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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geschiedenis"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Geschiedenis</span> </div> </a> <ul id="toc-Geschiedenis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Getallenlijn" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Getallenlijn"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Getallenlijn</span> </div> </a> <ul id="toc-Getallenlijn-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symbolen" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Symbolen"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Symbolen</span> </div> </a> <ul id="toc-Symbolen-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="Inhoud" 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="Inhoudsopgave omschakelen" > <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">Inhoudsopgave omschakelen</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">Negatief getal: verschil tussen versies</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="Ga naar een artikel in een andere taal. Beschikbaar in 68 talen" > <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-68" 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">68 talen</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%B3%D8%A7%D9%84%D8%A8" title="عدد سالب – Arabisch" lang="ar" hreflang="ar" data-title="عدد سالب" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/N%C3%BAmberu_negativu" title="Númberu negativu – Asturisch" lang="ast" hreflang="ast" data-title="Númberu negativu" data-language-autonym="Asturianu" data-language-local-name="Asturisch" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/M%C9%99nfi_%C9%99d%C9%99dl%C9%99r" title="Mənfi ədədlər – Azerbeidzjaans" lang="az" hreflang="az" data-title="Mənfi ədədlər" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B4%D0%BC%D0%BE%D1%9E%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Адмоўны лік – Belarussisch" lang="be" hreflang="be" data-title="Адмоўны лік" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D0%B4%D0%BC%D0%BE%D1%9E%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Адмоўны лік – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Адмоўны лік" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%8B%E0%A6%A3%E0%A6%BE%E0%A6%A4%E0%A7%8D%E0%A6%AE%E0%A6%95_%E0%A6%93_%E0%A6%85%E0%A6%8B%E0%A6%A3%E0%A6%BE%E0%A6%A4%E0%A7%8D%E0%A6%AE%E0%A6%95_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="ঋণাত্মক ও অঋণাত্মক সংখ্যা – Bengaals" lang="bn" hreflang="bn" data-title="ঋণাত্মক ও অঋণাত্মক সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Niver_leiel" title="Niver leiel – Bretons" lang="br" hreflang="br" data-title="Niver leiel" data-language-autonym="Brezhoneg" data-language-local-name="Bretons" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Negativan_broj" title="Negativan broj – Bosnisch" lang="bs" hreflang="bs" data-title="Negativan broj" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D2%BA%D3%A9%D3%A9%D1%80%D0%B3%D1%8D_%D1%82%D0%BE%D0%BE" title="Һөөргэ тоо – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Һөөргэ тоо" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_negatiu" title="Nombre negatiu – Catalaans" lang="ca" hreflang="ca" data-title="Nombre negatiu" data-language-autonym="Català" data-language-local-name="Catalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95_%D9%86%DB%95%D8%B1%DB%8E%D9%86%DB%8C%DB%8C%DB%95%DA%A9%D8%A7%D9%86" title="ژمارە نەرێنییەکان – Soranî" lang="ckb" hreflang="ckb" data-title="ژمارە نەرێنییەکان" data-language-autonym="کوردی" data-language-local-name="Soranî" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%B8%D0%BD%D1%83%D1%81%D0%BB%C4%83_%D1%85%D0%B8%D1%81%D0%B5%D0%BF" title="Минуслă хисеп – Tsjoevasjisch" lang="cv" hreflang="cv" data-title="Минуслă хисеп" data-language-autonym="Чӑвашла" data-language-local-name="Tsjoevasjisch" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhif_negatif" title="Rhif negatif – Welsh" lang="cy" hreflang="cy" data-title="Rhif negatif" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Negative_Zahl" title="Negative Zahl – Duits" lang="de" hreflang="de" data-title="Negative Zahl" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CE%BD%CE%B7%CF%84%CE%B9%CE%BA%CF%8C%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82" title="Αρνητικός αριθμός – Grieks" lang="el" hreflang="el" data-title="Αρνητικός αριθμός" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Negative_number" title="Negative number – Engels" lang="en" hreflang="en" data-title="Negative number" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_negativo" title="Número negativo – Spaans" lang="es" hreflang="es" data-title="Número negativo" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki_negatibo" title="Zenbaki negatibo – Baskisch" lang="eu" hreflang="eu" data-title="Zenbaki negatibo" data-language-autonym="Euskara" data-language-local-name="Baskisch" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D9%85%D9%86%D9%81%DB%8C" title="عدد منفی – Perzisch" lang="fa" hreflang="fa" data-title="عدد منفی" data-language-autonym="فارسی" data-language-local-name="Perzisch" 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/Nombre_n%C3%A9gatif" title="Nombre négatif – Frans" lang="fr" hreflang="fr" data-title="Nombre négatif" data-language-autonym="Français" data-language-local-name="Frans" 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/N%C3%BAmero_negativo" title="Número negativo – Galicisch" lang="gl" hreflang="gl" data-title="Número negativo" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%97%D7%99%D7%95%D7%91%D7%99%D7%99%D7%9D_%D7%95%D7%A9%D7%9C%D7%99%D7%9C%D7%99%D7%99%D7%9D" title="מספרים חיוביים ושליליים – Hebreeuws" lang="he" hreflang="he" data-title="מספרים חיוביים ושליליים" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%8B%E0%A4%A3%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%AE%E0%A4%95_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="ऋणात्मक संख्या – Hindi" lang="hi" hreflang="hi" data-title="ऋणात्मक संख्या" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%A1%D6%81%D5%A1%D5%BD%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A9%D5%AB%D5%BE" title="Բացասական թիվ – Armeens" lang="hy" hreflang="hy" data-title="Բացասական թիվ" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Lumur_negatif" title="Lumur negatif – Iban" lang="iba" hreflang="iba" data-title="Lumur negatif" data-language-autonym="Jaku Iban" data-language-local-name="Iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan_riil_negatif" title="Bilangan riil negatif – Indonesisch" lang="id" hreflang="id" data-title="Bilangan riil negatif" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Neikv%C3%A6%C3%B0_tala" title="Neikvæð tala – IJslands" lang="is" hreflang="is" data-title="Neikvæð tala" data-language-autonym="Íslenska" data-language-local-name="IJslands" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_negativo" title="Numero negativo – Italiaans" lang="it" hreflang="it" data-title="Numero negativo" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%AD%A3%E3%81%AE%E6%95%B0%E3%81%A8%E8%B2%A0%E3%81%AE%E6%95%B0" title="正の数と負の数 – Japans" lang="ja" hreflang="ja" data-title="正の数と負の数" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A3%E1%83%90%E1%83%A0%E1%83%A7%E1%83%9D%E1%83%A4%E1%83%98%E1%83%97%E1%83%98_%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%98" title="უარყოფითი რიცხვი – Georgisch" lang="ka" hreflang="ka" data-title="უარყოფითი რიცხვი" data-language-autonym="ქართული" data-language-local-name="Georgisch" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%85%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%93%E1%9E%A2%E1%9E%9C%E1%9E%B7%E1%9E%87%E1%9F%92%E1%9E%87%E1%9E%98%E1%9E%B6%E1%9E%93" title="ចំនួនអវិជ្ជមាន – Khmer" lang="km" hreflang="km" data-title="ចំនួនអវិជ្ជមាន" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%8C%EC%88%98" title="음수 – Koreaans" lang="ko" hreflang="ko" data-title="음수" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Isa_miiba" title="Isa miiba – Malagassisch" lang="mg" hreflang="mg" data-title="Isa miiba" data-language-autonym="Malagasy" data-language-local-name="Malagassisch" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%8B%E0%B4%A3%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF" title="ഋണസംഖ്യ – Malayalam" lang="ml" hreflang="ml" data-title="ഋണസംഖ്യ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%8B%E0%A4%A3_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="ऋण संख्या – Marathi" lang="mr" hreflang="mr" data-title="ऋण संख्या" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Nombor_negatif" title="Nombor negatif – Maleis" lang="ms" hreflang="ms" data-title="Nombor negatif" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Numru_negattiv" title="Numru negattiv – Maltees" lang="mt" hreflang="mt" data-title="Numru negattiv" data-language-autonym="Malti" data-language-local-name="Maltees" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Negativt_tal" title="Negativt tal – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Negativt tal" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Negativt_tall" title="Negativt tall – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Negativt tall" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Nombre_negatiu" title="Nombre negatiu – Occitaans" lang="oc" hreflang="oc" data-title="Nombre negatiu" data-language-autonym="Occitan" data-language-local-name="Occitaans" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Lakkoofsa_wawwee" title="Lakkoofsa wawwee – Afaan Oromo" lang="om" hreflang="om" data-title="Lakkoofsa wawwee" data-language-autonym="Oromoo" data-language-local-name="Afaan Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Znak_liczby" title="Znak liczby – Pools" lang="pl" hreflang="pl" data-title="Znak liczby" data-language-autonym="Polski" data-language-local-name="Pools" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%86%DB%8C%DA%AF%DB%8C%D9%B9%D9%88_%D9%86%D9%85%D8%A8%D8%B1" title="نیگیٹو نمبر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="نیگیٹو نمبر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero_negativo" title="Número negativo – Portugees" lang="pt" hreflang="pt" data-title="Número negativo" data-language-autonym="Português" data-language-local-name="Portugees" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_negativ" title="Număr negativ – Roemeens" lang="ro" hreflang="ro" data-title="Număr negativ" data-language-autonym="Română" data-language-local-name="Roemeens" 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%9E%D1%82%D1%80%D0%B8%D1%86%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Отрицательное число – Russisch" lang="ru" hreflang="ru" data-title="Отрицательное число" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9C%D1%8D%D0%BB%D0%B4%D1%8C%D1%8D%D1%85%D1%82%D1%8D%D1%8D%D1%85_%D1%87%D1%8B%D1%8B%D2%BB%D1%8B%D0%BB%D0%B0%D0%BB%D0%B0%D1%80" title="Мэлдьэхтээх чыыһылалар – Jakoets" lang="sah" hreflang="sah" data-title="Мэлдьэхтээх чыыһылалар" data-language-autonym="Саха тыла" data-language-local-name="Jakoets" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Negative_number" title="Negative number – Simple English" lang="en-simple" hreflang="en-simple" data-title="Negative number" 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/Z%C3%A1porn%C3%A9_%C4%8D%C3%ADslo" title="Záporné číslo – Slowaaks" lang="sk" hreflang="sk" data-title="Záporné číslo" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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/Negativno_%C5%A1tevilo" title="Negativno število – Sloveens" lang="sl" hreflang="sl" data-title="Negativno število" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Nhamba_Hwaradada" title="Nhamba Hwaradada – Shona" lang="sn" hreflang="sn" data-title="Nhamba Hwaradada" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Thiinada_taban" title="Thiinada taban – Somalisch" lang="so" hreflang="so" data-title="Thiinada taban" data-language-autonym="Soomaaliga" data-language-local-name="Somalisch" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9D%D0%B5%D0%B3%D0%B0%D1%82%D0%B8%D0%B2%D0%B0%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Негативан број – Servisch" lang="sr" hreflang="sr" data-title="Негативан број" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Negativa_tal" title="Negativa tal – Zweeds" lang="sv" hreflang="sv" data-title="Negativa tal" data-language-autonym="Svenska" data-language-local-name="Zweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Namba_hasi" title="Namba hasi – Swahili" lang="sw" hreflang="sw" data-title="Namba hasi" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8E%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AF%8D%E0%AE%AE_%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="எதிர்ம எண் – Tamil" lang="ta" hreflang="ta" data-title="எதிர்ம எண்" 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%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%A5%E0%B8%9A%E0%B9%81%E0%B8%A5%E0%B8%B0%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%84%E0%B8%A1%E0%B9%88%E0%B9%80%E0%B8%9B%E0%B9%87%E0%B8%99%E0%B8%A5%E0%B8%9A" title="จำนวนลบและจำนวนไม่เป็นลบ – Thai" lang="th" hreflang="th" data-title="จำนวนลบและจำนวนไม่เป็นลบ" 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/Negatif_say%C4%B1" title="Negatif sayı – Turks" lang="tr" hreflang="tr" data-title="Negatif sayı" data-language-autonym="Türkçe" data-language-local-name="Turks" 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%92%D1%96%D0%B4%27%D1%94%D0%BC%D0%BD%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Від'ємне число – Oekraïens" lang="uk" hreflang="uk" data-title="Від'ємне число" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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%86%D9%81%DB%8C_%D8%B9%D8%AF%D8%AF" title="منفی عدد – Urdu" lang="ur" hreflang="ur" data-title="منفی عدد" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Manfiy_sonlar" title="Manfiy sonlar – Oezbeeks" lang="uz" hreflang="uz" data-title="Manfiy sonlar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91_%C3%A2m" title="Số âm – Vietnamees" lang="vi" hreflang="vi" data-title="Số âm" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%B4%9F%E6%95%B0" title="负数 – Wuyu" lang="wuu" hreflang="wuu" data-title="负数" data-language-autonym="吴语" data-language-local-name="Wuyu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%AD%D1%81%D1%80%D0%B5%D0%B3%D2%AF_%D1%82%D0%BE%D0%B9%D0%B3" title="Эсрегү тойг – Kalmuks" lang="xal" hreflang="xal" data-title="Эсрегү тойг" data-language-autonym="Хальмг" data-language-local-name="Kalmuks" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B4%B0%E2%B5%8E%E2%B4%B9%E2%B4%B0%E2%B5%8F_%E2%B4%B0%E2%B5%8E%E2%B4%B0%E2%B4%BD%E2%B4%BD%E2%B4%B0%E2%B5%99" title="ⴰⵎⴹⴰⵏ ⴰⵎⴰⴽⴽⴰⵙ – Standaard Marokkaanse Tamazight" lang="zgh" hreflang="zgh" data-title="ⴰⵎⴹⴰⵏ ⴰⵎⴰⴽⴽⴰⵙ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="Standaard Marokkaanse Tamazight" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B4%9F%E6%95%B0" title="负数 – Chinees" lang="zh" hreflang="zh" data-title="负数" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E8%B2%A0%E6%95%B8" title="負數 – Klassiek Chinees" lang="lzh" hreflang="lzh" data-title="負數" data-language-autonym="文言" data-language-local-name="Klassiek Chinees" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%B2%A0%E6%95%B8" title="負數 – Kantonees" lang="yue" hreflang="yue" data-title="負數" data-language-autonym="粵語" data-language-local-name="Kantonees" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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title="Gebruiker:YoshiDaSilva" data-mw-revid="41427043"><bdi>YoshiDaSilva</bdi></a> <span class="mw-usertoollinks">(<a href="/wiki/Overleg_gebruiker:YoshiDaSilva" class="mw-usertoollinks-talk" title="Overleg gebruiker:YoshiDaSilva">overleg</a> | <a href="/wiki/Speciaal:Bijdragen/YoshiDaSilva" class="mw-usertoollinks-contribs" title="Speciaal:Bijdragen/YoshiDaSilva">bijdragen</a>)</span><div