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id="toc-Mathematical_significance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cultural_or_practical_significance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cultural_or_practical_significance"> <div class="vector-toc-text"> 1.2 Cultural or practical significance </div> </a> <ul id="toc-Cultural_or_practical_significance-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Classes_of_natural_numbers" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Classes_of_natural_numbers"> <div class="vector-toc-text"> 2 Classes of natural numbers </div> </a> <button aria-controls="toc-Classes_of_natural_numbers-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Classes of natural numbers subsection </button> <ul id="toc-Classes_of_natural_numbers-sublist" class="vector-toc-list"> <li id="toc-Prime_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Prime_numbers"> <div class="vector-toc-text"> 2.1 Prime numbers </div> </a> <ul id="toc-Prime_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Highly_composite_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Highly_composite_numbers"> <div class="vector-toc-text"> 2.2 Highly composite numbers </div> </a> <ul id="toc-Highly_composite_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Perfect_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Perfect_numbers"> <div class="vector-toc-text"> 2.3 Perfect numbers </div> </a> <ul id="toc-Perfect_numbers-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Integers" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Integers"> <div class="vector-toc-text"> 3 Integers </div> </a> <button aria-controls="toc-Integers-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Integers subsection </button> <ul id="toc-Integers-sublist" class="vector-toc-list"> <li id="toc-SI_prefixes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#SI_prefixes"> <div class="vector-toc-text"> 3.1 SI prefixes </div> </a> <ul id="toc-SI_prefixes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Rational_numbers" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Rational_numbers"> <div class="vector-toc-text"> 4 Rational numbers </div> </a> <ul id="toc-Rational_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Real_numbers" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Real_numbers"> <div class="vector-toc-text"> 5 Real numbers </div> </a> <button aria-controls="toc-Real_numbers-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Real numbers subsection </button> <ul id="toc-Real_numbers-sublist" class="vector-toc-list"> <li id="toc-Algebraic_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Algebraic_numbers"> <div class="vector-toc-text"> 5.1 Algebraic numbers </div> </a> <ul id="toc-Algebraic_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Transcendental_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Transcendental_numbers"> <div class="vector-toc-text"> 5.2 Transcendental numbers </div> </a> <ul id="toc-Transcendental_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Irrational_but_not_known_to_be_transcendental" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Irrational_but_not_known_to_be_transcendental"> <div class="vector-toc-text"> 5.3 Irrational but not known to be transcendental </div> </a> <ul id="toc-Irrational_but_not_known_to_be_transcendental-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Real_but_not_known_to_be_irrational,_nor_transcendental" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Real_but_not_known_to_be_irrational,_nor_transcendental"> <div class="vector-toc-text"> 5.4 Real but not known to be irrational, nor transcendental </div> </a> <ul id="toc-Real_but_not_known_to_be_irrational,_nor_transcendental-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Numbers_not_known_with_high_precision" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Numbers_not_known_with_high_precision"> <div class="vector-toc-text"> 5.5 Numbers not known with high precision </div> </a> <ul id="toc-Numbers_not_known_with_high_precision-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Hypercomplex_numbers" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Hypercomplex_numbers"> <div class="vector-toc-text"> 6 Hypercomplex numbers </div> </a> <button aria-controls="toc-Hypercomplex_numbers-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Hypercomplex numbers subsection </button> <ul id="toc-Hypercomplex_numbers-sublist" class="vector-toc-list"> <li id="toc-Algebraic_complex_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Algebraic_complex_numbers"> <div class="vector-toc-text"> 6.1 Algebraic complex numbers </div> </a> <ul id="toc-Algebraic_complex_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_hypercomplex_numbers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_hypercomplex_numbers"> <div class="vector-toc-text"> 6.2 Other hypercomplex numbers </div> </a> <ul id="toc-Other_hypercomplex_numbers-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Transfinite_numbers" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Transfinite_numbers"> <div class="vector-toc-text"> 7 Transfinite numbers </div> </a> <ul id="toc-Transfinite_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Numbers_representing_physical_quantities" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Numbers_representing_physical_quantities"> <div class="vector-toc-text"> 8 Numbers representing physical quantities </div> </a> <ul id="toc-Numbers_representing_physical_quantities-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Numbers_representing_geographical_and_astronomical_distances" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Numbers_representing_geographical_and_astronomical_distances"> <div class="vector-toc-text"> 9 Numbers representing geographical and astronomical distances </div> </a> <ul id="toc-Numbers_representing_geographical_and_astronomical_distances-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Numbers_without_specific_values" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Numbers_without_specific_values"> <div class="vector-toc-text"> 10 Numbers without specific values </div> </a> <ul id="toc-Numbers_without_specific_values-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Named_numbers" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Named_numbers"> <div class="vector-toc-text"> 11 Named numbers </div> </a> <ul id="toc-Named_numbers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 12 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 13 References </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 14 Further reading </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 15 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </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">List of numbers</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 40 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-40" aria-hidden="true" > 40 languages </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/%D9%82%D8%A7%D8%A6%D9%85%D8%A9_%D8%A7%D9%84%D8%A3%D8%B9%D8%AF%D8%A7%D8%AF" title="قائمة الأعداد – Arabic" lang="ar" hreflang="ar" data-title="قائمة الأعداد" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Lis_angka" title="Lis angka – Balinese" lang="ban" hreflang="ban" data-title="Lis angka" data-language-autonym="Basa Bali" data-language-local-name="Balinese" class="interlanguage-link-target">Basa Bali</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B0_%E0%A6%A4%E0%A6%BE%E0%A6%B2%E0%A6%BF%E0%A6%95%E0%A6%BE" title="সংখ্যার তালিকা – Bangla" lang="bn" hreflang="bn" data-title="সংখ্যার তালিকা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BC%D0%B5%D0%BD%D0%B0_%D0%BD%D0%B0_%D1%87%D0%B8%D1%81%D0%BB%D0%B0%D1%82%D0%B0" title="Имена на числата – Bulgarian" lang="bg" hreflang="bg" data-title="Имена на числата" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%91%E0%BD%80%E0%BD%A2%E0%BC%8B%E0%BD%86%E0%BD%82%E0%BC%8B%E0%BD%82%E0%BD%B2%E0%BC%8B%E0%BD%A8%E0%BD%84%E0%BC%8B%E0%BD%82%E0%BE%B2%E0%BD%84%E0%BD%A6%E0%BC%8D" title="དཀར་ཆག་གི་ཨང་གྲངས། – Tibetan" lang="bo" hreflang="bo" data-title="དཀར་ཆག་གི་ཨང་གྲངས།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target">བོད་ཡིག</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A5%D0%B8%D1%81%D0%B5%D0%BF%D1%81%D0%B5%D0%BD_%D1%8F%D1%87%C4%95%D1%81%D0%B5%D0%BC" title="Хисепсен ячĕсем – Chuvash" lang="cv" hreflang="cv" data-title="Хисепсен ячĕсем" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Seznam_%C4%8D%C3%ADsel" title="Seznam čísel – Czech" lang="cs" hreflang="cs" data-title="Seznam čísel" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Liste_besonderer_Zahlen" title="Liste besonderer Zahlen – German" lang="de" hreflang="de" data-title="Liste besonderer Zahlen" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Arvude_loend" title="Arvude loend – Estonian" lang="et" hreflang="et" data-title="Arvude loend" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/El%C3%A8inc_ed_n%C3%B9mer" title="Elèinc ed nùmer – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Elèinc ed nùmer" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target">Emiliàn e rumagnòl</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Anexo:N%C3%BAmeros" title="Anexo:Números – Spanish" lang="es" hreflang="es" data-title="Anexo:Números" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Listo_de_nombroj" title="Listo de nombroj – Esperanto" lang="eo" hreflang="eo" data-title="Listo de nombroj" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D9%87%D8%B1%D8%B3%D8%AA_%D8%B9%D8%AF%D8%AF%D9%87%D8%A7" title="فهرست عددها – Persian" lang="fa" hreflang="fa" data-title="فهرست عددها" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Liste_de_nombres" title="Liste de nombres – French" lang="fr" hreflang="fr" data-title="Liste de nombres" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%98_%EB%AA%A9%EB%A1%9D" title="수 목록 – Korean" lang="ko" hreflang="ko" data-title="수 목록" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%93%E0%A4%82_%E0%A4%95%E0%A5%80_%E0%A4%B8%E0%A5%82%E0%A4%9A%E0%A5%80" title="संख्याओं की सूची – Hindi" lang="hi" hreflang="hi" data-title="संख्याओं की सूची" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Daftar_angka" title="Daftar angka – Indonesian" lang="id" hreflang="id" data-title="Daftar angka" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</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%9E%D7%A2%D7%A0%D7%99%D7%99%D7%9F" title="מספר מעניין – Hebrew" lang="he" hreflang="he" data-title="מספר מעניין" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D1%96%D0%B7%D1%96%D0%BC%D1%96" title="Сандар тізімі – Kazakh" lang="kk" hreflang="kk" data-title="Сандар тізімі" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Getallen_en_getalverzamelingen" title="Getallen en getalverzamelingen – Dutch" lang="nl" hreflang="nl" data-title="Getallen en getalverzamelingen" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%95%B0%E3%81%AB%E9%96%A2%E3%81%99%E3%82%8B%E8%A8%98%E4%BA%8B%E3%81%AE%E4%B8%80%E8%A6%A7" title="数に関する記事の一覧 – Japanese" lang="ja" hreflang="ja" data-title="数に関する記事の一覧" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Sonlar_ro%CA%BByxati" title="Sonlar roʻyxati – Uzbek" lang="uz" hreflang="uz" data-title="Sonlar roʻyxati" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A9%B0%E0%A8%96%E0%A8%BF%E0%A8%86%E0%A8%B5%E0%A8%BE%E0%A8%82_%E0%A8%A6%E0%A9%80_%E0%A8%B8%E0%A9%82%E0%A8%9A%E0%A9%80" title="ਸੰਖਿਆਵਾਂ ਦੀ ਸੂਚੀ – Punjabi" lang="pa" hreflang="pa" data-title="ਸੰਖਿਆਵਾਂ ਦੀ ਸੂਚੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF%D8%A7%DA%BA_%D8%AF%DB%8C_%D9%84%D8%B3%D9%B9" title="عدداں دی لسٹ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="عدداں دی لسٹ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/List%C4%83_de_numere" title="Listă de numere – Romanian" lang="ro" hreflang="ro" data-title="Listă de