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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div 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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Background" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Background"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Background</span> </div> </a> <ul id="toc-Background-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Structure" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Structure"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Structure</span> </div> </a> <ul id="toc-Structure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_mathematics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>In mathematics</span> </div> </a> <ul id="toc-In_mathematics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_science" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_science"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>In science</span> </div> </a> <ul id="toc-In_science-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_natural_language" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_natural_language"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>In natural language</span> </div> </a> <ul id="toc-In_natural_language-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Further examples</span> </div> </a> <ul id="toc-Further_examples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dimensionless_quantity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dimensionless_quantity"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Dimensionless quantity</span> </div> </a> <ul id="toc-Dimensionless_quantity-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">8</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">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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" title="Table of Contents" > <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">Quantity</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 57 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-57" 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">57 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%AE%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BE" title="मात्रा – Angika" lang="anp" hreflang="anp" data-title="मात्रा" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D9%85%D9%8A%D8%A9" title="كمية – Arabic" lang="ar" hreflang="ar" data-title="كمية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Количество – Bulgarian" lang="bg" hreflang="bg" data-title="Количество" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Quantitat" title="Quantitat – Catalan" lang="ca" hreflang="ca" data-title="Quantitat" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A8%D1%83%D1%82%D0%BB%D0%B0%D0%B2%D0%BB%C4%83%D1%85" title="Шутлавлăх – Chuvash" lang="cv" hreflang="cv" data-title="Шутлавлăх" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kvantita" title="Kvantita – Czech" lang="cs" hreflang="cs" data-title="Kvantita" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kvantitet" title="Kvantitet – Danish" lang="da" hreflang="da" data-title="Kvantitet" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Quantit%C3%A4t" title="Quantität – German" lang="de" hreflang="de" data-title="Quantität" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kvantiteet" title="Kvantiteet – Estonian" lang="et" hreflang="et" data-title="Kvantiteet" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%BF%CF%83%CF%8C%CF%84%CE%B7%CF%84%CE%B1" title="Ποσότητα – Greek" lang="el" hreflang="el" data-title="Ποσότητα" 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/Cantidad" title="Cantidad – Spanish" lang="es" hreflang="es" data-title="Cantidad" 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/Kvanto" title="Kvanto – Esperanto" lang="eo" hreflang="eo" data-title="Kvanto" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kantitate" title="Kantitate – Basque" lang="eu" hreflang="eu" data-title="Kantitate" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D9%85%DB%8C%D8%AA" title="کمیت – Persian" lang="fa" hreflang="fa" data-title="کمیت" 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/Quantit%C3%A9" title="Quantité – French" lang="fr" hreflang="fr" data-title="Quantité" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Cainn%C3%ADocht" title="Cainníocht – Irish" lang="ga" hreflang="ga" data-title="Cainníocht" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Cantidade" title="Cantidade – Galician" lang="gl" hreflang="gl" data-title="Cantidade" 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/%EC%96%91_(%ED%81%AC%EA%B8%B0)" title="양 (크기) – Korean" lang="ko" hreflang="ko" data-title="양 (크기)" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AE%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BE" title="मात्रा – Hindi" lang="hi" hreflang="hi" data-title="मात्रा" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kvantiteta_(razdvojba)" title="Kvantiteta (razdvojba) – Croatian" lang="hr" hreflang="hr" data-title="Kvantiteta (razdvojba)" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Besaran" title="Besaran – Indonesian" lang="id" hreflang="id" data-title="Besaran" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Quantit%C3%A0_(filosofia)" title="Quantità (filosofia) – Italian" lang="it" hreflang="it" data-title="Quantità (filosofia)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9B%D7%9E%D7%95%D7%AA" title="כמות – Hebrew" lang="he" hreflang="he" data-title="כמות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AA%E0%B2%B0%E0%B2%BF%E0%B2%AE%E0%B2%BE%E0%B2%A3" title="ಪರಿಮಾಣ – Kannada" lang="kn" hreflang="kn" data-title="ಪರಿಮಾಣ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Idadi" title="Idadi – Swahili" lang="sw" hreflang="sw" data-title="Idadi" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Anpil" title="Anpil – Haitian Creole" lang="ht" hreflang="ht" data-title="Anpil" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BD_(%D3%A9%D0%BB%D1%87%D3%A9%D3%A9)" title="Сан (өлчөө) – Kyrgyz" lang="ky" hreflang="ky" data-title="Сан (өлчөө)" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Quantitas" title="Quantitas – Latin" lang="la" hreflang="la" data-title="Quantitas" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Mennyis%C3%A9g" title="Mennyiség – Hungarian" lang="hu" hreflang="hu" data-title="Mennyiség" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Количество – Macedonian" lang="mk" hreflang="mk" data-title="Количество" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%99%E1%80%90%E1%80%B9%E1%80%90%E1%80%AC" title="မတ္တာ – Burmese" lang="my" hreflang="my" data-title="မတ္တာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Iwiliwili" title="Iwiliwili – Fijian" lang="fj" hreflang="fj" data-title="Iwiliwili" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijian" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Grootheid" title="Grootheid – Dutch" lang="nl" hreflang="nl" data-title="Grootheid" 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/%E9%87%8F" title="量 – Japanese" lang="ja" hreflang="ja" data-title="量" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ilo%C5%9B%C4%87" title="Ilość – Polish" lang="pl" hreflang="pl" data-title="Ilość" 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/Quantidade" title="Quantidade – Portuguese" lang="pt" hreflang="pt" data-title="Quantidade" 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/Cantitate" title="Cantitate – Romanian" lang="ro" hreflang="ro" data-title="Cantitate" 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%9A%D0%BE%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Количество – Russian" lang="ru" hreflang="ru" data-title="Количество" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Quantitati" title="Quantitati – Sicilian" lang="scn" hreflang="scn" data-title="Quantitati" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Quantity" title="Quantity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Quantity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kvantita_(filozofia)" title="Kvantita (filozofia) – Slovak" lang="sk" hreflang="sk" data-title="Kvantita (filozofia)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Koli%C4%8Dina" title="Količina – Slovenian" lang="sl" hreflang="sl" data-title="Količina" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%86%DB%95%D9%86%D8%AF%DB%8E%D8%AA%DB%8C" title="چەندێتی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="چەندێتی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Kvantitet" title="Kvantitet – Serbian" lang="sr" hreflang="sr" data-title="Kvantitet" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Koli%C4%8Dina" title="Količina – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Količina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/M%C3%A4%C3%A4r%C3%A4" title="Määrä – Finnish" lang="fi" hreflang="fi" data-title="Määrä" 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/Kvantitet" title="Kvantitet – Swedish" lang="sv" hreflang="sv" data-title="Kvantitet" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kantidad" title="Kantidad – Tagalog" lang="tl" hreflang="tl" data-title="Kantidad" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tasmekta" title="Tasmekta – Kabyle" lang="kab" hreflang="kab" data-title="Tasmekta" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9C%D0%B8%D2%9B%D0%B4%D0%BE%D1%80" title="Миқдор – Tajik" lang="tg" hreflang="tg" data-title="Миқдор" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Nicelik" title="Nicelik – Turkish" lang="tr" hreflang="tr" data-title="Nicelik" 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%9A%D1%96%D0%BB%D1%8C%D0%BA%D1%96%D1%81%D1%82%D1%8C" title="Кількість – Ukrainian" lang="uk" hreflang="uk" data-title="Кількість" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D9%82%D8%AF%D8%A7%D8%B1" title="مقدار – Urdu" lang="ur" hreflang="ur" data-title="مقدار" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kantidad" title="Kantidad – Waray" lang="war" hreflang="war" data-title="Kantidad" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%87%8F%EF%BC%88%E7%89%A9%E7%90%86%EF%BC%89" title="量（物理） – Wu" lang="wuu" hreflang="wuu" data-title="量（物理）" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%87%8F_(%E7%89%A9%E7%90%86)" title="量 (物理) – Cantonese" lang="yue" hreflang="yue" data-title="量 (物理)" 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srcset="//upload.wikimedia.org/wikipedia/en/thumb/1/1b/Semi-protection-shackle.svg/30px-Semi-protection-shackle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/1/1b/Semi-protection-shackle.svg/40px-Semi-protection-shackle.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div></div> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Property of magnitude or multitude</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 the term in phonetics, see <a href="/wiki/Length_(phonetics)" title="Length (phonetics)">length (phonetics)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_footnotes_needed plainlinks metadata ambox ambox-style ambox-More_footnotes_needed" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article includes a list of <a href="/wiki/Wikipedia:Citing_sources#General_references" title="Wikipedia:Citing sources">general references</a>, but <b>it lacks sufficient corresponding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a></b>.<span class="hide-when-compact"> Please help to <a href="/wiki/Wikipedia:WikiProject_Reliability" title="Wikipedia:WikiProject Reliability">improve</a> this article by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations.</span> <span class="date-container"><i>(<span class="date">July 2010</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p><b>Quantity</b> or <b>amount</b> is a property that can exist as a <a href="/wiki/Counting" title="Counting">multitude</a> or <a href="/wiki/Magnitude_(mathematics)" title="Magnitude (mathematics)">magnitude</a>, which illustrate <a href="/wiki/Discontinuity_(mathematics)" class="mw-redirect" title="Discontinuity (mathematics)">discontinuity</a> and <a href="/wiki/Continuum_(theory)" class="mw-redirect" title="Continuum (theory)">continuity</a>. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a <a href="/wiki/Unit_of_measurement" title="Unit of measurement">unit of measurement</a>. <a href="/wiki/Mass" title="Mass">Mass</a>, <a href="/wiki/Time" title="Time">time</a>, <a href="/wiki/Distance" title="Distance">distance</a>, <a href="/wiki/Heat" title="Heat">heat</a>, and <a href="/wiki/Angle" title="Angle">angle</a> are among the familiar examples of quantitative properties. </p><p>Quantity is among the basic <a href="/wiki/Class_(philosophy)" title="Class (philosophy)">classes</a> of things along with <a href="/wiki/Quality_(philosophy)" title="Quality (philosophy)">quality</a>, <a href="/wiki/Substance_theory" title="Substance theory">substance</a>, change, and relation. Some quantities are such by their inner nature (as number), while others function as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. </p><p>Under the name of multitude comes what is discontinuous and discrete and divisible ultimately into indivisibles, such as: <i>army, fleet, flock, government, company, party, people, mess (military), chorus, crowd</i>, and <i>number</i>; all which are cases of <a href="/wiki/Collective_nouns" class="mw-redirect" title="Collective nouns">collective nouns</a>. Under the name of magnitude comes what is continuous and unified and divisible only into smaller divisibles, such as: <i>matter, mass, energy, liquid, material</i>—all cases of non-collective nouns. </p><p>Along with analyzing its nature and <a href="/wiki/Classification_(general_theory)" class="mw-redirect" title="Classification (general theory)">classification</a>, the issues of quantity involve such closely related topics as dimensionality, equality, proportion, the measurements of quantities, the units of measurements, number and numbering systems, the types of numbers and their relations to each other as numerical ratios. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Background">Background</h2></div> <p>In mathematics, the concept of quantity is an ancient one extending back to the time of <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> and earlier. Aristotle regarded quantity as a fundamental ontological and scientific category. In Aristotle's <a href="/wiki/Ontology" title="Ontology">ontology</a>, quantity or quantum was classified into two different types, which he characterized as follows: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p><i>Quantum</i> means that which is divisible into two or more constituent parts, of which each is by nature a <i>one</i> and a <i>this</i>. A quantum is a plurality if it is numerable, a magnitude if it is measurable. <i>Plurality</i> means that which is divisible potentially into non-continuous parts, magnitude that which is divisible into continuous parts; of magnitude, that which is continuous in one dimension is length; in two breadth, in three depth. Of these, limited plurality is number, limited length is a line, breadth a surface, depth a solid.</p><div class="templatequotecite">— <cite>Aristotle, <i><a href="/wiki/Metaphysics_(Aristotle)" title="Metaphysics (Aristotle)">Metaphysics</a></i>, Book V, Ch. 11-14</cite></div></blockquote> <p>In his <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements"><i>Elements</i></a>, <a href="/wiki/Euclid" title="Euclid">Euclid</a> developed the theory of ratios of magnitudes without studying the nature of magnitudes, as Archimedes, but giving the following significant definitions: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>A magnitude is a <i>part</i> of a magnitude, the less of the greater, when it measures the greater; A <i>ratio</i> is a sort of relation in respect of size between two magnitudes of the same kind.</p><div class="templatequotecite">— <cite>Euclid, <i>Elements</i></cite></div></blockquote> <p>For Aristotle and Euclid, relations were conceived as <a href="/wiki/Integer" title="Integer">whole numbers</a> (Michell, 1993). <a href="/wiki/John_Wallis" title="John Wallis">John Wallis</a> later conceived of ratios of magnitudes as <a href="/wiki/Real_numbers" class="mw-redirect" title="Real numbers">real numbers</a>: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>When a comparison in terms of ratio is made, the resultant ratio often [namely with the exception of the 'numerical genus' itself] leaves the genus of quantities compared, and passes into the numerical genus, whatever the genus of quantities compared may have been.</p><div class="templatequotecite">— <cite>John Wallis, <i>Mathesis Universalis</i></cite></div></blockquote> <p>That is, the ratio of magnitudes of any quantity, whether volume, mass, heat and so on, is a number. Following this, <a href="/wiki/Sir_Isaac_Newton" class="mw-redirect" title="Sir Isaac Newton">Newton</a> then defined number, and the relationship between quantity and number, in the following terms: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>By <i>number</i> we understand not so much a multitude of unities, as the abstracted ratio of any quantity to another quantity of the same kind, which we take for unity.</p><div class="templatequotecite">— <cite>Newton, 1728</cite></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="Structure">Structure</h2></div> <p>Continuous quantities possess a particular structure that was first explicitly characterized by <a href="/wiki/Otto_H%C3%B6lder" title="Otto Hölder">Hölder</a> (1901) as a set of axioms that define such features as <i>identities</i> and <i>relations</i> between magnitudes. In science, quantitative structure is the subject of <a href="/wiki/Empirical_research" title="Empirical research">empirical investigation</a> and cannot be assumed to exist <i><a href="/wiki/A_priori_and_a_posteriori" title="A priori and a posteriori">a priori</a></i> for any given property. The linear <a href="/wiki/Continuum_(theory)" class="mw-redirect" title="Continuum (theory)">continuum</a> represents the prototype of continuous quantitative structure as characterized by Hölder (1901) (translated in Michell & Ernst, 1996). A fundamental feature of any type of quantity is that the relationships of equality or inequality can in principle be stated in comparisons between particular magnitudes, unlike quality, which is marked by likeness, similarity and difference, diversity. Another fundamental feature is additivity. Additivity may involve concatenation, such as adding two lengths A and B to obtain a third A + B. Additivity is not, however, restricted to extensive quantities but may also entail relations between magnitudes that can be established through experiments