class="mw-diff-usermetadata"><div class="mw-diff-userroles"><a href="/wiki/Wikipedia:Uitgebreid_bevestigde_gebruikers" class="mw-redirect" title="Wikipedia:Uitgebreid bevestigde gebruikers">uitgebreid bevestigde gebruikers</a></div><div class="mw-diff-usereditcount"><span>13.870</span> bewerkingen</div></div></div><div id="mw-diff-otitle3"><abbr class="minoredit" title="Dit is een kleine bewerking">k</abbr> <span class="comment comment--without-parentheses">Wijzigingen door <a href="/wiki/Speciaal:Bijdragen/82.93.15.37" title="Speciaal:Bijdragen/82.93.15.37">82.93.15.37</a> (<a href="/wiki/Overleg_gebruiker:82.93.15.37" title="Overleg gebruiker:82.93.15.37">Overleg</a>) hersteld tot de laatste versie door <a href="/wiki/Gebruiker:Woeterman_94" title="Gebruiker:Woeterman 94">Woeterman 94</a></span></div><div id="mw-diff-otitle5"></div><div id="mw-diff-otitle4"><a href="/w/index.php?title=Negatief_getal&diff=prev&oldid=41427043" title="Negatief getal" id="differences-prevlink">← Oudere bewerking</a></div></td> <td colspan="2" class="diff-ntitle diff-side-added"><div id="mw-diff-ntitle1"><strong><a href="/w/index.php?title=Negatief_getal&oldid=64271977" title="Negatief getal">Huidige versie van 8 mei 2023 om 21:43</a> <span class="mw-diff-edit"><a href="/w/index.php?title=Negatief_getal&action=edit" title="Negatief getal">bewerken</a></span><span class="mw-diff-timestamp" data-timestamp="2023-05-08T20:43:22Z"></span> <span class="mw-diff-undo"><a href="/w/index.php?title=Negatief_getal&action=edit&undoafter=41427043&undo=64271977" title="Met "ongedaan maken" draait u deze bewerking terug en komt in het bewerkingsvenster. U kunt in de bewerkingssamenvatting een reden opgeven.">ongedaan maken</a></span></strong></div><div id="mw-diff-ntitle2"><a href="/wiki/Gebruiker:ChristiaanPR" class="mw-userlink" title="Gebruiker:ChristiaanPR" data-mw-revid="64271977"><bdi>ChristiaanPR</bdi></a> <span class="mw-usertoollinks">(<a href="/wiki/Overleg_gebruiker:ChristiaanPR" class="mw-usertoollinks-talk" title="Overleg gebruiker:ChristiaanPR">overleg</a> | <a href="/wiki/Speciaal:Bijdragen/ChristiaanPR" class="mw-usertoollinks-contribs" title="Speciaal:Bijdragen/ChristiaanPR">bijdragen</a>)</span><div class="mw-diff-usermetadata"><div class="mw-diff-userroles"><a href="/wiki/Wikipedia:Uitgebreid_bevestigde_gebruikers" class="mw-redirect" title="Wikipedia:Uitgebreid bevestigde gebruikers">uitgebreid bevestigde gebruikers</a>, <a href="/wiki/Wikipedia:Uitgezonderden_van_IP-adresblokkades" title="Wikipedia:Uitgezonderden van IP-adresblokkades">Uitgezonderden van IP-adresblokkades</a></div><div class="mw-diff-usereditcount"><span>36.333</span> bewerkingen</div></div></div><div id="mw-diff-ntitle3"><span class="comment mw-comment-none">Geen bewerkingssamenvatting</span></div><div id="mw-diff-ntitle5"></div><div id="mw-diff-ntitle4"> </div></td> </tr><tr><td colspan="4" class="diff-multi" lang="nl">(27 tussenliggende versies door 18 gebruikers niet weergegeven)</td></tr><tr> <td colspan="2" class="diff-lineno">Regel 1:</td> <td colspan="2" class="diff-lineno">Regel 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>Een '''negatief''' [[<del class="diffchange diffchange-inline">getal</del> (wiskunde)|getal]]<del class="diffchange diffchange-inline"> is in Nederland een getal</del> dat kleiner is dan [[0 (getal)|0]]. <del class="diffchange diffchange-inline">In</del> <del class="diffchange diffchange-inline">België</del> <del class="diffchange diffchange-inline">noemt</del> <del class="diffchange diffchange-inline">men</del> <del class="diffchange diffchange-inline">een</del> <del class="diffchange diffchange-inline">dergelijk</del> <del class="diffchange diffchange-inline">getal</del> <del class="diffchange diffchange-inline">een</del> <del class="diffchange diffchange-inline">'''strikt</del> negatief''<del class="diffchange diffchange-inline">' getal</del>.</div></td> <td class="diff-marker" data-marker="+"></td> <td class="diff-addedline diff-side-added"><div>Een '''negatief<ins class="diffchange diffchange-inline"> getal</ins>'''<ins class="diffchange diffchange-inline"> is in het</ins> [[<ins class="diffchange diffchange-inline">Nederlands]] een [[Getal</ins> (wiskunde)|getal]] dat kleiner is dan [[0 (getal)|0]].<ins class="diffchange diffchange-inline"><ref>[[Van</ins> <ins class="diffchange diffchange-inline">Dale</ins> <ins class="diffchange diffchange-inline">Groot</ins> <ins class="diffchange diffchange-inline">woordenboek</ins> <ins class="diffchange diffchange-inline">van</ins> <ins class="diffchange diffchange-inline">de</ins> <ins class="diffchange diffchange-inline">Nederlandse</ins> <ins class="diffchange diffchange-inline">taal|Van</ins> <ins class="diffchange diffchange-inline">Dale</ins> <ins class="diffchange diffchange-inline">Groot</ins> <ins class="diffchange diffchange-inline">woordenboek]]. [https://www.vandale.nl/gratis-woordenboek/nederlands/betekenis/</ins>negatief<ins class="diffchange diffchange-inline">#.ZFi_eHZBybg Betekenis </ins>'<ins class="diffchange diffchange-inline">negatief</ins>'<ins class="diffchange diffchange-inline">]</ins>.<ins class="diffchange diffchange-inline"></ref></ins></div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_4_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_1_0_rhs"></a>Een negatief getal is het [[<ins class="diffchange diffchange-inline">Tegengestelde</ins> (wiskunde)|tegengestelde]] van het overeenkomstige <ins class="diffchange diffchange-inline">[[Positief</ins> <ins class="diffchange diffchange-inline">getal|</ins>positieve getal<ins class="diffchange diffchange-inline">]]</ins>, wat inhoudt dat [[optellen]] van<ins class="diffchange diffchange-inline"> deze</ins> beide getallen als [[<ins class="diffchange diffchange-inline">Sommatie</ins>|som]] het getal [[0 (getal)|0]] oplevert<ins class="diffchange diffchange-inline">. Negatieve getallen zijn te herkennen aan het [[Minteken|minteken −]], dat voor het overeenkomstige positieve getal is geplaatst</ins>.</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_37_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_3_0_rhs"></a>== Geschiedenis ==</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_1_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_4_0_lhs"></a>Een<del class="diffchange diffchange-inline"> (strikt)</del> negatief getal is het [[<del class="diffchange diffchange-inline">tegengestelde</del> (wiskunde)|tegengestelde]] van het overeenkomstige <del class="diffchange diffchange-inline">(strikt)</del> positieve getal, wat inhoudt dat [[optellen<del class="diffchange diffchange-inline">|optelling</del>]] van beide getallen als [[<del class="diffchange diffchange-inline">sommatie</del>|som]] het getal [[0 (getal)|0]] oplevert.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_38_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_5_0_rhs"></a>Negatieve getallen verschijnen voor het eerst in de geschiedenis in [[<ins class="diffchange diffchange-inline">Negen</ins> hoofdstukken <ins class="diffchange diffchange-inline">over</ins> de <ins class="diffchange diffchange-inline">rekenkunde</ins>]]<ins class="diffchange diffchange-inline">,</ins> ''Jiu zhang suan-shu'', dat in zijn huidige vorm uit de periode van de [[Han-dynastie]] 202 v.Chr. - 220 n.Chr. <ins class="diffchange diffchange-inline">komt</ins>, maar dat ook veel ouder materiaal kan bevatten. <ins class="diffchange diffchange-inline">In de</ins> Negen hoofdstukken <ins class="diffchange diffchange-inline">worden</ins> positieve [[coëfficiënt]]en <ins class="diffchange diffchange-inline">met</ins> <ins class="diffchange diffchange-inline">rode</ins> <ins class="diffchange diffchange-inline">telstaafjes</ins> <ins class="diffchange diffchange-inline">en</ins> negatieve coëfficiënten <ins class="diffchange diffchange-inline">met</ins> <ins class="diffchange diffchange-inline">zwarte</ins> <ins class="diffchange diffchange-inline">staafjes aangegeven</ins>.