TeX">TeX</a> 'plus-or-minus' and 'minus-or-plus' symbols are denoted <code>\pm</code> and <code>\mp</code>, respectively.</li> <li>Although these characters may be approximated by underlining or overlining a <span class="nounderlines" style="border: 1px solid var(--border-color-muted,#ddd); color: var(--color-base); background-color: var( --background-color-neutral-subtle, #fdfdfd); padding: 1px 1px;">+</span> symbol ( <span style="text-decoration: underline;">+</span>  or <span style="text-decoration:overline;">+</span> ), this is discouraged because the formatting may be stripped at a later date, changing the meaning. It also makes the meaning less accessible to blind users with <a href="/wiki/Screen_reader" title="Screen reader">screen readers</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Typing">Typing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=8" title="Edit section: Typing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Microsoft_Windows" title="Microsoft Windows">Windows</a>: <style data-mw-deduplicate="TemplateStyles:r1249182868">.mw-parser-output .keyboard-key{border:1px solid #aaa;border-radius:0.2em;box-shadow:0.1em 0.1em 0.2em rgba(0,0,0,0.1);background-color:var(--background-color-neutral-subtle,#f8f9fa);background-image:linear-gradient(to bottom,var(--background-color-neutral,#eaecf0),var(--background-color-neutral-subtle,#f8f9fa),var(--background-color-neutral,#eaecf0));color:var(--color-base,#202122);padding:0.1em 0.3em;font-family:inherit;font-size:0.85em}</style><kbd class="keyboard-key nowrap"><a href="/wiki/Alt_code" title="Alt code">Alt</a></kbd>+<kbd class="keyboard-key nowrap">2</kbd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">4</kbd><kbd class="keyboard-key nowrap">1</kbd> or <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">Alt</kbd>+<kbd class="keyboard-key nowrap">0</kbd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">1</kbd><kbd class="keyboard-key nowrap">7</kbd><kbd class="keyboard-key nowrap">7</kbd> (numbers typed on the <a href="/wiki/Numeric_keypad" title="Numeric keypad">numeric keypad</a>).</li> <li>Macintosh: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">⌥ Option</kbd>+<kbd class="keyboard-key nowrap">⇧ Shift</kbd>+<kbd class="keyboard-key nowrap">=</kbd> (equal sign on the non-numeric keypad).</li> <li><a href="/wiki/Unix-like" title="Unix-like">Unix-like</a> systems: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap"><a href="/wiki/Compose_key" title="Compose key">Compose</a></kbd>,<kbd class="keyboard-key nowrap">+</kbd>,<kbd class="keyboard-key nowrap">-</kbd> or <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">⇧ Shift</kbd>+<kbd class="keyboard-key nowrap">Ctrl</kbd>+<kbd class="keyboard-key nowrap">u</kbd><span class="nowrap"> </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">B</kbd><kbd class="keyboard-key nowrap">1</kbd><kbd class="keyboard-key nowrap">space</kbd> (second works on <a href="/wiki/Chromebook" title="Chromebook">Chromebook</a>)</li> <li>In the <a href="/wiki/Vim_(text_editor)" title="Vim (text editor)">Vim text editor</a> (in Insert mode): <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">Ctrl</kbd>+<kbd class="keyboard-key nowrap">k</kbd> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">+</kbd><kbd class="keyboard-key nowrap">-</kbd> or <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">Ctrl</kbd>+<kbd class="keyboard-key nowrap">v</kbd> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">1</kbd><kbd class="keyboard-key nowrap">7</kbd><kbd class="keyboard-key nowrap">7</kbd> or <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">Ctrl</kbd>+<kbd class="keyboard-key nowrap">v</kbd> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">x</kbd> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">B</kbd><kbd class="keyboard-key nowrap">1</kbd> or <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">Ctrl</kbd>+<kbd class="keyboard-key nowrap">v</kbd> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">u</kbd> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">0</kbd><kbd class="keyboard-key nowrap">0</kbd><kbd class="keyboard-key nowrap">B</kbd><kbd class="keyboard-key nowrap">1</kbd></li> <li><a href="/wiki/AutoCAD" title="AutoCAD">AutoCAD</a> shortcut string: <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">%%p</code></li></ul> <div class="mw-heading mw-heading2"><h2 id="Similar_characters">Similar characters</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=9" title="Edit section: Similar characters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/%E5%A3%AB" class="extiw" title="wiktionary:士">士</a></b></i>, <i><b><a href="https://en.wiktionary.org/wiki/%E5%9C%9F" class="extiw" title="wiktionary:土">土</a></b></i>, or <i><b><a href="https://en.wiktionary.org/wiki/%E5%B9%B2" class="extiw" title="wiktionary:干">干</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <p>The plus–minus sign resembles the <a href="/wiki/Chinese_character" class="mw-redirect" title="Chinese character">Chinese characters</a> <span title="Chinese-language text"><span lang="zh">土</span></span> (<a href="/wiki/Radical_32" title="Radical 32">Radical 32</a>) and <span title="Chinese-language text"><span lang="zh">士</span></span> (<a href="/wiki/Radical_33" title="Radical 