that permit tests of hypothesized <a href="/wiki/Observable" title="Observable">observable</a> manifestations of the additive relations of magnitudes. Another feature is continuity, on which Michell (1999, p. 51) says of length, as a type of quantitative attribute, "what continuity means is that if any arbitrary length, a, is selected as a unit, then for every positive real number, <i>r</i>, there is a length b such that b = <i>r</i>a". A further generalization is given by the <a href="/wiki/Theory_of_conjoint_measurement" title="Theory of conjoint measurement">theory of conjoint measurement</a>, independently developed by French economist <a href="/wiki/G%C3%A9rard_Debreu" title="Gérard Debreu">Gérard Debreu</a> (1960) and by the American mathematical psychologist <a href="/wiki/R._Duncan_Luce" title="R. Duncan Luce">R. Duncan Luce</a> and statistician <a href="/wiki/John_Tukey" title="John Tukey">John Tukey</a> (1964). </p> <div class="mw-heading mw-heading2"><h2 id="In_mathematics">In mathematics</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Confusing plainlinks metadata ambox ambox-style ambox-confusing" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>may be <a href="/wiki/Wikipedia:Vagueness" title="Wikipedia:Vagueness">confusing or unclear</a> to readers</b>.<span class="hide-when-compact"> Please help <a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarify the section</a>. There might be a discussion about this on <a href="/wiki/Talk:Quantity" title="Talk:Quantity">the talk page</a>.</span> <span class="date-container"><i>(<span class="date">March 2012</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Magnitude (how much) and multitude (how many), the two principal types of quantities, are further divided as mathematical and physical. In formal terms, quantities—their ratios, proportions, order and formal relationships of equality and inequality—are studied by mathematics. The essential part of mathematical quantities consists of having a collection of <a href="/wiki/Variable_(mathematics)" title="Variable (mathematics)">variables</a>, each assuming a <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">set</a> of values. These can be a set of a single quantity, referred to as a <a href="/wiki/Scalar_(mathematics)" title="Scalar (mathematics)">scalar</a> when represented by real numbers, or have multiple quantities as do <a href="/wiki/Euclidean_vector" title="Euclidean vector">vectors</a> and <a href="/wiki/Tensor" title="Tensor">tensors</a>, two kinds of geometric objects. </p><p>The mathematical usage of a quantity can then be varied and so is situationally dependent. Quantities can be used as being <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimal</a>, <a href="/wiki/Argument_of_a_function" title="Argument of a function">arguments of a function</a>, variables in an <a href="/wiki/Expression_(mathematics)" title="Expression (mathematics)">expression</a> (independent or dependent), or probabilistic as in random and <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> quantities. In mathematics, magnitudes and multitudes are also not only two distinct kinds of quantity but furthermore relatable to each other. </p><p><a href="/wiki/Number_theory" title="Number theory">Number theory</a> covers the topics of the <a href="/wiki/Continuous_and_discrete_variables" class="mw-redirect" title="Continuous and discrete variables">discrete quantities</a> as numbers: number systems with their kinds and relations. <a href="/wiki/Geometry" title="Geometry">Geometry</a> studies the issues of spatial magnitudes: straight lines, curved lines, surfaces and solids, all with their respective measurements and relationships. </p><p>A traditional <a href="/wiki/Aristotelian_realist_philosophy_of_mathematics" title="Aristotelian realist philosophy of mathematics">Aristotelian realist philosophy of mathematics</a>, stemming from <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> and remaining popular until the eighteenth century, held that mathematics is the "science of quantity". Quantity was considered to be divided into the discrete (studied by arithmetic) and the continuous (studied by geometry and later <a href="/wiki/Calculus" title="Calculus">calculus</a>). The theory fits reasonably well elementary or school mathematics but less well the abstract topological and algebraic structures of modern mathematics.