<ref><ins class="diffchange diffchange-inline">R</ins> Temple<ins class="diffchange diffchange-inline">.</ins> The Genius of China: 3000 Years of Science, Discovery, and Invention<ins class="diffchange diffchange-inline">, 1986</ins>. <ins class="diffchange diffchange-inline">met</ins> een <ins class="diffchange diffchange-inline">voorwoord</ins> <ins class="diffchange diffchange-inline">van</ins> [[Joseph Needham]]<ins class="diffchange diffchange-inline">,</ins> <ins class="diffchange diffchange-inline">blz</ins> <ins class="diffchange diffchange-inline">141</ins> <ins class="diffchange diffchange-inline">{{</ins>ISBN<ins class="diffchange diffchange-inline">|</ins>0671620282<ins class="diffchange diffchange-inline">}}</ins></ref> Dit is <ins class="diffchange diffchange-inline">dus</ins> tegengesteld aan de hedendaagse gewoonte in de financiële wereld om rode cijfers te gebruiken om negatieve en zwarte cijfers om positieve bedragen weer te geven. De Chinezen waren ook in staat om simultane vergelijkingen met negatieve getallen op te lossen.</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_41_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_7_0_rhs"></a><ins class="diffchange diffchange-inline">Negatieve</ins> <ins class="diffchange diffchange-inline">oplossingen</ins> <ins class="diffchange diffchange-inline">voor</ins> <ins class="diffchange diffchange-inline">problemen</ins> <ins class="diffchange diffchange-inline">werden</ins> <ins class="diffchange diffchange-inline">lange</ins> <ins class="diffchange diffchange-inline">tijd</ins> als verkeerd beschouwd. <ins class="diffchange diffchange-inline">De</ins> [[<ins class="diffchange diffchange-inline">Oude</ins> <ins class="diffchange diffchange-inline">Griekenland</ins>|<ins class="diffchange diffchange-inline">Oudgriekse</ins>]] wiskundige [[Diophantus]]<ins class="diffchange diffchange-inline"> verwees in het Hellenistische Egypte</ins> in zijn [[Arithmetica]] in de [[<ins class="diffchange diffchange-inline">3e</ins> eeuw|derde eeuw n.Chr.]] naar een [[<ins class="diffchange diffchange-inline">Vergelijking</ins> (wiskunde)|vergelijking]] die [[Equivalentierelatie|gelijkwaardig]] was aan <ins class="diffchange diffchange-inline"><math>4x</ins>+20=0<ins class="diffchange diffchange-inline"></math></ins> <ins class="diffchange diffchange-inline">en vond dat een absurde vergelijking. Deze</ins> vergelijking heeft een negatieve [[Oplossen van vergelijkingen|oplossing]].</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>Negatieve getallen zijn te herkennen aan een [[minteken]] (−), dat voor het overeenkomstige [[positief getal|positieve]] getal is geplaatst.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_45_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_10_0_rhs"></a><ins class="diffchange diffchange-inline">Negatieve getallen werden in</ins> de 7e eeuw na Christus in [[India]] gebruikt om [[<ins class="diffchange diffchange-inline">Schuld</ins> (<ins class="diffchange diffchange-inline">debet</ins>)|<ins class="diffchange diffchange-inline">schulden</ins>]] weer te geven. De [[Indiase wiskunde|Indiase wiskundige]] [[Brahmagupta]] <ins class="diffchange diffchange-inline">besprak</ins> in <ins class="diffchange diffchange-inline">zijn </ins>[[Brahmasphuta-siddhanta]]<ins class="diffchange diffchange-inline">,</ins> geschreven in 628 n.Chr.<ins class="diffchange diffchange-inline">,</ins> het gebruik van negatieve getallen om zo de algemene vorm van een [[vierkantsvergelijking]] te produceren, die ook nu nog in gebruik is. Hij vond ook negatieve oplossingen van <ins class="diffchange diffchange-inline">deze vierkantsvergelijkingen</ins> en gaf regels met betrekking tot [[<ins class="diffchange diffchange-inline">Basisoperatie (wiskunde)|basisoperaties</ins>]], waarbij negatieve getallen en ook het getal [[0 (getal)|nul]] deel van uitmaakten, zoals 'Een schuld afgetrokken van het niets wordt een krediet, een krediet afgetrokken van het niets wordt een schuld.' Hij noemde positieve getallen <ins class="diffchange diffchange-inline">'</ins>fortuinen<ins class="diffchange diffchange-inline">'</ins>, nul <ins class="diffchange diffchange-inline">'</ins>een [[cijfer]]<ins class="diffchange diffchange-inline">'</ins> en negatieve getallen <ins class="diffchange diffchange-inline">'</ins>schulden<ins class="diffchange diffchange-inline">'</ins>.<ref>Colva M. Roney-Dougal, docent in de zuivere wiskunde aan de [[Universiteit van St Andrews]] verklaarde dit op [[<ins class="diffchange diffchange-inline">9</ins> <ins class="diffchange diffchange-inline">maart]]</ins> <ins class="diffchange diffchange-inline">[[2006</ins>]]<ins class="diffchange diffchange-inline"> op het</ins> programma In Our Time <ins class="diffchange diffchange-inline">van de</ins> [[<ins class="diffchange diffchange-inline">BBC</ins> <ins class="diffchange diffchange-inline">Radio</ins> <ins class="diffchange diffchange-inline">4</ins>]].</ref><ref>Knowledge Transfer and Perceptions of the Passage of Time, ICEE-2002 Keynote Address door Colin Adamson-Macedo <ins class="diffchange diffchange-inline"><br> </ins>Referring again to Brahmagupta's great work, all the necessary rules for algebra, including the 'rule of signs', were stipulated, but in a form which used the language and imagery of commerce and the market place. Thus 'dhana'<ins class="diffchange diffchange-inline">,</ins> fortunes<ins class="diffchange diffchange-inline">,</ins> is used to represent positive numbers, whereas 'rina'<ins class="diffchange diffchange-inline">,</ins> debts<ins class="diffchange diffchange-inline">,</ins> were negative.<ins class="diffchange diffchange-inline"> <br></ins></div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>==De getallenlijn==</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_49_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_12_0_rhs"></a>Opnieuw verwijzend naar het grote werk van Brahmagupta, alle nodige regels voor de algebra, met inbegrip van de 'tekenregels', waren hierin opgesteld, maar in een vorm die de taal en de beeldtaal van de handel en de markt gebruikte. Dus wordt 'dhana'<ins class="diffchange diffchange-inline">,</ins> fortuinen<ins class="diffchange diffchange-inline">,</ins> gebruikt om positieve getallen weer te geven, terwijl 'rina'<ins class="diffchange diffchange-inline">,</ins> schulden<ins class="diffchange diffchange-inline">',</ins> voor negatieve getallen wordt gebruikt.</ref></div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_25_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_13_0_lhs"></a>{{Zie hoofdartikel|Getallenlijn}}</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_50_1_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_15_0_rhs"></a>Kennis van de negatieve getallen bereikte dankzij [[Latijn]]se vertalingen van Arabische en <ins class="diffchange diffchange-inline">[[</ins>Indiase<ins class="diffchange diffchange-inline"> wiskunde|Indiase]]</ins> werken <ins class="diffchange diffchange-inline">[[Europa</ins> <ins class="diffchange diffchange-inline">(werelddeel)|</ins>Europa<ins class="diffchange diffchange-inline">]]</ins>.</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_29_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_16_0_lhs"></a>De relatie tussen negatieve getallen, positieve getallen en nul wordt vaak grafisch afgebeeld in de vorm van een <del class="diffchange diffchange-inline">''[[</del>getallenlijn<del class="diffchange diffchange-inline">]]''</del>:</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_32_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_17_0_lhs"></a>[[<del class="diffchange diffchange-inline">Bestand</del>:Number-line.svg|center|De getallenlijn]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_36_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_17_1_lhs"></a>Hoe meer naar rechts een getal zich op de getallenlijn bevindt hoe groter dit getal is. Van twee getallen op de getallenlijn is het rechter getal groter dan het linker. Op de grens van de positieve getallen en de negatieve getallen bevindt zich het getal [[0 (getal)|nul]]. Rechts daarvan staan de positieve getallen en links ervan de negatieve.