numere" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%B0_%D1%81_%D1%81%D0%BE%D0%B1%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%BD%D1%8B%D0%BC%D0%B8_%D0%B8%D0%BC%D0%B5%D0%BD%D0%B0%D0%BC%D0%B8" title="Числа с собственными именами – Russian" lang="ru" hreflang="ru" data-title="Числа с собственными именами" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/List_of_numbers" title="List of numbers – Simple English" lang="en-simple" hreflang="en-simple" data-title="List of numbers" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Zoznam_%C4%8D%C3%ADsel" title="Zoznam čísel – Slovak" lang="sk" hreflang="sk" data-title="Zoznam čísel" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Seznam_%C5%A1tevil" title="Seznam števil – Slovenian" lang="sl" hreflang="sl" data-title="Seznam števil" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Liiska_thiinada_(lambarada)" title="Liiska thiinada (lambarada) – Somali" lang="so" hreflang="so" data-title="Liiska thiinada (lambarada)" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target">Soomaaliga</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%B0%D0%BA_%D0%BF%D1%80%D0%B8%D1%80%D0%BE%D0%B4%D0%BD%D0%B8%D1%85_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B0" title="Списак природних бројева – Serbian" lang="sr" hreflang="sr" data-title="Списак природних бројева" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link 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.hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This is a <a href="/wiki/Wikipedia:WikiProject_Lists#Dynamic_lists" title="Wikipedia:WikiProject Lists">dynamic list</a> and may never be able to satisfy particular standards for completeness. You can help by <a href="/wiki/Special:EditPage/List_of_numbers" title="Special:EditPage/List of numbers">adding missing items</a> with <a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">reliable sources</a>.</div> This is a list of notable <a href="/wiki/Number" title="Number">numbers</a> and articles about notable numbers. The list does not contain all numbers in existence as most of the <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">number sets</a> are infinite. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities that could arguably make them notable. Even the smallest "uninteresting" number is paradoxically interesting for that very property. This is known as the <a href="/wiki/Interesting_number_paradox" title="Interesting number paradox">interesting number paradox</a>. The definition of what is classed as a number is rather diffuse and based on historical distinctions. For example, the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a <a href="/wiki/Complex_number" title="Complex number">complex number</a> (3+4i), but not when it is in the form of a <a href="/wiki/Vector_(mathematics_and_physics)" title="Vector (mathematics and physics)">vector</a> (3,4). This list will also be categorized with the standard convention of <a href="/wiki/List_of_types_of_numbers" title="List of types of numbers">types of numbers</a>. This list focuses on numbers as <a href="/wiki/Mathematical_objects" class="mw-redirect" title="Mathematical objects">mathematical objects</a> and is not a list of <a href="/wiki/Numeral_(linguistics)" title="Numeral (linguistics)">numerals</a>, which are linguistic devices: nouns, adjectives, or adverbs that designate numbers. The distinction is drawn between the number five (an <a href="/wiki/Abstract_object" class="mw-redirect" title="Abstract object">abstract object</a> equal to 2+3), and the numeral five (the <a href="/wiki/Noun" title="Noun">noun</a> referring to the number). <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Natural_numbers">Natural numbers</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=1" title="Edit section: Natural numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Natural_number" title="Natural number">Natural number</a></div> Natural numbers are a subset of the integers and are of historical and pedagogical value as they can be used for <a href="/wiki/Counting" title="Counting">counting</a> and often have ethno-cultural significance (see below). Beyond this, natural numbers are widely used as a building block for other number systems including the <a href="/wiki/Integers" class="mw-redirect" title="Integers">integers</a>, <a href="/wiki/Rational_number#Formal_construction" title="Rational number">rational numbers</a> and <a href="/wiki/Construction_of_the_real_numbers" title="Construction of the real numbers">real numbers</a>. Natural numbers are those used for <a href="/wiki/Counting" title="Counting">counting</a> (as in "there are six (6) coins on the table") and <a href="/wiki/Total_order" title="Total order">ordering</a> (as in "this is the third (3rd) largest city in the country"). In common language, words used for counting are "<a href="/wiki/Cardinal_number_(linguistics)" class="mw-redirect" title="Cardinal number (linguistics)">cardinal numbers</a>" and words used for ordering are "<a href="/wiki/Ordinal_number_(linguistics)" class="mw-redirect" title="Ordinal number (linguistics)">ordinal numbers</a>". Defined by the <a href="/wiki/Peano_axioms" title="Peano axioms">Peano axioms</a>, the natural numbers form an infinitely large set. Often referred to as "the naturals", the natural numbers are usually symbolised by a boldface N (or <a href="/wiki/Blackboard_bold" title="Blackboard bold">blackboard bold</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {\mathbb {N} } }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {\mathbb {N} } }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dcdf44171e54385806a87720a1968bb2c37536a" 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 {\mathbb {N} } }">, Unicode <style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style>U+2115 ℕ DOUBLE-STRUCK CAPITAL N). The inclusion of <a href="/wiki/Zero" class="mw-redirect" title="Zero">0</a> in the set of natural numbers is ambiguous and subject to individual definitions. In <a href="/wiki/Set_theory" title="Set theory">set theory</a> and <a href="/wiki/Computer_science" title="Computer science">computer science</a>, 0 is typically considered a natural number. In <a href="/wiki/Number_theory" title="Number theory">number theory</a>, it usually is not. The ambiguity can be solved with the terms "non-negative integers", which includes 0, and "positive integers", which does not. Natural numbers may be used as <a href="/wiki/Cardinal_numbers" class="mw-redirect" title="Cardinal numbers">cardinal numbers</a>, which may go by <a href="/wiki/Numeral_(linguistics)" title="Numeral (linguistics)">various names</a>. Natural numbers may also be used as <a href="/wiki/Ordinal_numbers" class="mw-redirect" title="Ordinal numbers">ordinal numbers</a>. <table class="wikitable sortable mw-collapsible" style="text-align:center;"> <caption class="nowrap">Table of small natural numbers </caption> <tbody><tr> <td><a href="/wiki/0" title="0">0</a> </td> <td><a href="/wiki/1" title="1">1</a> </td> <td><a href="/wiki/2" title="2">2</a> </td> <td><a href="/wiki/3" title="3">3</a> </td> <td><a href="/wiki/4" title="4">4</a> </td> <td><a href="/wiki/5" title="5">5</a> </td> <td><a href="/wiki/6" title="6">6</a> </td> <td><a href="/wiki/7" title="7">7</a> </td> <td><a href="/wiki/8" title="8">8</a> </td> <td><a href="/wiki/9" title="9">9</a> </td></tr> <tr> <td><a href="/wiki/10" title="10">10</a> </td> <td><a href="/wiki/11_(number)" title="11 (number)">11</a> </td> <td><a href="/wiki/12_(number)" title="12 (number)">12</a> </td> <td><a href="/wiki/13_(number)" title="13 (number)">13</a> </td> <td><a href="/wiki/14_(number)" title="14 (number)">14</a> </td> <td><a href="/wiki/15_(number)" title="15 (number)">15</a> </td> <td><a href="/wiki/16_(number)" title="16 (number)">16</a> </td> <td><a href="/wiki/17_(number)" title="17 (number)">17</a> </td> <td><a href="/wiki/18_(number)" title="18 (number)">18</a> </td> <td><a href="/wiki/19_(number)" title="19 (number)">19</a> </td></tr> <tr> <td><a href="/wiki/20_(number)" title="20 (number)">20</a> </td> <td><a href="/wiki/21_(number)" title="21 (number)">21</a> </td> <td><a href="/wiki/22_(number)" title="22 (number)">22</a> </td> <td><a href="/wiki/23_(number)" title="23 (number)">23</a> </td> <td><a href="/wiki/24_(number)" title="24 (number)">24</a> </td> <td><a href="/wiki/25_(number)" title="25 (number)">25</a> </td> <td><a href="/wiki/26_(number)" title="26 (number)">26</a> </td> <td><a href="/wiki/27_(number)" title="27 (number)">27</a> </td> <td><a href="/wiki/28_(number)" title="28 (number)">28</a> </td> <td><a href="/wiki/29_(number)" title="29 (number)">29</a> </td></tr> <tr> <td><a href="/wiki/30_(number)" title="30 (number)">30</a> </td> <td><a href="/wiki/31_(number)" title="31 (number)">31</a> </td> <td><a href="/wiki/32_(number)" title="32 (number)">32</a> </td> <td><a href="/wiki/33_(number)" title="33 (number)">33</a> </td> <td><a href="/wiki/34_(number)" title="34 (number)">34</a> </td> <td><a href="/wiki/35_(number)" title="35 (number)">35</a> </td> <td><a href="/wiki/36_(number)" title="36 (number)">36</a> </td> <td><a href="/wiki/37_(number)" title="37 (number)">37</a> </td> <td><a href="/wiki/38_(number)" title="38 (number)">38</a> </td> <td><a href="/wiki/39_(number)" title="39 (number)">39</a> </td></tr> <tr> <td><a href="/wiki/40_(number)" title="40 (number)">40</a> </td> <td><a href="/wiki/41_(number)" title="41 (number)">41</a> </td> <td><a href="/wiki/42_(number)" title="42 (number)">42</a> </td> <td><a href="/wiki/43_(number)" title="43 (number)">43</a> </td> <td><a href="/wiki/44_(number)" title="44 (number)">44</a> </td> <td><a href="/wiki/45_(number)" title="45 (number)">45</a> </td> <td><a href="/wiki/46_(number)" title="46 (number)">46</a> </td> <td><a href="/wiki/47_(number)" title="47 (number)">47</a> </td> <td><a href="/wiki/48_(number)" title="48 (number)">48</a> </td> <td><a href="/wiki/49_(number)" title="49 (number)">49</a> </td></tr> <tr> <td><a href="/wiki/50_(number)" title="50 (number)">50</a> </td> <td><a href="/wiki/51_(number)" title="51 (number)">51</a> </td> <td><a href="/wiki/52_(number)" title="52 (number)">52</a> </td> <td><a href="/wiki/53_(number)" title="53 (number)">53</a> </td> <td><a href="/wiki/54_(number)" title="54 (number)">54</a> </td> <td><a href="/wiki/55_(number)" title="55 (number)">55</a> </td> <td><a href="/wiki/56_(number)" title="56 (number)">56</a> </td> <td><a href="/wiki/57_(number)" title="57 (number)">57</a> </td> <td><a href="/wiki/58_(number)" title="58 (number)">58</a> </td> <td><a href="/wiki/59_(number)" title="59 (number)">59</a> </td></tr> <tr> <td><a href="/wiki/60_(number)" title="60 (number)">60</a> </td> <td><a href="/wiki/61_(number)" title="61 (number)">61</a> </td> <td><a href="/wiki/62_(number)" title="62 (number)">62</a> </td> <td><a href="/wiki/63_(number)" title="63 (number)">63</a> </td> <td><a href="/wiki/64_(number)" title="64 (number)">64</a> </td> <td><a href="/wiki/65_(number)" title="65 (number)">65</a> </td> <td><a href="/wiki/66_(number)" title="66 (number)">66</a> </td> <td><a href="/wiki/67_(number)" title="67 (number)">67</a> </td> <td><a href="/wiki/68_(number)" title="68 (number)">68</a> </td> <td><a href="/wiki/69_(number)" title="69 (number)">69</a> </td></tr> <tr> <td><a href="/wiki/70_(number)" title="70 (number)">70</a> </td> <td><a href="/wiki/71_(number)" title="71 (number)">71</a> </td> <td><a href="/wiki/72_(number)" title="72 (number)">72</a> </td> <td><a href="/wiki/73_(number)" title="73 (number)">73</a> </td> <td><a href="/wiki/74_(number)" title="74 (number)">74</a> </td> <td><a href="/wiki/75_(number)" title="75 (number)">75</a> </td> <td><a href="/wiki/76_(number)" title="76 (number)">76</a> </td> <td><a href="/wiki/77_(number)" title="77 (number)">77</a> </td> <td><a href="/wiki/78_(number)" title="78 (number)">78</a> </td> <td><a href="/wiki/79_(number)" title="79 (number)">79</a> </td></tr> <tr> <td><a href="/wiki/80_(number)" title="80 (number)">80</a> </td> <td><a href="/wiki/81_(number)" title="81 (number)">81</a> </td> <td><a href="/wiki/82_(number)" title="82 (number)">82</a> </td> <td><a href="/wiki/83_(number)" title="83 (number)">83</a> </td> <td><a href="/wiki/84_(number)" title="84 (number)">84</a> </td> <td><a href="/wiki/85_(number)" title="85 (number)">85</a> </td> <td><a href="/wiki/86_(number)" title="86 (number)">86</a> </td> <td><a href="/wiki/87_(number)" title="87 (number)">87</a> </td> <td><a href="/wiki/88_(number)" title="88 (number)">88</a> </td> <td><a href="/wiki/89_(number)" title="89 (number)">89</a> </td></tr> <tr> <td><a href="/wiki/90_(number)" title="90 (number)">90</a> </td> <td><a href="/wiki/91_(number)" title="91 (number)">91</a> </td> <td><a href="/wiki/92_(number)" title="92 (number)">92</a> </td> <td><a href="/wiki/93_(number)" title="93 (number)">93</a> </td> <td><a href="/wiki/94_(number)" title="94 (number)">94</a> </td> <td><a href="/wiki/95_(number)" title="95 (number)">95</a> </td> <td><a href="/wiki/96_(number)" title="96 (number)">96</a> </td> <td><a href="/wiki/97_(number)" title="97 (number)">97</a> </td> <td><a href="/wiki/98_(number)" title="98 (number)">98</a> </td> <td><a href="/wiki/99_(number)" title="99 (number)">99</a> </td></tr> <tr> <td><a href="/wiki/100" title="100">100</a> </td> <td><a href="/wiki/101_(number)" title="101 (number)">101</a> </td> <td><a href="/wiki/102_(number)" title="102 (number)">102</a> </td> <td><a href="/wiki/103_(number)" title="103 (number)">103</a> </td> <td><a href="/wiki/104_(number)" title="104 (number)">104</a> </td> <td><a href="/wiki/105_(number)" title="105 (number)">105</a> </td> <td><a href="/wiki/106_(number)" title="106 (number)">106</a> </td> <td><a href="/wiki/107_(number)" title="107 (number)">107</a> </td> <td><a href="/wiki/108_(number)" title="108 (number)">108</a> </td> <td><a href="/wiki/109_(number)" title="109 (number)">109</a> </td></tr> <tr> <td><a href="/wiki/110_(number)" title="110 (number)">110</a> </td> <td><a href="/wiki/111_(number)" title="111 (number)">111</a> </td> <td><a href="/wiki/112_(number)" title="112 (number)">112</a> </td> <td><a href="/wiki/113_(number)" title="113 (number)">113</a> </td> <td><a href="/wiki/114_(number)" title="114 (number)">114</a> </td> <td><a href="/wiki/115_(number)" title="115 (number)">115</a> </td> <td><a href="/wiki/116_(number)" title="116 (number)">116</a> </td> <td><a href="/wiki/117_(number)" title="117 (number)">117</a> </td> <td><a href="/wiki/118_(number)" title="118 (number)">118</a> </td> <td><a href="/wiki/119_(number)" title="119 (number)">119</a> </td></tr> <tr> <td><a href="/wiki/120_(number)" title="120 (number)">120</a> </td> <td><a href="/wiki/121_(number)" title="121 (number)">121</a> </td> <td><a href="/wiki/122_(number)" title="122 (number)">122</a> </td> <td><a href="/wiki/123_(number)" title="123 (number)">123</a> </td> <td><a href="/wiki/124_(number)" title="124 (number)">124</a> </td> <td><a href="/wiki/125_(number)" title="125 (number)">125</a> </td> <td><a href="/wiki/126_(number)" title="126 (number)">126</a> </td> <td><a href="/wiki/127_(number)" title="127 (number)">127</a> </td> <td><a href="/wiki/128_(number)" title="128 (number)">128</a> </td> <td><a href="/wiki/129_(number)" title="129 (number)">129</a> </td></tr> <tr> <td><a href="/wiki/130_(number)" title="130 (number)">130</a> </td> <td><a href="/wiki/131_(number)" title="131 (number)">131</a> </td> <td><a href="/wiki/132_(number)" title="132 (number)">132</a> </td> <td><a href="/wiki/133_(number)" title="133 (number)">133</a> </td> <td><a href="/wiki/134_(number)" title="134 (number)">134</a> </td> <td><a href="/wiki/135_(number)" title="135 (number)">135</a> </td> <td><a href="/wiki/136_(number)" title="136 (number)">136</a> </td> <td><a href="/wiki/137_(number)" title="137 (number)">137</a> </td> <td><a href="/wiki/138_(number)" title="138 (number)">138</a> </td> <td><a href="/wiki/139_(number)" title="139 (number)">139</a> </td></tr> <tr> <td><a href="/wiki/140_(number)" title="140 (number)">140</a> </td> <td><a href="/wiki/141_(number)" title="141 (number)">141</a> </td> <td><a href="/wiki/142_(number)" title="142 (number)">142</a> </td> <td><a href="/wiki/143_(number)" title="143 (number)">143</a> </td> <td><a href="/wiki/144_(number)" title="144 (number)">144</a> </td> <td><a href="/wiki/145_(number)" title="145 (number)">145</a> </td> <td><a href="/wiki/146_(number)" title="146 (number)">146</a> </td> <td><a href="/wiki/147_(number)" title="147 (number)">147</a> </td> <td><a href="/wiki/148_(number)" title="148 (number)">148</a> </td> <td><a href="/wiki/149_(number)" title="149 (number)">149</a> </td></tr> <tr> <td><a href="/wiki/150_(number)" title="150 (number)">150</a> </td> <td><a href="/wiki/151_(number)" title="151 (number)">151</a> </td> <td><a href="/wiki/152_(number)" title="152 (number)">152</a> </td> <td><a href="/wiki/153_(number)" title="153 (number)">153</a> </td> <td><a href="/wiki/154_(number)" title="154 (number)">154</a> </td> <td><a href="/wiki/155_(number)" title="155 (number)">155</a> </td> <td><a href="/wiki/156_(number)" title="156 (number)">156</a> </td> <td><a href="/wiki/157_(number)" title="157 (number)">157</a> </td> <td><a href="/wiki/158_(number)" title="158 (number)">158</a> </td> <td><a href="/wiki/159_(number)" title="159 (number)">159</a> </td></tr> <tr> <td><a href="/wiki/160_(number)" title="160 (number)">160</a> </td> <td><a href="/wiki/161_(number)" title="161 (number)">161</a> </td> <td><a href="/wiki/162_(number)" title="162 (number)">162</a> </td> <td><a href="/wiki/163_(number)" title="163 (number)">163</a> </td> <td><a href="/wiki/164_(number)" title="164 (number)">164</a> </td> <td><a href="/wiki/165_(number)" title="165 (number)">165</a> </td> <td><a href="/wiki/166_(number)" title="166 (number)">166</a> </td> <td><a href="/wiki/167_(number)" title="167 (number)">167</a> </td> <td><a href="/wiki/168_(number)" title="168 (number)">168</a> </td> <td><a href="/wiki/169_(number)" title="169 (number)">169</a> </td></tr> <tr> <td><a href="/wiki/170_(number)" title="170 (number)">170</a> </td> <td><a href="/wiki/171_(number)" title="171 (number)">171</a> </td> <td><a href="/wiki/172_(number)" title="172 (number)">172</a> </td> <td><a href="/wiki/173_(number)" title="173 (number)">173</a> </td> <td><a href="/wiki/174_(number)" title="174 (number)">174</a> </td> <td><a href="/wiki/175_(number)" title="175 (number)">175</a> </td> <td><a href="/wiki/176_(number)" title="176 (number)">176</a> </td> <td><a href="/wiki/177_(number)" title="177 (number)">177</a> </td> <td><a href="/wiki/178_(number)" title="178 (number)">178</a> </td> <td><a href="/wiki/179_(number)" title="179 (number)">179</a> </td></tr> <tr> <td><a href="/wiki/180_(number)" title="180 (number)">180</a> </td> <td><a href="/wiki/181_(number)" title="181 (number)">181</a> </td> <td><a href="/wiki/182_(number)" title="182 (number)">182</a> </td> <td><a href="/wiki/183_(number)" title="183 (number)">183</a> </td> <td><a href="/wiki/184_(number)" title="184 (number)">184</a> </td> <td><a href="/wiki/185_(number)" title="185 (number)">185</a> </td> <td><a href="/wiki/186_(number)" title="186 (number)">186</a> </td> <td><a href="/wiki/187_(number)" title="187 (number)">187</a> </td> <td><a href="/wiki/188_(number)" title="188 (number)">188</a> </td> <td><a href="/wiki/189_(number)" title="189 (number)">189</a> </td></tr> <tr> <td><a href="/wiki/190_(number)" title="190 (number)">190</a> </td> <td><a href="/wiki/191_(number)" title="191 (number)">191</a> </td> <td><a href="/wiki/192_(number)" title="192 (number)">192</a> </td> <td><a href="/wiki/193_(number)" title="193 (number)">193</a> </td> <td><a href="/wiki/194_(number)" title="194 (number)">194</a> </td> <td><a href="/wiki/195_(number)" title="195 (number)">195</a> </td> <td><a href="/wiki/196_(number)" title="196 (number)">196</a> </td> <td><a href="/wiki/197_(number)" title="197 (number)">197</a> </td> <td><a href="/wiki/198_(number)" title="198 (number)">198</a> </td> <td><a href="/wiki/199_(number)" title="199 (number)">199</a> </td></tr> <tr> <td><a href="/wiki/200_(number)" title="200 (number)">200</a> </td> <td><a href="/wiki/201_(number)" title="201 (number)">201</a> </td> <td><a href="/wiki/202_(number)" title="202 (number)">202</a> </td> <td><a href="/wiki/203_(number)" title="203 (number)">203</a> </td> <td><a href="/wiki/204_(number)" title="204 (number)">204</a> </td> <td><a href="/wiki/205_(number)" title="205 (number)">205</a> </td> <td><a href="/wiki/206_(number)" title="206 (number)">206</a> </td> <td><a href="/wiki/207_(number)" title="207 (number)">207</a> </td> <td><a href="/wiki/208_(number)" title="208 (number)">208</a> </td> <td><a href="/wiki/209_(number)" title="209 (number)">209</a> </td></tr> <tr> <td><a href="/wiki/210_(number)" title="210 (number)">210</a> </td> <td><a href="/wiki/211_(number)" title="211 (number)">211</a> </td> <td><a href="/wiki/212_(number)" title="212 (number)">212</a> </td> <td><a href="/wiki/213_(number)" title="213 (number)">213</a> </td> <td><a href="/wiki/214_(number)" title="214 (number)">214</a> </td> <td><a href="/wiki/215_(number)" title="215 (number)">215</a> </td> <td><a href="/wiki/216_(number)" title="216 (number)">216</a> </td> <td><a href="/wiki/217_(number)" title="217 (number)">217</a> </td> <td><a href="/wiki/218_(number)" title="218 (number)">218</a> </td> <td><a href="/wiki/219_(number)" title="219 (number)">219</a> </td></tr> <tr> <td><a href="/wiki/220_(number)" title="220 (number)">220</a> </td> <td><a href="/wiki/221_(number)" title="221 (number)">221</a> </td> <td><a href="/wiki/222_(number)" title="222 (number)">222</a> </td> <td><a href="/wiki/223_(number)" title="223 (number)">223</a> </td> <td><a href="/wiki/224_(number)" title="224 (number)">224</a> </td> <td><a href="/wiki/225_(number)" title="225 (number)">225</a> </td> <td><a href="/wiki/226_(number)" title="226 (number)">226</a> </td> <td><a href="/wiki/227_(number)" title="227 (number)">227</a> </td> <td><a href="/wiki/228_(number)" title="228 (number)">228</a> </td> <td><a href="/wiki/229_(number)" title="229 (number)">229</a> </td></tr> <tr> <td><a href="/wiki/230_(number)" title="230 (number)">230</a> </td> <td><a href="/wiki/231_(number)" title="231 (number)">231</a> </td> <td><a href="/wiki/232_(number)" title="232 (number)">232</a> </td> <td><a href="/wiki/233_(number)" title="233 (number)">233</a> </td> <td><a href="/wiki/234_(number)" title="234 (number)">234</a> </td> <td><a href="/wiki/235_(number)" title="235 (number)">235</a> </td> <td><a href="/wiki/236_(number)" title="236 (number)">236</a> </td> <td><a href="/wiki/237_(number)" title="237 (number)">237</a> </td> <td><a href="/wiki/238_(number)" title="238 (number)">238</a> </td> <td><a href="/wiki/239_(number)" title="239 (number)">239</a> </td></tr> <tr> <td><a href="/wiki/240_(number)" title="240 (number)">240</a> </td> <td><a href="/wiki/241_(number)" title="241 (number)">241</a> </td> <td><a href="/wiki/242_(number)" title="242 (number)">242</a> </td> <td><a href="/wiki/243_(number)" title="243 (number)">243</a> </td> <td><a href="/wiki/244_(number)" title="244 (number)">244</a> </td> <td><a href="/wiki/245_(number)" title="245 (number)">245</a> </td> <td><a href="/wiki/246_(number)" title="246 (number)">246</a> </td> <td><a href="/wiki/247_(number)" title="247 (number)">247</a> </td> <td><a href="/wiki/248_(number)" title="248 (number)">248</a> </td> <td><a href="/wiki/249_(number)" title="249 (number)">249</a> </td></tr> <tr> <td><a href="/wiki/250_(number)" title="250 (number)">250</a> </td> <td><a href="/wiki/251_(number)" title="251 (number)">251</a> </td> <td><a href="/wiki/252_(number)" title="252 (number)">252</a> </td> <td><a href="/wiki/253_(number)" title="253 (number)">253</a> </td> <td><a href="/wiki/254_(number)" title="254 (number)">254</a> </td> <td><a href="/wiki/255_(number)" title="255 (number)">255</a> </td> <td><a href="/wiki/256_(number)" title="256 (number)">256</a> </td> <td><a href="/wiki/257_(number)" title="257 (number)">257</a> </td> <td><a href="/wiki/258_(number)" title="258 (number)">258</a> </td> <td><a href="/wiki/259_(number)" title="259 (number)">259</a> </td></tr> <tr> <td><a href="/wiki/260_(number)" title="260 (number)">260</a> </td> <td><a href="/wiki/261_(number)" title="261 (number)">261</a> </td> <td><a href="/wiki/262_(number)" title="262 (number)">262</a> </td> <td><a href="/wiki/263_(number)" title="263 (number)">263</a> </td> <td><a href="/wiki/264_(number)" title="264 (number)">264</a> </td> <td><a href="/wiki/265_(number)" title="265 (number)">265</a> </td> <td><a href="/wiki/266_(number)" title="266 (number)">266</a> </td> <td><a href="/wiki/267_(number)" title="267 (number)">267</a> </td> <td><a href="/wiki/268_(number)" title="268 (number)">268</a> </td> <td><a href="/wiki/269_(number)" title="269 (number)">269</a> </td></tr> <tr> <td><a href="/wiki/270_(number)" title="270 (number)">270</a> </td> <td><a href="/wiki/271_(number)" title="271 (number)">271</a> </td> <td><a href="/wiki/272_(number)" title="272 (number)">272</a> </td> <td><a href="/wiki/273_(number)" title="273 (number)">273</a> </td> <td><a href="/wiki/274_(number)" title="274 (number)">274</a> </td> <td><a href="/wiki/275_(number)" title="275 (number)">275</a> </td> <td><a href="/wiki/276_(number)" title="276 (number)">276</a> </td> <td><a href="/wiki/277_(number)" title="277 (number)">277</a> </td> <td><a href="/wiki/278_(number)" title="278 (number)">278</a> </td> <td><a href="/wiki/279_(number)" title="279 (number)">279</a> </td></tr> <tr> <td><a href="/wiki/280_(number)" title="280 (number)">280</a> </td> <td><a href="/wiki/281_(number)" title="281 (number)">281</a> </td> <td><a href="/wiki/282_(number)" title="282 (number)">282</a> </td> <td><a href="/wiki/283_(number)" title="283 (number)">283</a> </td> <td><a href="/wiki/284_(number)" title="284 (number)">284</a> </td> <td><a href="/wiki/285_(number)" title="285 (number)">285</a> </td> <td><a href="/wiki/286_(number)" title="286 (number)">286</a> </td> <td><a href="/wiki/287_(number)" title="287 (number)">287</a> </td> <td><a href="/wiki/288_(number)" title="288 (number)">288</a> </td> <td><a href="/wiki/289_(number)" title="289 (number)">289</a> </td></tr> <tr> <td><a href="/wiki/290_(number)" title="290 (number)">290</a> </td> <td><a href="/wiki/291_(number)" title="291 (number)">291</a> </td> <td><a href="/wiki/292_(number)" title="292 (number)">292</a> </td> <td><a href="/wiki/293_(number)" title="293 (number)">293</a> </td> <td><a href="/wiki/294_(number)" title="294 (number)">294</a> </td> <td><a href="/wiki/295_(number)" title="295 (number)">295</a> </td> <td><a href="/wiki/296_(number)" title="296 (number)">296</a> </td> <td><a href="/wiki/297_(number)" title="297 (number)">297</a> </td> <td><a href="/wiki/298_(number)" title="298 (number)">298</a> </td> <td><a href="/wiki/299_(number)" title="299 (number)">299</a> </td></tr> <tr> <td><a href="/wiki/300_(number)" title="300 (number)">300</a> </td> <td><a href="/wiki/301_(number)" title="301 (number)">301</a> </td> <td><a href="/wiki/302_(number)" title="302 (number)">302</a> </td> <td><a href="/wiki/303_(number)" title="303 (number)">303</a> </td> <td><a href="/wiki/304_(number)" title="304 (number)">304</a> </td> <td><a href="/wiki/305_(number)" title="305 (number)">305</a> </td> <td><a href="/wiki/306_(number)" title="306 (number)">306</a> </td> <td><a href="/wiki/307_(number)" title="307 (number)">307</a> </td> <td><a href="/wiki/308_(number)" title="308 (number)">308</a> </td> <td><a href="/wiki/309_(number)" title="309 (number)">309</a> </td></tr> <tr> <td><a href="/wiki/310_(number)" title="310 (number)">310</a> </td> <td><a href="/wiki/311_(number)" title="311 (number)">311</a> </td> <td><a href="/wiki/312_(number)" title="312 (number)">312</a> </td> <td><a href="/wiki/313_(number)" title="313 (number)">313</a> </td> <td><a href="/wiki/314_(number)" title="314 (number)">314</a> </td> <td> </td> <td> </td> <td> </td> <td><a href="/wiki/318_(number)" title="318 (number)">318</a> </td> <td> </td></tr> <tr> <td> </td> <td> </td> <td> </td> <td> </td> <td><a href="/wiki/400_(number)" title="400 (number)">400</a> </td> <td><a href="/wiki/500_(number)" title="500 (number)">500</a> </td> <td><a href="/wiki/600_(number)" title="600 (number)">600</a> </td> <td><a href="/wiki/700_(number)" title="700 (number)">700</a> </td> <td><a href="/wiki/800_(number)" title="800 (number)">800</a> </td> <td><a href="/wiki/900_(number)" title="900 (number)">900</a> </td></tr> <tr> <td> </td> <td><a href="/wiki/1000_(number)" title="1000 (number)">1000</a> </td> <td><a href="/wiki/2000_(number)" title="2000 (number)">2000</a> </td> <td><a href="/wiki/3000_(number)" title="3000 (number)">3000</a> </td> <td><a href="/wiki/4000_(number)" title="4000 (number)">4000</a> </td> <td><a href="/wiki/5000_(number)" title="5000 (number)">5000</a> </td> <td><a href="/wiki/6000_(number)" title="6000 (number)">6000</a> </td> <td><a href="/wiki/7000_(number)" title="7000 (number)">7000</a> </td> <td><a href="/wiki/8000_(number)" title="8000 (number)">8000</a> </td> <td><a href="/wiki/9000_(number)" title="9000 (number)">9000</a> </td></tr> <tr> <td> </td> <td><a href="/wiki/10,000" title="10,000">10,000</a> </td> <td><a href="/wiki/20,000" title="20,000">20,000</a> </td> <td><a href="/wiki/30,000" title="30,000">30,000</a> </td> <td><a href="/wiki/40,000" title="40,000">40,000</a> </td> <td><a href="/wiki/50,000" title="50,000">50,000</a> </td> <td><a href="/wiki/60,000" title="60,000">60,000</a> </td> <td><a href="/wiki/70,000" title="70,000">70,000</a> </td> <td><a href="/wiki/80,000" title="80,000">80,000</a> </td> <td><a href="/wiki/90,000" title="90,000">90,000</a> </td></tr> <tr> <td><a href="/wiki/100,000" title="100,000">105</a> </td> <td><a href="/wiki/1,000,000" title="1,000,000">106</a> </td> <td><a href="/wiki/10,000,000" title="10,000,000">107</a> </td> <td><a href="/wiki/100,000,000" title="100,000,000">108</a> </td> <td><a href="/wiki/1,000,000,000" title="1,000,000,000">109</a> </td> <td colspan="5"><a href="/wiki/Trillion" title="Trillion">1012</a> </td></tr> <tr> <td colspan="10"><a href="/wiki/Order_of_magnitude" title="Order of magnitude">larger numbers</a>, including <a href="/wiki/Googol" title="Googol">10100</a> and <a href="/wiki/Googolplex" title="Googolplex">1010100</a> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Mathematical_significance">Mathematical significance</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=2" title="Edit section: Mathematical significance">edit</a>]</div> Natural numbers may have properties specific to the individual number or may be part of a set (such as prime numbers) of numbers with a particular property.<style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="collapsible-list mw-collapsible" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold;"><div>List of mathematically significant natural numbers</div></div> <ul class="mw-collapsible-content hlist" style="margin-top: 0; margin-bottom: 0; line-height: inherit;"><li style="line-height: inherit; margin: 0"><a href="/wiki/1_(number)" class="mw-redirect" title="1 (number)">1</a>, the multiplicative identity. Also the only natural number (not including 0) that is not prime or composite.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/2_(number)" class="mw-redirect" title="2 (number)">2</a>, the base of the <a href="/wiki/Binary_number" title="Binary number">binary number</a> system, used in almost all modern computers and information systems. Also the only natural even number to also be prime.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/3_(number)" class="mw-redirect" title="3 (number)">3</a>, 22-1, the first <a href="/wiki/Mersenne_prime" title="Mersenne prime">Mersenne prime</a> and first <a href="/wiki/Fermat_number" title="Fermat number">Fermat number</a>. It is the first odd prime, and it is also the 2 bit integer maximum value.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/4_(number)" class="mw-redirect" title="4 (number)">4</a>, the first <a href="/wiki/Composite_number" title="Composite number">composite number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/5_(number)" class="mw-redirect" title="5 (number)">5</a>, the sum of the first two primes and only prime which is the sum of 2 consecutive primes. The ratio of the length from the side to a diagonal of a regular pentagon is the <a href="/wiki/Golden_ratio" title="Golden ratio">golden ratio</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/6_(number)" class="mw-redirect" title="6 (number)">6</a>, the first of the series of <a href="/wiki/Perfect_number" title="Perfect number">perfect numbers</a>, whose proper factors sum to the number itself.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/9_(number)" class="mw-redirect" title="9 (number)">9</a>, the first <a href="/wiki/Parity_(mathematics)" title="Parity (mathematics)">odd</a> number that is <a href="/wiki/Composite_number" title="Composite number">composite</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/11_(number)" title="11 (number)">11</a>, the fifth prime and first palindromic multi-digit number in base 10.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/12_(number)" title="12 (number)">12</a>, the first <a href="/wiki/Sublime_number" title="Sublime number">sublime number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/17_(number)" title="17 (number)">17</a>, the sum of the first 4 prime numbers, and the only prime which is the sum of 4 consecutive primes.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/24_(number)" title="24 (number)">24</a>, all <a href="/wiki/Dirichlet_character" title="Dirichlet character">Dirichlet characters</a> <a href="/wiki/Modular_arithmetic" title="Modular arithmetic">mod</a> n are <a href="/wiki/Real_number" title="Real number">real</a> <a href="/wiki/If_and_only_if" title="If and only if">if and only if</a> n is a divisor of 24.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/25_(number)" title="25 (number)">25</a>, the first <a href="/wiki/Centered_square_number" title="Centered square number">centered square number</a> besides 1 that is also a square number.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/27_(number)" title="27 (number)">27</a>, the <a href="/wiki/Cube_(algebra)" title="Cube (algebra)">cube</a> of 3, the value of 33.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/28_(number)" title="28 (number)">28</a>, the second <a href="/wiki/Perfect_number" title="Perfect number">perfect number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/30_(number)" title="30 (number)">30</a>, the smallest <a href="/wiki/Sphenic_number" title="Sphenic number">sphenic number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/32_(number)" title="32 (number)">32</a>, the smallest nontrivial <a href="/wiki/Fifth_power_(algebra)" title="Fifth power (algebra)">fifth power</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/36_(number)" title="36 (number)">36</a>, the smallest number which is a <a href="/wiki/Perfect_power" title="Perfect power">perfect power</a> but not a <a href="/wiki/Prime_power" title="Prime power">prime power</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/70_(number)" title="70 (number)">70</a>, the smallest <a href="/wiki/Weird_number" title="Weird number">weird number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/72_(number)" title="72 (number)">72</a>, the smallest <a href="/wiki/Achilles_number" title="Achilles number">Achilles number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/108_(number)" title="108 (number)">108</a>, the second <a href="/wiki/Achilles_number" title="Achilles number">Achilles number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/255_(number)" title="255 (number)">255</a>, 28 − 1, the smallest <a href="/wiki/Perfect_totient_number" title="Perfect totient number">perfect totient number</a> that is neither a power of three nor thrice a prime; it is also the largest number that can be represented using an <a href="/wiki/8-bit" class="mw-redirect" title="8-bit">8-bit</a> unsigned <a href="/wiki/Integer_(computer_science)" title="Integer (computer science)">integer</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/341_(number)" class="mw-redirect" title="341 (number)">341</a>, the smallest base 2 <a href="/wiki/Fermat_pseudoprime" title="Fermat pseudoprime">Fermat pseudoprime</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/496_(number)" title="496 (number)">496</a>, the third <a href="/wiki/Perfect_number" title="Perfect number">perfect number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/1729_(number)" title="1729 (number)">1729</a>, the <a href="/wiki/Hardy%E2%80%93Ramanujan_number" class="mw-redirect" title="Hardy–Ramanujan number">Hardy–Ramanujan number</a>, also known as the second <a href="/wiki/Taxicab_number" title="Taxicab number">taxicab number</a>; that is, the smallest positive integer that can be written as the sum of two positive cubes in two different ways.