<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="In_science">In science</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Quantity_(science)" class="mw-redirect" title="Quantity (science)">Quantity (science)</a></div> <p>Establishing quantitative structure and relationships <i>between</i> different quantities is the cornerstone of modern science, especially but not restricted to physical sciences. Physics is fundamentally a quantitative science; chemistry, biology and others are increasingly so. Their progress is chiefly achieved due to rendering the abstract qualities of material entities into physical quantities, by postulating that all material bodies marked by quantitative properties or physical dimensions are subject to some measurements and observations. Setting the units of measurement, physics covers such fundamental quantities as space (length, breadth, and depth) and time, mass and force, temperature, energy, and <a href="/wiki/Quantum" title="Quantum">quanta</a>. </p><p>A distinction has also been made between <a href="/wiki/Intensive_quantity" class="mw-redirect" title="Intensive quantity">intensive quantity</a> and <a href="/wiki/Extensive_quantity" class="mw-redirect" title="Extensive quantity">extensive quantity</a> as two types of quantitative property, state or relation. The magnitude of an <i>intensive quantity</i> does not depend on the size, or extent, of the object or system of which the quantity is a property, whereas magnitudes of an <i>extensive quantity</i> are additive for parts of an entity or subsystems. Thus, magnitude does depend on the extent of the entity or system in the case of extensive quantity. Examples of intensive quantities are <a href="/wiki/Density" title="Density">density</a> and <a href="/wiki/Pressure" title="Pressure">pressure</a>, while examples of extensive quantities are <a href="/wiki/Energy" title="Energy">energy</a>, <a href="/wiki/Volume" title="Volume">volume</a>, and <a href="/wiki/Mass" title="Mass">mass</a>. </p> <div class="mw-heading mw-heading2"><h2 id="In_natural_language">In natural language</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Confusing plainlinks metadata ambox ambox-style ambox-confusing" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>may be <a href="/wiki/Wikipedia:Vagueness" title="Wikipedia:Vagueness">confusing or unclear</a> to readers</b>.<span class="hide-when-compact"> Please help <a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarify the section</a>. There might be a discussion about this on <a href="/wiki/Talk:Quantity" title="Talk:Quantity">the talk page</a>.</span> <span class="date-container"><i>(<span class="date">May 2021</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>In human languages, including <a href="/wiki/English_language" title="English language">English</a>, <a href="/wiki/Grammatical_number" title="Grammatical number">number</a> is a <a href="/wiki/Syntactic_category" title="Syntactic category">syntactic category</a>, along with <a href="/wiki/Person" title="Person">person</a> and <a href="/wiki/Gender" title="Gender">gender</a>. The quantity is expressed by identifiers, definite and indefinite, and <a href="/wiki/Quantifier_(linguistics)" class="mw-redirect" title="Quantifier (linguistics)">quantifiers</a>, definite and indefinite, as well as by three types of <a href="/wiki/Noun" title="Noun">nouns</a>: 1. count unit nouns or countables; 2. <a href="/wiki/Mass_nouns" class="mw-redirect" title="Mass nouns">mass nouns</a>, uncountables, referring to the indefinite, unidentified amounts; 3. nouns of multitude (<a href="/wiki/Collective_noun" title="Collective noun">collective nouns</a>). The word ‘number’ belongs to a noun of multitude standing either for a single entity or for the individuals making the whole. An amount in general is expressed by a special class of words called identifiers, indefinite and definite and quantifiers, definite and indefinite.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (October 2017)">clarification needed</span></a></i>]</sup> The amount may be expressed by: singular form and plural from, ordinal numbers before a count noun singular (first, second, third...), the demonstratives; definite and indefinite numbers and measurements (hundred/hundreds, million/millions), or cardinal numbers before count nouns. The set of language quantifiers covers "a few, a great number, many, several (for count names); a bit of, a little, less, a great deal (amount) of, much (for mass names); all, plenty of, a lot of, enough, more, most, some, any, both, each, either, neither, every, no". For the complex case of unidentified amounts, the parts and examples of a mass are indicated with respect to the following: a measure of a mass (two kilos of rice and twenty bottles of milk or ten pieces of paper); a piece or part of a mass (part, element, atom, item, article, drop); or a shape of a container (a basket, box, case, cup, bottle, vessel, jar). </p> <div class="mw-heading mw-heading2"><h2 id="Further_examples">Further