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_50_3_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_19_0_rhs"></a>Europese wiskundigen verzetten zich voor het grootste deel tot in de 17e eeuw tegen het concept van negatieve getallen, hoewel [[Fibonacci]] <ins class="diffchange diffchange-inline">negatieve</ins> oplossingen in financiële problemen toestond, waar zij als schulden konden worden geïnterpreteerd<ins class="diffchange diffchange-inline"><ref></ins>[[<ins class="diffchange diffchange-inline">Fibonacci]]. </ins>Liber Abaci, 1202 n.Chr<ins class="diffchange diffchange-inline">. hoofdstuk 13</ref></ins> en later als<ins class="diffchange diffchange-inline"> verliezen, in zijn boek Flos. De</ins> [[<ins class="diffchange diffchange-inline">Frankrijk</ins>|<ins class="diffchange diffchange-inline">Franse</ins>]] <ins class="diffchange diffchange-inline">wiskundige Nicolas Chuquet gebruikte </ins>in <ins class="diffchange diffchange-inline">de</ins> <ins class="diffchange diffchange-inline">15e</ins> <ins class="diffchange diffchange-inline">eeuw</ins> <ins class="diffchange diffchange-inline">negatieve getallen als [[exponent</ins>]]<ins class="diffchange diffchange-inline"> en noemde het absurde getallen</ins>.</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_40_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_20_0_lhs"></a>== Symbolen ==</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_42_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_21_0_lhs"></a>De volgende symbolen worden in de [[wiskunde]] voor negatieve getallen gebruikt:</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td class="diff-addedline diff-side-added"><div>== Getallenlijn ==</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_44_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_24_0_lhs"></a>* De verzameling<del class="diffchange diffchange-inline"> der</del> negatieve [[Reëel getal|reële getallen]]: <math>\<del class="diffchange diffchange-inline">mathbb{</del>R<del class="diffchange diffchange-inline">}</del>^{-}</math></div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_13_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_25_0_rhs"></a>{{Zie hoofdartikel|Getallenlijn}}</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_46_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_26_0_lhs"></a>* De verzameling<del class="diffchange diffchange-inline"> der</del> negatieve [[Rationaal getal|rationale getallen]]: <math>\<del class="diffchange diffchange-inline">mathbb{</del>Q<del class="diffchange diffchange-inline">}</del>^{-}</math></div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_48_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_27_0_lhs"></a>* De verzameling<del class="diffchange diffchange-inline"> der</del> negatieve [[Geheel getal|gehele getallen]]: <math>\<del class="diffchange diffchange-inline">mathbb{</del>Z<del class="diffchange diffchange-inline">}</del>^{-}</math></div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_16_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_29_0_rhs"></a>De relatie tussen negatieve getallen, positieve getallen en nul wordt vaak grafisch afgebeeld in de vorm van een getallenlijn:</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_52_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_30_0_lhs"></a><del class="diffchange diffchange-inline">Voor</del> <del class="diffchange diffchange-inline">de</del> [[Natuurlijk getal|natuurlijke getallen]] <del class="diffchange diffchange-inline">bestaat</del> <del class="diffchange diffchange-inline">uiteraard geen symbool, gezien deze</del> geen negatieve getallen<del class="diffchange diffchange-inline"> bevat</del>.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_17_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_32_0_rhs"></a>[[<ins class="diffchange diffchange-inline">Afbeelding</ins>:Number-line.svg|center<ins class="diffchange diffchange-inline">|450px</ins>|De getallenlijn]]</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>== Verschil in definitie tussen Nederland en België ==</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>In België en Frankrijk wordt het getal 0 als zowel positief als negatief beschouwd. In Nederland geldt het getal 0 noch als negatief noch als positief. Getallen kleiner dan nul worden in België ''strikt negatief'' genoemd.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_17_1_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_36_0_rhs"></a>Hoe meer naar rechts een getal zich op de getallenlijn bevindt<ins class="diffchange diffchange-inline">,</ins> hoe groter dit getal is. Van twee getallen op de getallenlijn is het rechter getal groter dan het linker. Op de grens van de positieve getallen en de negatieve getallen bevindt zich het getal [[0 (getal)|nul]]. Rechts daarvan staan de positieve getallen en links ervan de negatieve.</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_3_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_37_0_lhs"></a>== Geschiedenis ==</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_5_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_38_0_lhs"></a>Negatieve getallen verschijnen voor het eerst in de geschiedenis in <del class="diffchange diffchange-inline">''</del>[[<del class="diffchange diffchange-inline">De negen</del> hoofdstukken <del class="diffchange diffchange-inline">van</del> de <del class="diffchange diffchange-inline">wiskundige kunst</del>]]<del class="diffchange diffchange-inline">''</del> <del class="diffchange diffchange-inline">(</del>''Jiu zhang suan-shu''<del class="diffchange diffchange-inline">)</del>, dat in zijn huidige vorm uit de periode van de [[Han-dynastie]] <del class="diffchange diffchange-inline">(</del>202 v.Chr. - 220 n.Chr.<del class="diffchange diffchange-inline">)</del> <del class="diffchange diffchange-inline">dateert</del>, maar dat ook veel ouder materiaal kan bevatten. <del class="diffchange diffchange-inline">De</del> <del class="diffchange diffchange-inline">''</del>Negen hoofdstukken<del class="diffchange diffchange-inline">''</del> <del class="diffchange diffchange-inline">gebruiken rode [[telstaafje]]s om</del> positieve [[coëfficiënt]]en <del class="diffchange diffchange-inline">en</del> <del class="diffchange diffchange-inline">zwarte</del> <del class="diffchange diffchange-inline">staafjes</del> <del class="diffchange diffchange-inline">om</del> negatieve coëfficiënten <del class="diffchange diffchange-inline">aan</del> <del class="diffchange diffchange-inline">te</del> <del class="diffchange diffchange-inline">geven</del>.<ref><del class="diffchange diffchange-inline">{{en}}</del> <del class="diffchange diffchange-inline">{{aut|</del>Temple<del class="diffchange diffchange-inline">,</del> <del class="diffchange diffchange-inline">Robert}} (1986), ''</del>The Genius of China: 3000 Years of Science, Discovery, and Invention<del class="diffchange diffchange-inline">''</del>. <del class="diffchange diffchange-inline">Met</del> een <del class="diffchange diffchange-inline">voorword</del> <del class="diffchange diffchange-inline">door</del> [[Joseph Needham]]<del class="diffchange diffchange-inline">.</del> <del class="diffchange diffchange-inline">New</del> <del class="diffchange diffchange-inline">York: [[Simon & Schuster]], Inc.</del> ISBN<del class="diffchange diffchange-inline"> </del>0671620282<del class="diffchange diffchange-inline">. blz. 141.</del></ref> Dit<del class="diffchange diffchange-inline"> kleursysteem</del> is <del class="diffchange diffchange-inline">merkwaardigerwijs precies</del> tegengesteld aan de hedendaagse gewoonte in de financiële wereld om <del class="diffchange diffchange-inline">[[</del>rode cijfers<del class="diffchange diffchange-inline">]]</del> te gebruiken om negatieve<del class="diffchange diffchange-inline"> -</del> en zwarte cijfers om positieve bedragen weer te geven. De Chinezen waren ook in staat om simultane vergelijkingen met negatieve getallen op te lossen.