33">Radical 33</a>), whereas the minus–plus sign resembles <span title="Chinese-language text"><span lang="zh">干</span></span> (<a href="/wiki/Radical_51" title="Radical 51">Radical 51</a>). </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E2%89%88" class="mw-redirect" title="≈">≈</a> (approximately equal to)</li> <li><a href="/wiki/Engineering_tolerance" title="Engineering tolerance">Engineering tolerance</a></li> <li><a href="/wiki/Plus_and_minus_signs" title="Plus and minus signs">Plus and minus signs</a></li> <li><a href="/wiki/Sign_(mathematics)" title="Sign (mathematics)">Sign (mathematics)</a></li> <li><a href="/wiki/Table_of_mathematical_symbols" class="mw-redirect" title="Table of mathematical symbols">Table of mathematical symbols</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Plus%E2%80%93minus_sign&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 25em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFCajori1928" class="citation cs2"><a href="/wiki/Florian_Cajori" title="Florian Cajori">Cajori, Florian</a> (1928), <a href="/wiki/A_History_of_Mathematical_Notations" title="A History of Mathematical Notations"><i>A History of Mathematical Notations, Volume I: Notations in Elementary Mathematics</i></a>, Open Court, p. <a rel="nofollow" class="external text" href="http://archive.org/details/historyofmathema031756mbp/page/n263">245</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Mathematical+Notations%2C+Volume+I%3A+Notations+in+Elementary+Mathematics&rft.pages=245&rft.pub=Open+Court&rft.date=1928&rft.aulast=Cajori&rft.aufirst=Florian&rfr_id=info%3Asid%2Fen.wikipedia.org%3APlus%E2%80%93minus+sign" class="Z3988"></span>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.merriam-webster.com/dictionary/plus%2Fminus+sign">"Definition of PLUS/MINUS SIGN"</a>. <i>merriam-webster.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-08-28</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=merriam-webster.com&rft.atitle=Definition+of+PLUS%2FMINUS+SIGN&rft_id=http%3A%2F%2Fwww.merriam-webster.com%2Fdictionary%2Fplus%252Fminus%2Bsign&rfr_id=info%3Asid%2Fen.wikipedia.org%3APlus%E2%80%93minus+sign" class="Z3988"></span></span> </li> <li id="cite_note-stderror-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-stderror_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrown1982" class="citation journal cs1">Brown, George W. (1982). "Standard deviation, standard error: Which 'standard' should we use?". <i>American Journal of Diseases of Children</i>. <b>136</b> (10): 937–941. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1001%2Farchpedi.1982.03970460067015">10.1001/archpedi.1982.03970460067015</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/7124681">7124681</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Diseases+of+Children&rft.atitle=Standard+deviation%2C+standard+error%3A+Which+%27standard%27+should+we+use%3F&rft.volume=136&rft.issue=10&rft.pages=937-941&rft.date=1982&rft_id=info%3Adoi%2F10.1001%2Farchpedi.1982.03970460067015&rft_id=info%3Apmid%2F7124681&rft.aulast=Brown&rft.aufirst=George+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APlus%E2%80%93minus+sign" class="Z3988"></span></span> </li> <li id="cite_note-chess-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-chess_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEade2005" class="citation cs2">Eade, James (2005), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7eZxKNQu-JoC&pg=PA272"><i>Chess For Dummies</i></a> (2nd ed.), John Wiley & Sons, p. 272, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780471774334" title="Special:BookSources/9780471774334"><bdi>9780471774334</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chess+For+Dummies&rft.pages=272&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons&rft.date=2005&rft.isbn=9780471774334&rft.aulast=Eade&rft.aufirst=James&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7eZxKNQu-JoC%26pg%3DPA272&rfr_id=info%3Asid%2Fen.wikipedia.org%3APlus%E2%80%93minus+sign" class="Z3988"></span>.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">For details, see <a href="/wiki/Chess_annotation_symbols#Positions" title="Chess annotation symbols">Chess annotation symbols § Positions</a>.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNaessChristiansenRomundstadCannegieter2007" class="citation journal cs1">Naess, I. A.; Christiansen, S. C.; Romundstad, P.; Cannegieter, S. C.; Rosendaal, F. R.; Hammerstrøm, J. (2007). "Incidence and mortality of venous thrombosis: a population-based study". <i>Journal of Thrombosis and Haemostasis</i>. <b>5</b> (4): 692–699. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1538-7836.2007.02450.x">10.1111/j.1538-7836.2007.02450.x</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1538-7933">1538-7933</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17367492">17367492</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:23648224">23648224</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Thrombosis+and+Haemostasis&rft.atitle=Incidence+and+mortality+of+venous+thrombosis%3A+a+population-based+study&rft.volume=5&rft.issue=4&rft.pages=692-699&rft.date=2007&rft.issn=1538-7933&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A23648224%23id-name%3DS2CID&rft_id=info%3Apmid%2F17367492&rft_id=info%3Adoi%2F10.1111%2Fj.1538-7836.2007.02450.x&rft.aulast=Naess&rft.aufirst=I.