examples</h2></div> <p>Some further examples of quantities are: </p> <ul><li>1.76 litres (<a href="/wiki/Liter" class="mw-redirect" title="Liter">liters</a>) of milk, a continuous quantity</li> <li>2<i>πr</i> metres, where <i>r</i> is the length of a <a href="/wiki/Radius" title="Radius">radius</a> of a <a href="/wiki/Circle" title="Circle">circle</a> expressed in metres (or meters), also a continuous quantity</li> <li>one apple, two apples, three apples, where the number is an integer representing the count of a denumerable collection of objects (apples)</li> <li>500 people (also a type of <a href="/wiki/Count_data" title="Count data">count data</a>)</li> <li>a <i>couple</i> conventionally refers to two objects.</li> <li><i>a few</i> usually refers to an indefinite, but usually small number, greater than one.</li> <li><i>quite a few</i> also refers to an indefinite, but surprisingly (in relation to the context) large number.</li> <li><i>several</i> refers to an indefinite, but usually small, number – usually indefinitely greater than "a few".</li></ul> <div class="mw-heading mw-heading2"><h2 id="Dimensionless_quantity">Dimensionless quantity</h2></div> <div class="excerpt-block"><style data-mw-deduplicate="TemplateStyles:r1066933788">.mw-parser-output .excerpt-hat .mw-editsection-like{font-style:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable dablink excerpt-hat selfref">This section is an excerpt from <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">Dimensionless quantity</a>.<span class="mw-editsection-like plainlinks"><span class="mw-editsection-bracket">[</span><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Dimensionless_quantity&action=edit">edit</a><span class="mw-editsection-bracket">]</span></span></div><div class="excerpt"> <p><a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">Dimensionless quantities</a>, or quantities of dimension one,<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> are quantities <a href="/wiki/Implicitly_defined" class="mw-redirect" title="Implicitly defined">implicitly defined</a> in a manner that prevents their aggregation into <a href="/wiki/Unit_of_measurement" title="Unit of measurement">units of measurement</a>.<sup id="cite_ref-Dimensionless_quantity_SI_Brochure_3-0" class="reference"><a href="#cite_note-Dimensionless_quantity_SI_Brochure-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Typically expressed as <a href="/wiki/Ratio" title="Ratio">ratios</a> that align with another system, these quantities do not necessitate explicitly defined <a href="/wiki/Unit_of_measurement" title="Unit of measurement">units</a>. For instance, <a href="/wiki/Alcohol_by_volume" title="Alcohol by volume">alcohol by volume</a> (ABV) represents a <a href="/wiki/Volumetric_ratio" class="mw-redirect" title="Volumetric ratio">volumetric ratio</a>; its value remains independent of the specific <a href="/wiki/Unit_of_volume" title="Unit of volume">units of volume</a> used, such as in <a href="/wiki/Milliliter" class="mw-redirect" title="Milliliter">milliliters</a> per milliliter (mL/mL). </p><p>The <a href="/wiki/1" title="1">number one</a> is recognized as a dimensionless <a href="/wiki/Base_unit_of_measurement" title="Base unit of measurement">base quantity</a>.<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> <a href="/wiki/Radian" title="Radian">Radians</a> serve as dimensionless units for <a href="/wiki/Angle" title="Angle">angular measurements</a>, derived from the universal ratio of 2π times the <a href="/wiki/Radius" title="Radius">radius</a> of a circle being equal to its circumference.<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> </p> Dimensionless quantities play a crucial role serving as <a href="/wiki/Parameter" title="Parameter">parameters</a> in <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a> in various technical disciplines. In <a href="/wiki/Calculus" title="Calculus">calculus</a>, concepts like the unitless ratios in <a href="/wiki/Limits_of_integration" title="Limits of integration">limits</a> or <a href="/wiki/Derivative" title="Derivative">derivatives</a> often involve dimensionless quantities. In <a href="/wiki/Differential_geometry" title="Differential geometry">differential geometry</a>, the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the <a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds number</a> in <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>,<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> the <a href="/wiki/Fine-structure_constant" title="Fine-structure constant">fine-structure constant</a> in <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>,<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> and the <a href="/wiki/Lorentz_factor" title="Lorentz factor">Lorentz factor</a> in <a href="/wiki/Special_relativity" title="Special relativity">relativity</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, <a href="/wiki/Equation_of_state" title="Equation of state">state properties</a> and ratios such as <a href="/wiki/Mole_fraction" title="Mole fraction">mole fractions</a> <a href="/wiki/Concentration_ratio" title="Concentration ratio">concentration ratios</a> are dimensionless.