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_20_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_40_0_rhs"></a>== Symbolen ==</div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_7_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_41_0_lhs"></a><del class="diffchange diffchange-inline">Lange</del> <del class="diffchange diffchange-inline">tijd</del> <del class="diffchange diffchange-inline">werden</del> <del class="diffchange diffchange-inline">negatieve</del> <del class="diffchange diffchange-inline">oplossingen</del> <del class="diffchange diffchange-inline">voor</del> <del class="diffchange diffchange-inline">problemen</del> als <del class="diffchange diffchange-inline">"</del>verkeerd<del class="diffchange diffchange-inline">"</del> beschouwd. <del class="diffchange diffchange-inline">In het</del> [[<del class="diffchange diffchange-inline">Hellenistische</del> <del class="diffchange diffchange-inline">Egypte]] verwees de [[Oud-Griekse wiskunde</del>|<del class="diffchange diffchange-inline">Oud-Griekse</del>]] wiskundige [[Diophantus]] in zijn <del class="diffchange diffchange-inline">''</del>[[Arithmetica]]<del class="diffchange diffchange-inline">''</del> in de [[<del class="diffchange diffchange-inline">derde</del> eeuw|derde eeuw n.Chr.]] naar een [[<del class="diffchange diffchange-inline">vergelijking</del> (wiskunde)|vergelijking]] die [[Equivalentierelatie|gelijkwaardig]] was aan <del class="diffchange diffchange-inline">4''x'' </del>+<del class="diffchange diffchange-inline"> </del>20<del class="diffchange diffchange-inline"> </del>=<del class="diffchange diffchange-inline"> </del>0 <del class="diffchange diffchange-inline">(deze</del> vergelijking heeft een negatieve [[Oplossen van vergelijkingen|oplossing]]<del class="diffchange diffchange-inline">) als zijnde een absurde vergelijking</del>.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_21_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_42_0_rhs"></a>De volgende <ins class="diffchange diffchange-inline">[[Symbool|</ins>symbolen<ins class="diffchange diffchange-inline">]]</ins> worden in de [[wiskunde]] voor<ins class="diffchange diffchange-inline"> verzamelingen van</ins> negatieve getallen gebruikt:</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_24_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_44_0_rhs"></a>* De verzameling negatieve [[Reëel getal|reële getallen]]: <math>\R^{-}</math></div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_10_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_45_0_lhs"></a><del class="diffchange diffchange-inline">In</del> de 7e eeuw na Christus<del class="diffchange diffchange-inline"> werden negatieve getallen</del> in [[India]] gebruikt om [[<del class="diffchange diffchange-inline">schuld</del> (<del class="diffchange diffchange-inline">economie</del>)|<del class="diffchange diffchange-inline">schuld</del>]]<del class="diffchange diffchange-inline">en</del> weer te geven. De [[Indiase wiskunde|Indiase wiskundige]] [[Brahmagupta]] <del class="diffchange diffchange-inline">bediscussieert</del> in <del class="diffchange diffchange-inline">''</del>[[Brahmasphuta-siddhanta]]<del class="diffchange diffchange-inline">''</del> <del class="diffchange diffchange-inline">(</del>geschreven in 628 n.Chr.<del class="diffchange diffchange-inline">)</del> het gebruik van negatieve getallen om zo de algemene vorm van een [[vierkantsvergelijking<del class="diffchange diffchange-inline">|kwadratische formule</del>]] te produceren, die ook nu nog in gebruik is. Hij vond ook negatieve oplossingen van <del class="diffchange diffchange-inline">[[vierkantsvergelijking]]en</del> en gaf regels met betrekking tot [[<del class="diffchange diffchange-inline">basisoperatie</del>]]<del class="diffchange diffchange-inline">s</del>, waarbij negatieve getallen en ook het getal [[0 (getal)|nul]] deel van uitmaakten, zoals <del class="diffchange diffchange-inline">''</del>'Een schuld afgetrokken van het niets wordt een krediet, een krediet afgetrokken van het niets wordt een schuld.<del class="diffchange diffchange-inline">"'</del>' Hij noemde positieve getallen <del class="diffchange diffchange-inline">"</del>fortuinen<del class="diffchange diffchange-inline">"</del>, nul <del class="diffchange diffchange-inline">"</del>een [[cijfer]]<del class="diffchange diffchange-inline">"</del> en negatieve getallen <del class="diffchange diffchange-inline">"</del>schulden<del class="diffchange diffchange-inline">"</del>.<ref><del class="diffchange diffchange-inline"> </del>Colva M. Roney-Dougal, docent in de zuivere wiskunde aan de [[Universiteit van St<del class="diffchange diffchange-inline">.</del> Andrews]] verklaarde dit op<del class="diffchange diffchange-inline"> de</del> [[<del class="diffchange diffchange-inline">BBC</del> <del class="diffchange diffchange-inline">Radio</del> <del class="diffchange diffchange-inline">4</del>]] programma <del class="diffchange diffchange-inline">"</del>In Our Time<del class="diffchange diffchange-inline">",</del> <del class="diffchange diffchange-inline">op</del> [[<del class="diffchange diffchange-inline">9</del> <del class="diffchange diffchange-inline">maart]]</del> <del class="diffchange diffchange-inline">[[2006</del>]].</ref><ref><del class="diffchange diffchange-inline"> ''</del>Knowledge Transfer and Perceptions of the Passage of Time<del class="diffchange diffchange-inline">''</del>, ICEE-2002 Keynote Address door Colin Adamson-Macedo<del class="diffchange diffchange-inline">.</del> <del class="diffchange diffchange-inline">"''</del>Referring again to Brahmagupta's great work, all the necessary rules for algebra, including the 'rule of signs', were stipulated, but in a form which used the language and imagery of commerce and the market place. Thus 'dhana'<del class="diffchange diffchange-inline"> (=</del> fortunes<del class="diffchange diffchange-inline">)</del> is used to represent positive numbers, whereas 'rina'<del class="diffchange diffchange-inline"> (=</del> debts<del class="diffchange diffchange-inline">)</del> were negative<del class="diffchange diffchange-inline">''"</del>.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_26_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_46_0_rhs"></a>* De verzameling negatieve [[Rationaal getal|rationale getallen]]: <math>\Q^{-}</math></div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_27_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_48_0_rhs"></a>* De verzameling negatieve [[Geheel getal|gehele getallen]]: <math>\Z^{-}</math></div></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_12_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_49_0_lhs"></a><del class="diffchange diffchange-inline">"''</del>Opnieuw verwijzend naar het grote werk van Brahmagupta, alle nodige regels voor de algebra, met inbegrip van de 'tekenregels', waren hierin opgesteld, maar in een vorm die de taal en de beeldtaal van de handel en de markt gebruikte. Dus wordt 'dhana' <del class="diffchange diffchange-inline">(=</del>fortuinen<del class="diffchange diffchange-inline">)</del> gebruikt om positieve getallen weer te geven, terwijl 'rina' <del class="diffchange diffchange-inline">(=</del>schulden<del class="diffchange diffchange-inline">)</del> voor negatieve getallen wordt gebruikt<del class="diffchange diffchange-inline">''"</del>.</ref></div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_15_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_50_1_lhs"></a>Kennis van de negatieve getallen bereikte dankzij [[Latijn]]se vertalingen van Arabische en Indiase werken <del class="diffchange diffchange-inline">uiteindelijk</del> Europa.