<a href="#cite_note-1">[1]</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/8128_(number)" class="mw-redirect" title="8128 (number)">8128</a>, the fourth perfect number.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/142857_(number)" class="mw-redirect" title="142857 (number)">142857</a>, the smallest <a href="/wiki/Base_10" class="mw-redirect" title="Base 10">base 10</a> <a href="/wiki/Cyclic_number" title="Cyclic number">cyclic number</a>.</li><li style="line-height: inherit; margin: 0"><a href="/wiki/9814072356_(number)" class="mw-redirect" title="9814072356 (number)">9814072356</a>, the largest <a href="/wiki/Perfect_power" title="Perfect power">perfect power</a> that contains no repeated digits in base ten. </li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Cultural_or_practical_significance">Cultural or practical significance</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=3" title="Edit section: Cultural or practical significance">edit</a>]</div> Along with their mathematical properties, many integers have <a href="/wiki/Culture" title="Culture">cultural</a> significance<a href="#cite_note-2">[2]</a> or are also notable for their use in computing and measurement. As mathematical properties (such as divisibility) can confer practical utility, there may be interplay and connections between the cultural or practical significance of an integer and its mathematical properties. <div class="collapsible-list mw-collapsible" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold;"><div>List of integers notable for their cultural meanings</div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit;"><li style="line-height: inherit; margin: 0"><a href="/wiki/3_(number)" class="mw-redirect" title="3 (number)">3</a>, significant in <a href="/wiki/Christianity" title="Christianity">Christianity</a> as the <a href="/wiki/Trinity" title="Trinity">Trinity</a>. Also considered significant in <a href="/wiki/Hinduism" title="Hinduism">Hinduism</a> (<a href="/wiki/Trimurti" title="Trimurti">Trimurti</a>, <a href="/wiki/Tridevi" title="Tridevi">Tridevi</a>). Holds significance in a number of ancient mythologies. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/4_(number)" class="mw-redirect" title="4 (number)">4</a>, considered an <a href="/wiki/Tetraphobia" title="Tetraphobia">"unlucky" number</a> in modern China, Japan and Korea due to its audible similarity to the word "death" in their respective languages. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/7_(number)" class="mw-redirect" title="7 (number)">7</a>, the number of days in a week, and considered a "lucky" number in Western cultures. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/8_(number)" class="mw-redirect" title="8 (number)">8</a>, considered a <a href="/wiki/Chinese_numerology#Eight" title="Chinese numerology">"lucky" number in Chinese culture</a> due to its aural similarity to the Chinese term for prosperity. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/12_(number)" title="12 (number)">12</a>, a common grouping known as a <a href="/wiki/Dozen" title="Dozen">dozen</a> and the number of months in a year, of constellations of the <a href="/wiki/Zodiac" title="Zodiac">Zodiac</a> and <a href="/wiki/Astrological_sign" title="Astrological sign">astrological signs</a> and of <a href="/wiki/Apostles_in_the_New_Testament" title="Apostles in the New Testament">Apostles</a> of <a href="/wiki/Jesus" title="Jesus">Jesus</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/13_(number)" title="13 (number)">13</a>, considered an <a href="/wiki/Triskaidekaphobia" title="Triskaidekaphobia">"unlucky" number</a> in Western superstition. Also known as a "<a href="/wiki/Baker%27s_dozen" class="mw-redirect" title="Baker's dozen">Baker's dozen</a>".<a href="#cite_note-3">[3]</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/17_(number)" title="17 (number)">17</a>, considered <a href="/wiki/Heptadecaphobia" title="Heptadecaphobia">ill-fated</a> in Italy and other countries of Greek and Latin origins. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/18_(number)" title="18 (number)">18</a>, considered a "lucky" number due to it being the value for the <a href="/wiki/Chai_(symbol)" title="Chai (symbol)">Hebrew word for life</a> in <a href="/wiki/Gematria" title="Gematria">Jewish numerology</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/40_(number)" title="40 (number)">40</a>, considered a significant number in <a href="/wiki/Tengrism" title="Tengrism">Tengrism</a> and Turkish folklore. Multiple customs, such as those relating to how many days one must visit someone after a death in the family, include the number forty. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/42_(number)" title="42 (number)">42</a>, the "answer to the ultimate question of life, the universe, and everything" in the popular 1979 science fiction work <a href="/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy" title="The Hitchhiker's Guide to the Galaxy">The Hitchhiker's Guide to the Galaxy</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/69_(number)" title="69 (number)">69</a>, a slang term for reciprocal <a href="/wiki/Oral_sex" title="Oral sex">oral sex</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/86_(number)" title="86 (number)">86</a>, a slang term that is used in the American popular culture as a transitive verb to mean throw out or get rid of.<a href="#cite_note-mw-4">[4]</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/108_(number)" title="108 (number)">108</a>, considered sacred by the <a href="/wiki/Dharmic_religions" class="mw-redirect" title="Dharmic religions">Dharmic religions</a>. Approximately equal to the ratio of the distance from Earth to Sun and diameter of the Sun. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/420_(number)" title="420 (number)">420</a>, a code-term that refers to the consumption of <a href="/wiki/420_(cannabis_culture)" title="420 (cannabis culture)">cannabis</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/666_(number)" title="666 (number)">666</a>, the <a href="/wiki/Number_of_the_beast" title="Number of the beast">number of the beast</a> from the <a href="/wiki/Book_of_Revelation" title="Book of Revelation">Book of Revelation</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/786_(number)" title="786 (number)">786</a>, regarded as sacred in the Muslim <a href="/wiki/Abjad_numerals" title="Abjad numerals">Abjad numerology</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/5040_(number)" title="5040 (number)">5040</a>, mentioned by <a href="/wiki/Plato" title="Plato">Plato</a> in the <a href="/wiki/Laws_(dialogue)" title="Laws (dialogue)">Laws</a> as one of the most important numbers for the city. </li></ul> </div> <div class="collapsible-list mw-collapsible" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold;"><div>List of integers notable for their use in units, measurements and scales</div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit;"><li style="line-height: inherit; margin: 0"><a href="/wiki/10" title="10">10</a>, the number of digits in the <a href="/wiki/Decimal" title="Decimal">decimal</a> number system. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/12_(number)" title="12 (number)">12</a>, the <a href="/wiki/Duodecimal" title="Duodecimal">number base</a> for measuring time in many civilizations. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/14_(number)" title="14 (number)">14</a>, the number of days in a <a href="/wiki/Fortnight" title="Fortnight">fortnight</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/16_(number)" title="16 (number)">16</a>, the number of digits in the <a href="/wiki/Hexadecimal" title="Hexadecimal">hexadecimal</a> number system. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/24_(number)" title="24 (number)">24</a>, number of <a href="/wiki/Hour" title="Hour">hours</a> in a <a href="/wiki/Day" title="Day">day</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/31_(number)" title="31 (number)">31</a>, the number of days most months of the year have. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/60_(number)" title="60 (number)">60</a>, the <a href="/wiki/Sexagesimal" title="Sexagesimal">number base</a> for some ancient counting systems, such as the <a href="/wiki/Babylonian_numerals" class="mw-redirect" title="Babylonian numerals">Babylonians'</a>, and the basis for many modern measuring systems. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/360_(number)" title="360 (number)">360</a>, the number of <a href="/wiki/Degree_(angle)" title="Degree (angle)">sexagesimal degrees</a> in a full <a href="/wiki/Circle" title="Circle">circle</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/365_(number)" title="365 (number)">365</a>, the number of days in the common year, while there are 366 days in a <a href="/wiki/Leap_year" title="Leap year">leap year</a> of the solar <a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian calendar</a>. </li></ul> </div> <div class="collapsible-list mw-collapsible" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold;"><div>List of integers notable in computing</div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit;"><li style="line-height: inherit; margin: 0"><a href="/wiki/4" title="4">4</a>, the number of <a href="/wiki/Bit" title="Bit">bits</a> in a <a href="/wiki/Nibble" title="Nibble">nibble</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/8" title="8">8</a>, the number of bits in an <a href="/wiki/Octet_(computing)" title="Octet (computing)">octet</a> and usually in a <a href="/wiki/Byte" title="Byte">byte</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/256_(number)" title="256 (number)">256</a>, The number of possible combinations within <a href="/wiki/8-bit" class="mw-redirect" title="8-bit">8 bits</a>, or an octet. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/1024_(number)" title="1024 (number)">1024</a>, the number of bytes in a <a href="/wiki/Kibibyte" class="mw-redirect" title="Kibibyte">kibibyte</a>, and bits in a <a href="/wiki/Kibibit" class="mw-redirect" title="Kibibit">kibibit</a>. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/65535_(number)" class="mw-redirect" title="65535 (number)">65535</a>, 216 − 1, the maximum value of a <a href="/wiki/16-bit" class="mw-redirect" title="16-bit">16-bit</a> unsigned integer. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/65536_(number)" class="mw-redirect" title="65536 (number)">65536</a>, 216, the number of possible <a href="/wiki/16-bit" class="mw-redirect" title="16-bit">16-bit</a> combinations. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/65537_(number)" class="mw-redirect" title="65537 (number)">65537</a>, 216 + 1, the most popular RSA public key prime exponent in most SSL/TLS certificates on the Web/Internet. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/16777216_(number)" class="mw-redirect" title="16777216 (number)">16777216</a>, 224, or 166; the hexadecimal "million" (0x1000000), and the total number of possible color combinations in 24/32-bit <a href="/wiki/24-bit_color" class="mw-redirect" title="24-bit color">True Color</a> computer graphics. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/2147483647" class="mw-redirect" title="2147483647">2147483647</a>, 231 − 1, the maximum value of a <a href="/wiki/32-bit" class="mw-redirect" title="32-bit">32-bit</a> <a href="/wiki/Integer_(computer_science)" title="Integer (computer science)">signed integer</a> using <a href="/wiki/Two%27s_complement" title="Two's complement">two's complement</a> representation. </li><li style="line-height: inherit; margin: 0"><a href="/wiki/9223372036854775807" class="mw-redirect" title="9223372036854775807">9223372036854775807</a>, 263 − 1, the maximum value of a <a href="/wiki/64-bit" class="mw-redirect" title="64-bit">64-bit</a> <a href="/wiki/Integer_(computer_science)" title="Integer (computer science)">signed integer</a> using <a href="/wiki/Two%27s_complement" title="Two's complement">two's complement</a> representation. </li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Classes_of_natural_numbers">Classes of natural numbers</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=4" title="Edit section: Classes of natural numbers">edit</a>]</div> Subsets of the natural numbers, such as the prime numbers, may be grouped into sets, for instance based on the divisibility of their members. Infinitely many such sets are possible. A list of notable classes of natural numbers may be found at <a href="/wiki/Template:Classes_of_natural_numbers" title="Template:Classes of natural numbers">classes of natural numbers</a>. <div class="mw-heading mw-heading3"><h3 id="Prime_numbers">Prime numbers</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=5" title="Edit section: Prime numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Prime_number" title="Prime number">Prime number</a> and <a href="/wiki/List_of_prime_numbers" title="List of prime numbers">List of prime numbers</a></div> A prime number is a positive integer which has exactly two <a href="/wiki/Divisor" title="Divisor">divisors</a>: 1 and itself. The first 100 prime numbers are: <table class="wikitable sortable mw-collapsible" style="text-align:center;"> <caption class="nowrap">Table of first 100 prime numbers </caption> <tbody><tr> <td>  <a href="/wiki/2_(number)" class="mw-redirect" title="2 (number)">2</a></td> <td>  <a href="/wiki/3_(number)" class="mw-redirect" title="3 (number)">3</a></td> <td>  <a href="/wiki/5_(number)" class="mw-redirect" title="5 (number)">5</a></td> <td>  <a href="/wiki/7_(number)" class="mw-redirect" title="7 (number)">7</a></td> <td> <a href="/wiki/11_(number)" title="11 (number)">11</a></td> <td> <a href="/wiki/13_(number)" title="13 (number)">13</a></td> <td> <a href="/wiki/17_(number)" title="17 (number)">17</a></td> <td> <a href="/wiki/19_(number)" title="19 (number)">19</a></td> <td> <a href="/wiki/23_(number)" title="23 (number)">23</a></td> <td> <a href="/wiki/29_(number)" title="29 (number)">29</a> </td></tr> <tr> <td> <a href="/wiki/31_(number)" title="31 (number)">31</a></td> <td> <a href="/wiki/37_(number)" title="37 (number)">37</a></td> <td> <a href="/wiki/41_(number)" title="41 (number)">41</a></td> <td> <a href="/wiki/43_(number)" title="43 (number)">43</a></td> <td> <a href="/wiki/47_(number)" title="47 (number)">47</a></td> <td> <a href="/wiki/53_(number)" title="53 (number)">53</a></td> <td> <a href="/wiki/59_(number)" title="59 (number)">59</a></td> <td> <a href="/wiki/61_(number)" title="61 (number)">61</a></td> <td> <a href="/wiki/67_(number)" title="67 (number)">67</a></td> <td> <a href="/wiki/71_(number)" title="71 (number)">71</a> </td></tr> <tr> <td> <a href="/wiki/73_(number)" title="73 (number)">73</a></td> <td> <a href="/wiki/79_(number)" title="79 (number)">79</a></td> <td> <a href="/wiki/83_(number)" title="83 (number)">83</a></td> <td> <a href="/wiki/89_(number)" title="89 (number)">89</a></td> <td> <a href="/wiki/97_(number)" title="97 (number)">97</a></td> <td><a href="/wiki/101_(number)" title="101 (number)">101</a></td> <td><a href="/wiki/103_(number)" title="103 (number)">103</a></td> <td><a href="/wiki/107_(number)" title="107 (number)">107</a></td> <td><a href="/wiki/109_(number)" title="109 (number)">109</a></td> <td><a href="/wiki/113_(number)" title="113 (number)">113</a> </td></tr> <tr> <td><a href="/wiki/127_(number)" title="127 (number)">127</a></td> <td><a href="/wiki/131_(number)" title="131 (number)">131</a></td> <td><a href="/wiki/137_(number)" title="137 (number)">137</a></td> <td><a href="/wiki/139_(number)" title="139 (number)">139</a></td> <td><a href="/wiki/149_(number)" title="149 (number)">149</a></td> <td><a href="/wiki/151_(number)" title="151 (number)">151</a></td> <td><a href="/wiki/157_(number)" title="157 (number)">157</a></td> <td><a href="/wiki/163_(number)" title="163 (number)">163</a></td> <td><a href="/wiki/167_(number)" title="167 (number)">167</a></td> <td><a href="/wiki/173_(number)" title="173 (number)">173</a> </td></tr> <tr> <td><a href="/wiki/179_(number)" title="179 (number)">179</a></td> <td><a href="/wiki/181_(number)" title="181 (number)">181</a></td> <td><a href="/wiki/191_(number)" title="191 (number)">191</a></td> <td><a href="/wiki/193_(number)" title="193 (number)">193</a></td> <td><a href="/wiki/197_(number)" title="197 (number)">197</a></td> <td><a href="/wiki/199_(number)" title="199 (number)">199</a></td> <td><a href="/wiki/211_(number)" title="211 (number)">211</a></td> <td><a href="/wiki/223_(number)" title="223 (number)">223</a></td> <td><a href="/wiki/227_(number)" title="227 (number)">227</a></td> <td><a href="/wiki/229_(number)" title="229 (number)">229</a> </td></tr> <tr> <td><a href="/wiki/233_(number)" title="233 (number)">233</a></td> <td><a href="/wiki/239_(number)" title="239 (number)">239</a></td> <td><a href="/wiki/241_(number)" title="241 (number)">241</a></td> <td><a href="/wiki/251_(number)" title="251 (number)">251</a></td> <td><a href="/wiki/257_(number)" title="257 (number)">257</a></td> <td><a href="/wiki/263_(number)" title="263 (number)">263</a></td> <td><a href="/wiki/269_(number)" title="269 (number)">269</a></td> <td><a href="/wiki/271_(number)" title="271 (number)">271</a></td> <td><a href="/wiki/277_(number)" title="277 (number)">277</a></td> <td><a href="/wiki/281_(number)" title="281 (number)">281</a> </td></tr> <tr> <td><a href="/wiki/283_(number)" title="283 (number)">283</a></td> <td><a href="/wiki/293_(number)" title="293 (number)">293</a></td> <td><a href="/wiki/307_(number)" title="307 (number)">307</a></td> <td><a href="/wiki/311_(number)" title="311 (number)">311</a></td> <td><a href="/wiki/313_(number)" title="313 (number)">313</a></td> <td><a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a></td> <td><a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a></td> <td><a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a></td> <td><a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a></td> <td><a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a> </td></tr> <tr> <td><a href="/wiki/353_(number)" title="353 (number)">353</a></td> <td><a href="/wiki/359_(number)" title="359 (number)">359</a></td> <td><a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a></td> <td><a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a></td> <td><a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a></td> <td><a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a></td> <td><a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a></td> <td><a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a></td> <td><a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a></td> <td><a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a> </td></tr> <tr> <td><a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a></td> <td><a href="/wiki/421_(number)" class="mw-redirect" title="421 (number)">421</a></td> <td><a href="/wiki/431_(number)" class="mw-redirect" title="431 (number)">431</a></td> <td><a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a></td> <td><a href="/wiki/439_(number)" class="mw-redirect" title="439 (number)">439</a></td> <td><a href="/wiki/443_(number)" class="mw-redirect" title="443 (number)">443</a></td> <td><a href="/wiki/449_(number)" class="mw-redirect" title="449 (number)">449</a></td> <td><a href="/wiki/457_(number)" class="mw-redirect" title="457 (number)">457</a></td> <td><a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a></td> <td><a href="/wiki/463_(number)" class="mw-redirect" title="463 (number)">463</a> </td></tr> <tr> <td><a href="/wiki/467_(number)" class="mw-redirect" title="467 (number)">467</a></td> <td><a href="/wiki/479_(number)" class="mw-redirect" title="479 (number)">479</a></td> <td><a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a></td> <td><a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a></td> <td><a href="/wiki/499_(number)" class="mw-redirect" title="499 (number)">499</a></td> <td><a href="/wiki/503_(number)" class="mw-redirect" title="503 (number)">503</a></td> <td><a href="/wiki/509_(number)" class="mw-redirect" title="509 (number)">509</a></td> <td><a href="/wiki/521_(number)" class="mw-redirect" title="521 (number)">521</a></td> <td><a href="/wiki/523_(number)" class="mw-redirect" title="523 (number)">523</a></td> <td><a href="/wiki/541_(number)" class="mw-redirect" title="541 (number)">541</a> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Highly_composite_numbers">Highly composite numbers</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=6" title="Edit section: Highly composite numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Highly_composite_number" title="Highly composite number">Highly composite number</a></div> A highly composite number (HCN) is a positive integer with more divisors than any smaller positive integer. They are often used in <a href="/wiki/Geometry" title="Geometry">geometry</a>, grouping and time measurement. The first 20 highly composite numbers are: <a href="/wiki/1_(number)" class="mw-redirect" title="1 (number)">1</a>, <a href="/wiki/2_(number)" class="mw-redirect" title="2 (number)">2</a>, <a href="/wiki/4_(number)" class="mw-redirect" title="4 (number)">4</a>, <a href="/wiki/6_(number)" class="mw-redirect" title="6 (number)">6</a>, <a href="/wiki/12_(number)" title="12 (number)">12</a>, <a href="/wiki/24_(number)" title="24 (number)">24</a>, <a href="/wiki/36_(number)" title="36 (number)">36</a>, <a href="/wiki/48_(number)" title="48 (number)">48</a>, <a href="/wiki/60_(number)" title="60 (number)">60</a>, <a href="/wiki/120_(number)" title="120 (number)">120</a>, <a href="/wiki/180_(number)" title="180 (number)">180</a>, <a href="/wiki/240_(number)" title="240 (number)">240</a>, <a href="/wiki/360_(number)" title="360 (number)">360</a>, <a href="/wiki/720_(number)" title="720 (number)">720</a>, <a href="/wiki/840_(number)" title="840 (number)">840</a>, <a href="/wiki/1260_(number)" class="mw-redirect" title="1260 (number)">1260</a>, <a href="/wiki/1680_(number)" class="mw-redirect" title="1680 (number)">1680</a>, <a href="/wiki/2520_(number)" title="2520 (number)">2520</a>, <a href="/wiki/5040_(number)" title="5040 (number)">5040</a>, <a href="/wiki/7560_(number)" class="mw-redirect" title="7560 (number)">7560</a> <div class="mw-heading mw-heading3"><h3 id="Perfect_numbers">Perfect numbers</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=7" title="Edit section: Perfect numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Perfect_number" title="Perfect number">Perfect number</a></div> A perfect number is an integer that is the sum of its positive proper divisors (all divisors except itself). The first 10 perfect numbers: <div><ol style="list-style-type:decimal"><li>  <a href="/wiki/6_(number)" class="mw-redirect" title="6 (number)">6</a></li><li>  <a href="/wiki/28_(number)" title="28 (number)">28</a></li><li>  <a href="/wiki/496_(number)" title="496 (number)">496</a></li><li>  <a href="/wiki/8128_(number)" class="mw-redirect" title="8128 (number)">8128</a></li><li>  33 550 336</li><li>  8 589 869 056</li><li>  137 438 691 328</li><li>  2 305 843 008 139 952 128</li><li>  2 658 455 991 569 831 744 654 692 615 953 842 176</li><li>  191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216</li></ol></div> <div class="mw-heading mw-heading2"><h2 id="Integers">Integers</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=8" title="Edit section: Integers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Integer" title="Integer">Integer</a></div> The integers are a <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">set</a> of numbers commonly encountered in <a href="/wiki/Arithmetic" title="Arithmetic">arithmetic</a> and <a href="/wiki/Number_theory" title="Number theory">number theory</a>. There are many <a href="/wiki/Subsets" class="mw-redirect" title="Subsets">subsets</a> of the integers, including the <a href="/wiki/Natural_numbers" class="mw-redirect" title="Natural numbers">natural numbers</a>, <a href="/wiki/Prime_numbers" class="mw-redirect" title="Prime numbers">prime numbers</a>, <a href="/wiki/Perfect_numbers" class="mw-redirect" title="Perfect numbers">perfect numbers</a>, etc. Many integers are notable for their mathematical properties. Integers are usually symbolised by a boldface Z (or <a href="/wiki/Blackboard_bold" title="Blackboard bold">blackboard bold</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {\mathbb {Z} } }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {\mathbb {Z} } }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51a1b510a6d23815b082c857b064ad1741203a01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle \mathbb {\mathbb {Z} } }">, Unicode <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734">U+2124 ℤ DOUBLE-STRUCK CAPITAL Z); this became the symbol for the integers based on the German word for "numbers" (<a href="https://en.wiktionary.org/wiki/Zahlen" class="extiw" title="wiktionary:Zahlen">Zahlen</a>). Notable integers include <a href="/wiki/%E2%88%921" title="−1">−1</a>, the additive inverse of unity, and <a href="/wiki/0" title="0">0</a>, the <a href="/wiki/Additive_identity" title="Additive identity">additive identity</a>. As with the natural numbers, the integers may also have cultural or practical significance. For instance, <a href="/wiki/%E2%88%9240_(number)" class="mw-redirect" title="−40 (number)">−40</a> is the equal point in the <a href="/wiki/Fahrenheit" title="Fahrenheit">Fahrenheit</a> and <a href="/wiki/Celsius" title="Celsius">Celsius</a> scales. <div class="mw-heading mw-heading3"><h3 id="SI_prefixes">SI prefixes</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=9" title="Edit section: SI prefixes">edit</a>]</div> One important use of integers is in <a href="/wiki/Orders_of_magnitude_(numbers)" title="Orders of magnitude (numbers)">orders of magnitude</a>. A <a href="/wiki/Power_of_10" title="Power of 10">power of 10</a> is a number 10k, where k is an integer. For instance, with k = 0, 1, 2, 3, ..., the appropriate powers of ten are 1, 10, 100, 1000, ... Powers of ten can also be fractional: for instance, k = -3 gives 1/1000, or 0.001. This is used in <a href="/wiki/Scientific_notation" title="Scientific notation">scientific notation</a>, real numbers are written in the form m × 10n. The number 394,000 is written in this form as 3.94 × 105. Integers are used as <a href="/wiki/Metric_prefix" title="Metric prefix">prefixes</a> in the <a href="/wiki/SI_system" class="mw-redirect" title="SI system">SI system</a>. A metric prefix is a <a href="/wiki/Unit_prefix" title="Unit prefix">unit prefix</a> that precedes a basic unit of measure to indicate a <a href="/wiki/Multiple_(mathematics)" title="Multiple (mathematics)">multiple</a> or <a href="/wiki/Fraction_(mathematics)" class="mw-redirect" title="Fraction (mathematics)">fraction</a> of the unit. Each prefix has a unique symbol that is prepended to the unit symbol. The prefix <a href="/wiki/Kilo-" title="Kilo-">kilo-</a>, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix <a href="/wiki/Milli-" title="Milli-">milli-</a>, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre. <table class="wikitable sortable"> <tbody><tr> <th>Value </th> <th>1000m </th> <th>Name </th> <th>Symbol </th></tr> <tr> <td style="text-align:right;">1000</td> <td>10001</td> <td><a href="/wiki/Kilo-" title="Kilo-">Kilo</a> </td> <td>k </td></tr> <tr> <td style="text-align:right;">1000000</td> <td>10002</td> <td><a href="/wiki/Mega-" title="Mega-">Mega</a> </td> <td>M </td></tr> <tr> <td style="text-align:right;">1000000000</td> <td>10003</td> <td><a href="/wiki/Giga-" title="Giga-">Giga</a> </td> <td>G </td></tr> <tr> <td style="text-align:right;">1000000000000</td> <td>10004</td> <td><a href="/wiki/Tera-" class="mw-redirect" title="Tera-">Tera</a> </td> <td>T </td></tr> <tr> <td style="text-align:right;">1000000000000000</td> <td>10005</td> <td><a href="/wiki/Peta-" class="mw-redirect" title="Peta-">Peta</a> </td> <td>P </td></tr> <tr> <td style="text-align:right;">1000000000000000000</td> <td>10006</td> <td><a href="/wiki/Exa-" class="mw-redirect" title="Exa-">Exa</a> </td> <td>E </td></tr> <tr> <td style="text-align:right;">1000000000000000000000</td> <td>10007</td> <td><a href="/wiki/Zetta-" class="mw-redirect" title="Zetta-">Zetta</a> </td> <td>Z </td></tr> <tr> <td style="text-align:right;">1000000000000000000000000</td> <td>10008</td> <td><a href="/wiki/Yotta-" class="mw-redirect" title="Yotta-">Yotta</a> </td> <td>Y </td></tr> <tr> <td style="text-align:right;">1000000000000000000000000000</td> <td>10009</td> <td><a href="/wiki/Ronna-" class="mw-redirect" title="Ronna-">Ronna</a> </td> <td>R </td></tr> <tr> <td style="text-align:right;">1000000000000000000000000000000</td> <td>100010</td> <td><a href="/wiki/Quetta-" class="mw-redirect" title="Quetta-">Quetta</a> </td> <td>Q </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Rational_numbers">Rational numbers</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=10" title="Edit section: Rational numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Rational_number" title="Rational number">Rational number</a></div> A rational number is any number that can be expressed as the <a href="/wiki/Quotient" title="Quotient">quotient</a> or <a href="/wiki/Fraction_(mathematics)" class="mw-redirect" title="Fraction (mathematics)">fraction</a> p/q of two <a href="/wiki/Integer" title="Integer">integers</a>, a <a href="/wiki/Numerator" class="mw-redirect" title="Numerator">numerator</a> p and a non-zero <a href="/wiki/Denominator" class="mw-redirect" title="Denominator">denominator</a> q.<a href="#cite_note-Rosen-5">[5]</a> Since q may be equal to 1, every integer is trivially a rational number. The <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">set</a> of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q (or <a href="/wiki/Blackboard_bold" title="Blackboard bold">blackboard bold</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="{\displaystyle \mathbb {Q} }">, Unicode <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734">U+211A ℚ DOUBLE-STRUCK CAPITAL Q);<a href="#cite_note-6">[6]</a> it was thus denoted in 1895 by <a href="/wiki/Giuseppe_Peano" title="Giuseppe Peano">Giuseppe Peano</a> after <a href="https://en.wiktionary.org/wiki/quoziente" class="extiw" title="wikt:quoziente">quoziente</a>, Italian for "<a href="/wiki/Quotient" title="Quotient">quotient</a>". Rational numbers such as 0.12 can be represented in <a href="/wiki/Infinity" title="Infinity">infinitely</a> many ways, e.g. zero-point-one-two (0.12), three twenty-fifths (<style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style>⁠3/25⁠), nine seventy-fifths (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠9/75⁠), etc. This can be mitigated by representing rational numbers in a canonical form as an irreducible fraction. A list of rational numbers is shown below. The names of fractions can be found at <a href="/wiki/Numeral_(linguistics)" title="Numeral (linguistics)">numeral (linguistics)</a>. <style data-mw-deduplicate="TemplateStyles:r1253789634">@media screen{.mw-parser-output .sticky-header>thead>tr:first-child,.mw-parser-output .sticky-header>caption+tbody>tr:first-child,.mw-parser-output .sticky-header>tbody:first-child>tr:first-child,.mw-parser-output .sticky-header-multi>thead{position:sticky;top:0;z-index:10}.mw-parser-output .sticky-header:not(.wikitable),.mw-parser-output .sticky-header-multi:not(.wikitable){background-color:white}.mw-parser-output .sticky-header:not(.wikitable)>*,.mw-parser-output .sticky-header:not(.wikitable)>thead>tr:first-child,.mw-parser-output .sticky-header:not(.wikitable)>caption+tbody>tr:first-child,.mw-parser-output .sticky-header:not(.wikitable)>tbody:first-child>tr:first-child,.mw-parser-output .sticky-header-multi:not(.wikitable)>thead,.mw-parser-output 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.sticky-header-multi.static-row-numbers.wikitable>tbody>tr:not(.static-row-header)::before{border-bottom-width:0!important;border-right-width:0!important}body.skin-timeless .mw-parser-output .content-table-scrollbar,body.skin-timeless .mw-parser-output .overflowed,body.skin-timeless .mw-parser-output .overflowed .content-table{overflow:visible}body.skin-timeless .mw-parser-output .scroll-right.overflowed .content-table-right{box-shadow:none;border-left:none}}@media screen and (min-width:1120px){body.vector-sticky-header-visible .mw-parser-output .sticky-header>thead>tr:first-child,body.vector-sticky-header-visible .mw-parser-output .sticky-header>caption+tbody>tr:first-child,body.vector-sticky-header-visible .mw-parser-output .sticky-header>tbody:first-child>tr:first-child,body.vector-sticky-header-visible .mw-parser-output .sticky-header-multi>thead{top:3.125rem}}@media screen and (min-width:851px){body.skin-timeless .mw-parser-output .sticky-header>thead>tr:first-child,body.skin-timeless .mw-parser-output .sticky-header>caption+tbody>tr:first-child,body.skin-timeless .mw-parser-output .sticky-header>tbody:first-child>tr:first-child,body.skin-timeless .mw-parser-output .sticky-header-multi>thead{top:3.51em}}@media screen and (max-width:639px){body.skin-minerva .mw-parser-output .sticky-header,body.skin-minerva .mw-parser-output .sticky-header-multi,body.skin-monobook .mw-parser-output .sticky-header,body.skin-monobook .mw-parser-output .sticky-header-multi,body.skin-vector-legacy .mw-parser-output .sticky-header,body.skin-vector-legacy .mw-parser-output .sticky-header-multi,body.skin-vector-2022 .mw-parser-output .sticky-header,body.skin-vector-2022 .mw-parser-output .sticky-header-multi{display:table}body.skin-minerva .mw-parser-output .sticky-header>caption,body.skin-minerva .mw-parser-output .sticky-header-multi>caption{display:table-caption}}@media screen{html.skin-theme-clientpref-night body.skin-minerva .mw-parser-output .sticky-header-multi.wikitable{background-color:#101418}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os body.skin-minerva .mw-parser-output .sticky-header-multi.wikitable{background-color:#101418}}</style> <table class="wikitable sortable sticky-header"> <caption>Table of notable rational numbers </caption> <tbody><tr> <th>Decimal expansion</th> <th>Fraction </th> <th>Notability </th></tr> <tr> <td>1.0 </td> <td rowspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/1⁠ </td> <td rowspan="2">One is the multiplicative identity. One is a rational number, as it is equal to 1/1. </td></tr> <tr> <td>1 </td></tr> <tr> <td>−0.083 333... </td> <td style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠−+1/12⁠ </td> <td>The value assigned to the series <a href="/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF" title="1 + 2 + 3 + 4 + ⋯">1+2+3...