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></div></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <ul><li><a href="/wiki/Physical_quantity" title="Physical quantity">Physical quantity</a></li> <li><a href="/wiki/Quantification_(science)" title="Quantification (science)">Quantification (science)</a></li> <li><a href="/wiki/Observable_quantity" class="mw-redirect" title="Observable quantity">Observable quantity</a></li> <li><a href="/wiki/Numerical_value_equation" class="mw-redirect" title="Numerical value equation">Numerical value equation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></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"> <div class="mw-references-wrap"><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="CITEREFFranklin2014" class="citation book cs1"><a href="/wiki/James_Franklin_(philosopher)" title="James Franklin (philosopher)">Franklin, James</a> (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0YKEAwAAQBAJ"><i>An Aristotelian Realist Philosophy of Mathematics</i></a>. Basingstoke: Palgrave Macmillan. p. 31-2. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781137400734" title="Special:BookSources/9781137400734"><bdi>9781137400734</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Aristotelian+Realist+Philosophy+of+Mathematics&rft.place=Basingstoke&rft.pages=31-2&rft.pub=Palgrave+Macmillan&rft.date=2014&rft.isbn=9781137400734&rft.aulast=Franklin&rft.aufirst=James&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D0YKEAwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantity" 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.iso.org/sites/JCGM/VIM/JCGM_200e_FILES/MAIN_JCGM_200e/01_e.html#L_1_8">"1.8 (1.6) quantity of dimension one dimensionless quantity"</a>. <i>International vocabulary of metrology — Basic and general concepts and associated terms (VIM)</i>. <a href="/wiki/International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a>. 2008<span class="reference-accessdate">. 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Rutgers University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8135-2898-4" title="Special:BookSources/978-0-8135-2898-4"><bdi>978-0-8135-2898-4</bdi></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+the+Circle%3A+Mathematical+Reasoning+and+the+Physical+Universe&rft.pub=Rutgers+University+Press&rft.date=1999&rft.isbn=978-0-8135-2898-4&rft.aulast=Zebrowski&rft.aufirst=Ernest&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D2twRfiUwkxYC%26dq%3Duniversal%2Bratio%2Bof%2B2%25CF%2580%2Btimes%2Bthe%2Bradius%2Bof%2Ba%2Bcircle%2Bbeing%2Bequal%2Bto%2Bits%2Bcircumference%26pg%3DPR9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantity" 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="CITEREFCengelCimbala2013" class="citation book cs1">Cengel, Yunus; Cimbala, John (2013-10-16). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=LIZvEAAAQBAJ&dq=calculus,+concepts+like+the+unitless+ratios+in+limits+or+derivatives+often+involve+dimensionless+quantities&pg=PP1"><i>EBOOK: Fluid Mechanics Fundamentals and Applications (SI units)</i></a>. McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-717359-3" title="Special:BookSources/978-0-07-717359-3"><bdi>978-0-07-717359-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=EBOOK%3A+Fluid+Mechanics+Fundamentals+and+Applications+%28SI+units%29&rft.pub=McGraw+Hill&rft.date=2013-10-16&rft.isbn=978-0-07-717359-3&rft.aulast=Cengel&rft.aufirst=Yunus&rft.au=Cimbala%2C+John&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DLIZvEAAAQBAJ%26dq%3Dcalculus%2C%2Bconcepts%2Blike%2Bthe%2Bunitless%2Bratios%2Bin%2Blimits%2Bor%2Bderivatives%2Boften%2Binvolve%2Bdimensionless%2Bquantities%26pg%3DPP1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantity" 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="CITEREFWebbKingMurphyFlambaum2011" class="citation journal cs1">Webb, J. 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New York: Johnson Reprint Corp.</li> <li>Wallis, J. <i>Mathesis universalis</i> (as quoted in Klein, 1968).</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></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 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