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"><a class="mw-diff-movedpara-left" title="Deze alinea is verplaatst. Klik om naar de nieuwe locatie te springen." href="#movedpara_19_0_rhs">⚫</a></td> <td class="diff-deletedline diff-side-deleted"><div><a name="movedpara_50_3_lhs"></a>Europese wiskundigen verzetten zich voor het grootste deel tot in de 17e eeuw tegen het concept van negatieve getallen, hoewel [[<del class="diffchange diffchange-inline">Leonardo van Pisa#Belangrijke publicaties|</del>Fibonacci]] <del class="diffchange diffchange-inline">negatieve</del> oplossingen in financiële problemen toestond, waar zij als schulden konden worden geïnterpreteerd<del class="diffchange diffchange-inline"> (hoofdstuk 13 van ''</del>[[Liber Abaci<del class="diffchange diffchange-inline">]]''</del>, 1202 n.Chr<del class="diffchange diffchange-inline">)</del> en later als [[<del class="diffchange diffchange-inline">verlies (economie)</del>|<del class="diffchange diffchange-inline">verliezen</del>]] <del class="diffchange diffchange-inline">(</del>in <del class="diffchange diffchange-inline">''[[Leonardo</del> <del class="diffchange diffchange-inline">van</del> <del class="diffchange diffchange-inline">Pisa</del> <del class="diffchange diffchange-inline">|Flos</del>]]<del class="diffchange diffchange-inline">'')</del>.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>In de 15e eeuw gebruikte de [[Frankrijk|Franse]] wiskundige, [[Nicolas Chuquet]] negatieve getallen als [[Machtsverheffen|exponenten]] en verwees hiernaar als "absurde getallen".</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker"><a class="mw-diff-movedpara-right" title="Deze alinea is verplaatst. Klik om naar de oude locatie te springen." href="#movedpara_30_0_lhs">⚫</a></td> <td class="diff-addedline diff-side-added"><div><a name="movedpara_52_0_rhs"></a><ins class="diffchange diffchange-inline">De</ins> <ins class="diffchange diffchange-inline">verzameling</ins> [[Natuurlijk getal|natuurlijke getallen]] <ins class="diffchange diffchange-inline"><math>\N</math></ins> <ins class="diffchange diffchange-inline">bevat</ins> geen negatieve getallen.</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>== Zie ook ==</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>* [[Positief getal]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div><del class="diffchange diffchange-inline">== </del>Voetnoten<del class="diffchange diffchange-inline"> ==</del></div></td> <td class="diff-marker" data-marker="+"></td> <td class="diff-addedline diff-side-added"><div><ins class="diffchange diffchange-inline">{{Appendix|</ins>Voetnoten<ins class="diffchange diffchange-inline">}}</ins></div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>{{references|85%}}</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>[[Categorie:Getal]]</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>[[Categorie:Getal]]</div></td> </tr> </table><hr class='diff-hr' id='mw-oldid' /> <h2 class='diff-currentversion-title'>Huidige versie van 8 mei 2023 om 21:43</h2> <div class="mw-content-ltr mw-parser-output" lang="nl" dir="ltr"><p>Een <b>negatief getal</b> is in het <a href="/wiki/Nederlands" title="Nederlands">Nederlands</a> een <a href="/wiki/Getal_(wiskunde)" title="Getal (wiskunde)">getal</a> dat kleiner is dan <a href="/wiki/0_(getal)" title="0 (getal)">0</a>.<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> Een negatief getal is het <a href="/wiki/Tegengestelde_(wiskunde)" title="Tegengestelde (wiskunde)">tegengestelde</a> van het overeenkomstige <a href="/wiki/Positief_getal" title="Positief getal">positieve getal</a>, wat inhoudt dat <a href="/wiki/Optellen" title="Optellen">optellen</a> van deze beide getallen als <a href="/wiki/Sommatie" title="Sommatie">som</a> het getal <a href="/wiki/0_(getal)" title="0 (getal)">0</a> oplevert. Negatieve getallen zijn te herkennen aan het <a href="/wiki/Minteken" title="Minteken">minteken −</a>, dat voor het overeenkomstige positieve getal is geplaatst. </p> <div class="mw-heading mw-heading2"><h2 id="Geschiedenis">Geschiedenis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Negatief_getal&veaction=edit&section=1" title="Bewerk dit kopje: Geschiedenis" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Negatief_getal&action=edit&section=1" title="De broncode bewerken van de sectie: Geschiedenis"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Negatieve getallen verschijnen voor het eerst in de geschiedenis in <a href="/wiki/Negen_hoofdstukken_over_de_rekenkunde" title="Negen hoofdstukken over de rekenkunde">Negen hoofdstukken over de rekenkunde</a>, <i>Jiu zhang suan-shu</i>, dat in zijn huidige vorm uit de periode van de <a href="/wiki/Han-dynastie" title="Han-dynastie">Han-dynastie</a> 202 v.Chr. - 220 n.Chr. komt, maar dat ook veel ouder materiaal kan bevatten. In de Negen hoofdstukken worden positieve <a href="/wiki/Co%C3%ABffici%C3%ABnt" title="Coëfficiënt">coëfficiënten</a> met rode telstaafjes en negatieve coëfficiënten met zwarte staafjes aangegeven.<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> Dit is dus tegengesteld aan de hedendaagse gewoonte in de financiële wereld om rode cijfers te gebruiken om negatieve en zwarte cijfers om positieve bedragen weer te geven. De Chinezen waren ook in staat om simultane vergelijkingen met negatieve getallen op te lossen. </p><p>Negatieve oplossingen voor problemen werden lange tijd als verkeerd beschouwd. De <a href="/wiki/Oude_Griekenland" title="Oude Griekenland">Oudgriekse</a> wiskundige <a href="/wiki/Diophantus" title="Diophantus">Diophantus</a> verwees in het Hellenistische Egypte in zijn <a href="/wiki/Arithmetica" title="Arithmetica">Arithmetica</a> in de <a href="/wiki/3e_eeuw" title="3e eeuw">derde eeuw n.Chr.</a> naar een <a href="/wiki/Vergelijking_(wiskunde)" title="Vergelijking (wiskunde)">vergelijking</a> die <a href="/wiki/Equivalentierelatie" title="Equivalentierelatie">gelijkwaardig</a> was aan <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 4x+20=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mi>x</mi> <mo>+</mo> <mn>20</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4x+20=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c36f014cee4e54147994ef39de819f5b29f8afe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.918ex; height:2.343ex;" alt="{\displaystyle 4x+20=0}"></span> en vond dat een absurde vergelijking. Deze vergelijking heeft een negatieve <a href="/wiki/Oplossen_van_vergelijkingen" title="Oplossen van vergelijkingen">oplossing</a>. </p><p>Negatieve getallen werden in de 7e eeuw na Christus in <a href="/wiki/India" title="India">India</a> gebruikt om <a href="/wiki/Schuld_(debet)" title="Schuld (debet)">schulden</a> weer te geven. De <a href="/wiki/Indiase_wiskunde" title="Indiase wiskunde">Indiase wiskundige</a> <a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a> besprak in zijn <a href="/wiki/Brahmasphuta-siddhanta" title="Brahmasphuta-siddhanta">Brahmasphuta-siddhanta</a>, geschreven in 628 n.Chr., het gebruik van negatieve getallen om zo de algemene vorm van een <a href="/wiki/Vierkantsvergelijking" title="Vierkantsvergelijking">vierkantsvergelijking</a> te produceren, die ook nu nog in gebruik is. Hij vond ook negatieve oplossingen van deze vierkantsvergelijkingen en gaf regels met betrekking tot <a href="/wiki/Basisoperatie_(wiskunde)" title="Basisoperatie (wiskunde)">basisoperaties</a>, waarbij negatieve getallen en ook het getal <a href="/wiki/0_(getal)" title="0 (getal)">nul</a> deel van uitmaakten, zoals 'Een schuld afgetrokken van het niets wordt een krediet, een krediet afgetrokken van het niets wordt een schuld.' Hij noemde positieve getallen 'fortuinen', nul 'een <a href="/wiki/Cijfer" title="Cijfer">cijfer</a>' en negatieve getallen 'schulden'.