+A.&rft.au=Christiansen%2C+S.+C.&rft.au=Romundstad%2C+P.&rft.au=Cannegieter%2C+S.+C.&rft.au=Rosendaal%2C+F.+R.&rft.au=Hammerstr%C3%B8m%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APlus%E2%80%93minus+sign" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeitSilversteinMohrPetterson1999" class="citation journal cs1">Heit, J. A.; Silverstein, M. D.; Mohr, D. N.; Petterson, T. M.; O'Fallon, W. M.; Melton, L. J. (1999-03-08). "Predictors of survival after deep vein thrombosis and pulmonary embolism: a population-based, cohort study". <i>Archives of Internal Medicine</i>. <b>159</b> (5): 445–453. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1001%2Farchinte.159.5.445">10.1001/archinte.159.5.445</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0003-9926">0003-9926</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10074952">10074952</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archives+of+Internal+Medicine&rft.atitle=Predictors+of+survival+after+deep+vein+thrombosis+and+pulmonary+embolism%3A+a+population-based%2C+cohort+study&rft.volume=159&rft.issue=5&rft.pages=445-453&rft.date=1999-03-08&rft.issn=0003-9926&rft_id=info%3Apmid%2F10074952&rft_id=info%3Adoi%2F10.1001%2Farchinte.159.5.445&rft.aulast=Heit&rft.aufirst=J.+A.&rft.au=Silverstein%2C+M.+D.&rft.au=Mohr%2C+D.+N.&rft.au=Petterson%2C+T.+M.&rft.au=O%27Fallon%2C+W.+M.&rft.au=Melton%2C+L.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APlus%E2%80%93minus+sign" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHornsby" class="citation book cs1">Hornsby, David. <i>Linguistics, A Complete Introduction</i>. p. 99. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781444180336" title="Special:BookSources/9781444180336"><bdi>9781444180336</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Linguistics%2C+A+Complete+Introduction&rft.pages=99&rft.isbn=9781444180336&rft.aulast=Hornsby&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3APlus%E2%80%93minus+sign" class="Z3988"></span></span> </li> </ol></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline 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.navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Navbox_punctuation" title="Template:Navbox punctuation"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Navbox_punctuation" title="Template talk:Navbox punctuation"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Navbox_punctuation" title="Special:EditPage/Template:Navbox punctuation"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Common_punctuation_and_other_typographical_symbols" style="font-size:114%;margin:0 4em">Common <a href="/wiki/Punctuation" title="Punctuation">punctuation</a> and other <a href="/wiki/Typography" title="Typography">typographical</a> symbols</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">   </span>  <span style="font-size:95%"><a href="/wiki/Space_(punctuation)" title="Space (punctuation)">space</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> , </span>  <span style="font-size:95%"><a href="/wiki/Comma" title="Comma">comma</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> : </span>  <span style="font-size:95%"><a href="/wiki/Colon_(punctuation)" title="Colon (punctuation)">colon</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ; </span>  <span style="font-size:95%"><a href="/wiki/Semicolon" title="Semicolon">semicolon</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‐ </span>  <span style="font-size:95%"><a href="/wiki/Hyphen" title="Hyphen">hyphen</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ’ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ' </span>  <span style="font-size:95%"><a href="/wiki/Apostrophe" title="Apostrophe">apostrophe</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ′ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ″ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‴ </span>  <span style="font-size:95%"><a href="/wiki/Prime_(symbol)" title="Prime (symbol)">prime</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> . </span>  <span style="font-size:95%"><a href="/wiki/Full_stop" title="Full stop">full stop</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> & </span>  <span style="font-size:95%"><a href="/wiki/Ampersand" title="Ampersand">ampersand</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> @ </span>  <span style="font-size:95%"><a href="/wiki/At_sign" title="At sign">at sign</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ^ </span>  <span style="font-size:95%"><a href="/wiki/Caret" title="Caret">caret</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> / </span>  <span style="font-size:95%"><a href="/wiki/Slash_(punctuation)" title="Slash (punctuation)">slash</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> \ </span>  <span style="font-size:95%"><a href="/wiki/Backslash" title="Backslash">backslash</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> … </span>  <span style="font-size:95%"><a href="/wiki/Ellipsis" title="Ellipsis">ellipsis</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> * </span>  <span style="font-size:95%"><a href="/wiki/Asterisk" title="Asterisk">asterisk</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ※ </span>  <span style="font-size:95%"><a href="/wiki/Reference_mark" title="Reference mark">Reference mark</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ⁂ </span>  <span style="font-size:95%"><a href="/wiki/Asterism_(typography)" title="Asterism (typography)">asterism</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> <span class="nowrap"> </span><span class="nowrap"> </span>*<span class="nowrap"> </span><span class="nowrap"> </span>*<span class="nowrap"> </span><span class="nowrap"> </span>*<span class="nowrap"> </span><span class="nowrap"> </span><span class="nowrap"> </span> </span>  <span style="font-size:95%"><a href="/wiki/Dinkus" title="Dinkus">dinkus</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> - </span>  <span style="font-size:95%"><a href="/wiki/Hyphen-minus" title="Hyphen-minus">hyphen-minus</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‒ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> – </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> — </span>  <span style="font-size:95%"><a href="/wiki/Dash" title="Dash">dash</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ⹀ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ⸗ </span>  <span style="font-size:95%"><a href="/wiki/Double_hyphen" title="Double hyphen">double hyphen</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ? </span>  <span style="font-size:95%"><a href="/wiki/Question_mark" title="Question mark">question mark</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ! </span>  <span style="font-size:95%"><a href="/wiki/Exclamation_mark" title="Exclamation mark">exclamation mark</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‽ </span>  <span style="font-size:95%"><a href="/wiki/Interrobang" title="Interrobang">interrobang</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ¡ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ¿ </span>  <span style="font-size:95%"><a href="/wiki/Inverted_question_and_exclamation_marks" class="mw-redirect" title="Inverted question and exclamation marks">inverted ! and ?</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ⸮ </span>  <span style="font-size:95%"><a href="/wiki/Irony_punctuation" title="Irony punctuation">irony punctuation</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> # </span>  <span style="font-size:95%"><a href="/wiki/Number_sign" title="Number sign">number sign</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> № </span>  <span style="font-size:95%"><a href="/wiki/Numero_sign" title="Numero sign">numero sign</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> º </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ª </span>  <span style="font-size:95%"><a href="/wiki/Ordinal_indicator" title="Ordinal indicator">ordinal indicator</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> % </span>  <span style="font-size:95%"><a href="/wiki/Percent_sign" title="Percent sign">percent sign</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‰ </span>  <span style="font-size:95%"><a href="/wiki/Per_mille" title="Per mille">per mille</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‱ </span>  <span style="font-size:95%"><a href="/wiki/Basis_point" title="Basis point">basis point</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ° </span>  <span style="font-size:95%"><a href="/wiki/Degree_symbol" title="Degree symbol">degree symbol</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ⌀ </span>  <span style="font-size:95%"><a href="/wiki/Diameter#Symbol" title="Diameter">diameter sign</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> + </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> − </span>  <span style="font-size:95%"><a href="/wiki/Plus_and_minus_signs" title="Plus and minus signs">plus and minus signs</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> × </span>  <span style="font-size:95%"><a href="/wiki/Multiplication_sign" title="Multiplication sign">multiplication sign</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ÷ </span>  <span style="font-size:95%"><a href="/wiki/Division_sign" title="Division sign">division sign</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ~ </span>  <span style="font-size:95%"><a href="/wiki/Tilde" title="Tilde">tilde</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ± </span>  <span style="font-size:95%"><a class="mw-selflink selflink">plus–minus sign</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ∓ </span>  <span style="font-size:95%"><a href="/wiki/Minus-plus_sign" class="mw-redirect" title="Minus-plus sign">minus-plus sign</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> √ </span>  <span style="font-size:95%"><a href="/wiki/Radical_symbol" title="Radical symbol">radical symbol</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> _ </span>  <span style="font-size:95%"><a href="/wiki/Underscore" title="Underscore">underscore</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> <span style="position: relative; top: 0.25em;">⁀</span> </span>  <span style="font-size:95%"><a href="/wiki/Tie_(typography)" title="Tie (typography)">tie</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> | </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ¦ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‖ </span>  <span style="font-size:95%"><a href="/wiki/Vertical_bar" title="Vertical bar">vertical bar</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> • </span>  <span style="font-size:95%"><a href="/wiki/Bullet_(typography)" title="Bullet (typography)">bullet</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> · </span>  <span style="font-size:95%"><a href="/wiki/Interpunct" title="Interpunct">interpunct</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> © </span>  <span style="font-size:95%"><a href="/wiki/Copyright_symbol" title="Copyright symbol">copyright symbol</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ℗ </span>  <span style="font-size:95%"><a href="/wiki/Sound_recording_copyright_symbol" title="Sound recording copyright symbol">sound recording copyright</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ® </span>  <span style="font-size:95%"><a href="/wiki/Registered_trademark_symbol" title="Registered trademark symbol">registered trademark</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> <sup><span style="font-size:85%">SM</span></sup> </span>  <span style="font-size:95%"><a href="/wiki/Service_mark_symbol" title="Service mark symbol">service mark symbol</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> <sup><span style="font-size:85%">TM</span></sup> </span>  <span style="font-size:95%"><a href="/wiki/Trademark_symbol" title="Trademark symbol">trademark symbol</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‘ ’ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> “ ” </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ' ' </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> " " </span>  <span style="font-size:95%"><a href="/wiki/Quotation_mark" title="Quotation mark">quotation mark</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‹ › </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> « » </span>  <span style="font-size:95%"><a href="/wiki/Guillemet" title="Guillemet">guillemet</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ( ) </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> [ ] </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> { } </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ⟨ ⟩ </span>  <span style="font-size:95%"><a href="/wiki/Bracket" title="Bracket">bracket</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ” </span>  <span style="font-size:95%"><a href="/wiki/Ditto_mark" title="Ditto mark">ditto mark</a></span></span> </li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> † </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ‡ </span>  <span style="font-size:95%"><a href="/wiki/Dagger_(mark)" title="Dagger (mark)">dagger</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ❧ </span>  <span style="font-size:95%"><a href="/wiki/Fleuron_(typography)" title="Fleuron (typography)">fleuron</a> (hedera, aldus)</span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ☞ </span>  <span style="font-size:95%"><a href="/wiki/Manicule" title="Manicule">manicule</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ◊ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ⌑ </span>  <span style="font-size:95%"><a href="/wiki/Lozenge_(shape)" title="Lozenge (shape)">lozenge</a></span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ¶ </span> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> ⸿ </span>  <span style="font-size:95%"><a href="/wiki/Pilcrow" title="Pilcrow">pilcrow</a> (paragraph mark)</span></span> </li> <li><span class="nowrap"> <span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;"> § </span>  <span style="font-size:95%"><a href="/wiki/Section_sign" title="Section sign">section mark</a></span></span> </li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/List_of_typographical_symbols_and_punctuation_marks" title="List of typographical symbols and punctuation marks">Version of this table as a sortable list</a></li></ul> <ul><li><a href="/wiki/Currency_symbol" title="Currency symbol">Currency symbols</a></li> <li><a href="/wiki/Diacritic" title="Diacritic">Diacritics</a> (accents)</li> <li><a href="/wiki/List_of_logic_symbols" title="List of logic symbols">Logic symbols</a></li> <li><a href="/wiki/List_of_mathematical_symbols" class="mw-redirect" title="List of mathematical symbols">Math symbols</a></li> <li><a href="/wiki/Whitespace_character" title="Whitespace character">Whitespace</a></li></ul> <ul><li><a href="/wiki/Chinese_punctuation" title="Chinese punctuation">Chinese punctuation</a></li> <li><a href="/wiki/Hebrew_punctuation" title="Hebrew punctuation">Hebrew punctuation</a></li> <li><a href="/wiki/Japanese_punctuation" title="Japanese punctuation">Japanese punctuation</a></li> <li><a href="/wiki/Korean_punctuation" title="Korean punctuation">Korean punctuation</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Plus–minus_sign&oldid=1255366845">https://en.wikipedia.org/w/index.php?title=Plus–minus_sign&oldid=1255366845</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Addition" title="Category:Addition">Addition</a></li><li><a href="/wiki/Category:Elementary_arithmetic" title="Category:Elementary arithmetic">Elementary arithmetic</a></li><li><a href="/wiki/Category:Mathematical_symbols" title="Category:Mathematical 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