<sup id="cite_ref-3" class="reference"><a href="#cite_note-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> </p><p>Kennis van de negatieve getallen bereikte dankzij <a href="/wiki/Latijn" title="Latijn">Latijnse</a> vertalingen van Arabische en <a href="/wiki/Indiase_wiskunde" title="Indiase wiskunde">Indiase</a> werken <a href="/wiki/Europa_(werelddeel)" title="Europa (werelddeel)">Europa</a>. </p><p>Europese wiskundigen verzetten zich voor het grootste deel tot in de 17e eeuw tegen het concept van negatieve getallen, hoewel <a href="/wiki/Fibonacci" title="Fibonacci">Fibonacci</a> negatieve oplossingen in financiële problemen toestond, waar zij als schulden konden worden geïnterpreteerd<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> en later als verliezen, in zijn boek Flos. De <a href="/wiki/Frankrijk" title="Frankrijk">Franse</a> wiskundige Nicolas Chuquet gebruikte in de 15e eeuw negatieve getallen als <a href="/wiki/Exponent" title="Exponent">exponent</a> en noemde het absurde getallen. </p> <div class="mw-heading mw-heading2"><h2 id="Getallenlijn">Getallenlijn</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Negatief_getal&veaction=edit&section=2" title="Bewerk dit kopje: Getallenlijn" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Negatief_getal&action=edit&section=2" title="De broncode bewerken van de sectie: Getallenlijn"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote" style="margin-bottom:0.5em; padding:0.5em 0 0.5em 1.6em; font-size:95%;" role="note"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/15px-1rightarrow_blue.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/23px-1rightarrow_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/30px-1rightarrow_blue.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span> <i>Zie <a href="/wiki/Getallenlijn" title="Getallenlijn">Getallenlijn</a> voor het hoofdartikel over dit onderwerp.</i></div> <p>De relatie tussen negatieve getallen, positieve getallen en nul wordt vaak grafisch afgebeeld in de vorm van een getallenlijn: </p> <figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/Bestand:Number-line.svg" class="mw-file-description" title="De getallenlijn"><img alt="De getallenlijn" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Number-line.svg/450px-Number-line.svg.png" decoding="async" width="450" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Number-line.svg/675px-Number-line.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Number-line.svg/900px-Number-line.svg.png 2x" data-file-width="750" data-file-height="50" /></a><figcaption>De getallenlijn</figcaption></figure> <p>Hoe meer naar rechts een getal zich op de getallenlijn bevindt, hoe groter dit getal is. Van twee getallen op de getallenlijn is het rechter getal groter dan het linker. Op de grens van de positieve getallen en de negatieve getallen bevindt zich het getal <a href="/wiki/0_(getal)" title="0 (getal)">nul</a>. Rechts daarvan staan de positieve getallen en links ervan de negatieve. </p> <div class="mw-heading mw-heading2"><h2 id="Symbolen">Symbolen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Negatief_getal&veaction=edit&section=3" title="Bewerk dit kopje: Symbolen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Negatief_getal&action=edit&section=3" title="De broncode bewerken van de sectie: Symbolen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De volgende <a href="/wiki/Symbool" title="Symbool">symbolen</a> worden in de <a href="/wiki/Wiskunde" title="Wiskunde">wiskunde</a> voor verzamelingen van negatieve getallen gebruikt: </p> <ul><li>De verzameling negatieve <a href="/wiki/Re%C3%ABel_getal" title="Reëel getal">reële getallen</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{-}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{-}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/158001a03e958f49f5885033776a420fc47b7267" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.189ex; height:2.509ex;" alt="{\displaystyle \mathbb {R} ^{-}}"></span></li> <li>De verzameling negatieve <a href="/wiki/Rationaal_getal" title="Rationaal getal">rationale getallen</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Q} ^{-}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} ^{-}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ce42e684e47c9f1d9985e8ddd841ed75b213dd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.319ex; height:2.843ex;" alt="{\displaystyle \mathbb {Q} ^{-}}"></span></li> <li>De verzameling negatieve <a href="/wiki/Geheel_getal" title="Geheel getal">gehele getallen</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} ^{-}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} ^{-}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d265f6ad41c1623a6477b2cb4336208c7b6c1d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.061ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} ^{-}}"></span></li></ul> <p>De verzameling <a href="/wiki/Natuurlijk_getal" title="Natuurlijk getal">natuurlijke getallen</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf9a96b565ea202d0f4322e9195613fb26a9bed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {N} }"></span> bevat geen negatieve getallen. </p> <div class="toccolours appendix" role="presentation" style="font-size:90%; margin:1em 0 -0.5em; clear:both;"> <div><span style="font-weight:bold">Voetnoten</span></div> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a href="/wiki/Van_Dale_Groot_woordenboek_van_de_Nederlandse_taal" title="Van Dale Groot woordenboek van de Nederlandse taal">Van Dale Groot woordenboek</a>. <a rel="nofollow" class="external text" href="https://www.vandale.nl/gratis-woordenboek/nederlands/betekenis/negatief#.ZFi_eHZBybg">Betekenis 'negatief'</a>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">R Temple. The Genius of China: 3000 Years of Science, Discovery, and Invention, 1986. met een voorwoord van <a href="/wiki/Joseph_Needham" title="Joseph Needham">Joseph Needham</a>, blz 141 <span class="ISBN"><a href="/wiki/Speciaal:Boekbronnen/0671620282" title="Speciaal:Boekbronnen/0671620282">ISBN 0671620282</a></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Colva M. Roney-Dougal, docent in de zuivere wiskunde aan de <a href="/wiki/Universiteit_van_St_Andrews" title="Universiteit van St Andrews">Universiteit van St Andrews</a> verklaarde dit op <a href="/wiki/9_maart" title="9 maart">9 maart</a> <a href="/wiki/2006" title="2006">2006</a> op het programma In Our Time van de <a href="/wiki/BBC_Radio_4" title="BBC Radio 4">BBC Radio 4</a>.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Knowledge Transfer and Perceptions of the Passage of Time, ICEE-2002 Keynote Address door Colin Adamson-Macedo <br /> Referring again to Brahmagupta's great work, all the necessary rules for algebra, including the 'rule of signs', were stipulated, but in a form which used the language and imagery of commerce and the market place. Thus 'dhana', fortunes, is used to represent positive numbers, whereas 'rina', debts, were negative. <br /> Opnieuw verwijzend naar het grote werk van Brahmagupta, alle nodige regels voor de algebra, met inbegrip van de 'tekenregels', waren hierin opgesteld, maar in een vorm die de taal en de beeldtaal van de handel en de markt gebruikte. Dus wordt 'dhana', fortuinen, gebruikt om positieve getallen weer te geven, terwijl 'rina', schulden', voor negatieve getallen wordt gebruikt.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><a href="/wiki/Fibonacci" title="Fibonacci">Fibonacci</a>. Liber Abaci, 1202 n.Chr. hoofdstuk 13</span> </li> </ol></div></div> </div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Negatief_getal&oldid=64271977">https://nl.wikipedia.org/w/index.php?title=Negatief_getal&oldid=64271977</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorie</a>: <ul><li><a href="/wiki/Categorie:Getal" title="Categorie:Getal">Getal</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Deze pagina is voor het laatst bewerkt op 8 mei 2023 om 21:43.</li> <li id="footer-info-copyright">De tekst is beschikbaar onder de licentie <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.nl">Creative Commons Naamsvermelding/Gelijk delen</a>, er kunnen aanvullende voorwaarden van toepassing zijn. 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