</a> by <a href="/wiki/Zeta_function_regularization" title="Zeta function regularization">zeta function regularization</a> and <a href="/wiki/Ramanujan_summation" title="Ramanujan summation">Ramanujan summation</a>. </td></tr> <tr> <td>0.5 </td> <td style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/2⁠ </td> <td><a href="/wiki/One_half" title="One half">One half</a> occurs commonly in mathematical equations and in real world proportions. One half appears in the formula for the area of a triangle: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/2⁠ × base × perpendicular height and in the formulae for <a href="/wiki/Figurate_numbers" class="mw-redirect" title="Figurate numbers">figurate numbers</a>, such as <a href="/wiki/Triangular_number" title="Triangular number">triangular numbers</a> and <a href="/wiki/Pentagonal_number" title="Pentagonal number">pentagonal numbers</a>. </td></tr> <tr> <td>3.142 857... </td> <td style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠22/7⁠ </td> <td>A widely used approximation for the number <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }">. It can be <a href="/wiki/Proof_that_22/7_exceeds_%CF%80" title="Proof that 22/7 exceeds π">proven</a> that this number exceeds <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }">. </td></tr> <tr> <td>0.166 666... </td> <td style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035">⁠1/6⁠ </td> <td>One sixth. Often appears in mathematical equations, such as in the <a href="/wiki/List_of_mathematical_series" title="List of mathematical series">sum of squares of the integers</a> and in the solution to the Basel problem. </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Real_numbers">Real numbers</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=11" title="Edit section: Real numbers">edit</a>]</div> <a href="/wiki/Real_numbers" class="mw-redirect" title="Real numbers">Real numbers</a> are least upper bounds of sets of rational numbers that are bounded above, or greatest lower bounds of sets of rational numbers that are bounded below, or limits of convergent sequences of rational numbers. real numbers that are not rational numbers are called <a href="/wiki/Irrational_numbers" class="mw-redirect" title="Irrational numbers">irrational numbers</a>. The real numbers are categorised as algebraic numbers (which are the root of a polynomial with rational coefficients) or transcendental numbers, which are not; all rational numbers are algebraic. <div class="mw-heading mw-heading3"><h3 id="Algebraic_numbers">Algebraic numbers</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=12" title="Edit section: Algebraic numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Algebraic_number" title="Algebraic number">Algebraic number</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1253789634"> <table class="wikitable sortable sticky-header"> <tbody><tr> <th>Name </th> <th>Expression</th> <th>Decimal expansion</th> <th>Notability </th></tr> <tr> <td><a href="/wiki/Golden_ratio_conjugate" class="mw-redirect" title="Golden ratio conjugate">Golden ratio conjugate</a> (<math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" 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 \Phi }">) </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {{\sqrt {5}}-1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> <mo>−</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\sqrt {5}}-1}{2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cb82ebfedf3731743b3af4c09a3ec3abc2840be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.937ex; height:5.843ex;" alt="{\displaystyle {\frac {{\sqrt {5}}-1}{2}}}"> </td> <td>0.618033988749894848204586834366 </td> <td><a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">Reciprocal</a> of (and one less than) the <a href="/wiki/Golden_ratio" title="Golden ratio">golden ratio</a>. </td></tr> <tr> <td><a href="/wiki/Twelfth_root_of_two" title="Twelfth root of two">Twelfth root of two</a> </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{12}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{12}]{2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc835f27425fb3140e1f75a5faa35b1e8b9efc35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.107ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{12}]{2}}}"> </td> <td>1.059463094359295264561825294946 </td> <td>Proportion between the frequencies of adjacent <a href="/wiki/Semitone" title="Semitone">semitones</a> in the <a href="/wiki/12_tone_equal_temperament" class="mw-redirect" title="12 tone equal temperament">12 tone equal temperament</a> scale. </td></tr> <tr> <td><a href="/wiki/Cube_root" title="Cube root">Cube root</a> of two </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{3}]{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{3}]{2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ca071ab504481c2bb76081aacb03f5519930710" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{3}]{2}}}"> </td> <td>1.259921049894873164767210607278 </td> <td>Length of the edge of a <a href="/wiki/Cube" title="Cube">cube</a> with volume two. See <a href="/wiki/Doubling_the_cube" title="Doubling the cube">doubling the cube</a> for the significance of this number. </td></tr> <tr> <td><a href="/wiki/Conway_constant#Basic_properties" class="mw-redirect" title="Conway constant">Conway's constant</a> </td> <td style="text-align:center;">(cannot be written as expressions involving integers and the operations of addition, subtraction, multiplication, division, and the extraction of roots) </td> <td>1.303577269034296391257099112153 </td> <td>Defined as the unique positive real root of a certain polynomial of degree 71. The limit ratio between subsequent numbers in the binary <a href="/wiki/Look-and-say_sequence" title="Look-and-say sequence">Look-and-say sequence</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A014715" class="extiw" title="oeis:A014715">A014715</a>). </td></tr> <tr> <td><a href="/wiki/Plastic_ratio" title="Plastic ratio">Plastic ratio</a> </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>23</mn> <mn>3</mn> </mfrac> </msqrt> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>23</mn> <mn>3</mn> </mfrac> </msqrt> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/632f36cfd2cc1e85c932d625257359ebf7ed3330" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:32.133ex; height:7.509ex;" alt="{\displaystyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}}"> </td> <td>1.324717957244746025960908854478 </td> <td>The only real solution of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{3}=x+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}=x+1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0345ddb11d4101e841917b7a75f926704e633e5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.815ex; height:2.843ex;" alt="{\displaystyle x^{3}=x+1}">.(<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A060006" class="extiw" title="oeis:A060006">A060006</a>) The limit ratio between subsequent numbers in the <a href="/wiki/Plastic_ratio#Van_der_Laan_sequence" title="Plastic ratio">Van der Laan sequence</a>. (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A182097" class="extiw" title="oeis:A182097">A182097</a>) </td></tr> <tr> <td><a href="/wiki/Square_root_of_two" class="mw-redirect" title="Square root of two">Square root of two</a> </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"> </td> <td>1.414213562373095048801688724210 </td> <td>√2 = 2 sin 45° = 2 cos 45° <a href="/wiki/Square_root_of_two" class="mw-redirect" title="Square root of two">Square root of two</a> a.k.a. <a href="/wiki/Pythagoras%27_constant" class="mw-redirect" title="Pythagoras' constant">Pythagoras' constant</a>. Ratio of <a href="/wiki/Diagonal" title="Diagonal">diagonal</a> to side length in a <a href="/wiki/Square_(geometry)" class="mw-redirect" title="Square (geometry)">square</a>. Proportion between the sides of <a href="/wiki/Paper_size" title="Paper size">paper sizes</a> in the <a href="/wiki/ISO_216" title="ISO 216">ISO 216</a> series (originally <a href="/wiki/DIN" class="mw-redirect" title="DIN">DIN</a> 476 series). </td></tr> <tr> <td><a href="/wiki/Supergolden_ratio" title="Supergolden ratio">Supergolden ratio</a> </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dfrac {1+{\sqrt[{3}]{\dfrac {29+3{\sqrt {3\cdot 31}}}{2}}}+{\sqrt[{3}]{\dfrac {29-3{\sqrt {3\cdot 31}}}{2}}}}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>29</mn> <mo>+</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> <mo>⋅</mo> <mn>31</mn> </msqrt> </mrow> </mrow> <mn>2</mn> </mfrac> </mstyle> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>29</mn> <mo>−</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> <mo>⋅</mo> <mn>31</mn> </msqrt> </mrow> </mrow> <mn>2</mn> </mfrac> </mstyle> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mrow> <mn>3</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dfrac {1+{\sqrt[{3}]{\dfrac {29+3{\sqrt {3\cdot 31}}}{2}}}+{\sqrt[{3}]{\dfrac {29-3{\sqrt {3\cdot 31}}}{2}}}}{3}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f21b39f749d21a7cdab12f5c62d022b2cd8b3a1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:40.859ex; height:10.343ex;" alt="{\displaystyle {\dfrac {1+{\sqrt[{3}]{\dfrac {29+3{\sqrt {3\cdot 31}}}{2}}}+{\sqrt[{3}]{\dfrac {29-3{\sqrt {3\cdot 31}}}{2}}}}{3}}}"> </td> <td>1.465571231876768026656731225220 </td> <td>The only real solution of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{3}=x^{2}+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}=x^{2}+1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cab1579a96db79d879b29b8c893eaea62f2a8e4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.869ex; height:2.843ex;" alt="{\displaystyle x^{3}=x^{2}+1}">.(<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A092526" class="extiw" title="oeis:A092526">A092526</a>) The limit ratio between subsequent numbers in <a href="/wiki/Supergolden_ratio#Narayana_sequence" title="Supergolden ratio">Narayana's cows sequence</a>. (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A000930" class="extiw" title="oeis:A000930">A000930</a>) </td></tr> <tr> <td><a href="/wiki/Triangular_number#Triangular_roots_and_tests_for_triangular_numbers" title="Triangular number">Triangular root</a> of 2 </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {{\sqrt {17}}-1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>17</mn> </msqrt> </mrow> <mo>−</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\sqrt {17}}-1}{2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/059ae40553c3aacd61f3e936e7c156a702e6fdd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.1ex; height:5.843ex;" alt="{\displaystyle {\frac {{\sqrt {17}}-1}{2}}}"> </td> <td>1.561552812808830274910704927987 </td> <td> </td></tr> <tr> <td><a href="/wiki/Golden_ratio" title="Golden ratio">Golden ratio</a> (φ) </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {{\sqrt {5}}+1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\sqrt {5}}+1}{2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7092fcd8d54a8955b74df49a0de3bfbfb5d33638" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.937ex; height:5.843ex;" alt="{\displaystyle {\frac {{\sqrt {5}}+1}{2}}}"> </td> <td>1.618033988749894848204586834366 </td> <td>The larger of the two real roots of x2 = x + 1. </td></tr> <tr> <td><a href="/wiki/Square_root_of_three" class="mw-redirect" title="Square root of three">Square root of three</a> </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {3}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b19c09494138b5082459afac7f9a8d99c546fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.843ex;" alt="{\displaystyle {\sqrt {3}}}"> </td> <td>1.732050807568877293527446341506 </td> <td>√3 = 2 sin 60° = 2 cos 30° . A.k.a. <a href="/wiki/Vesica_piscis" title="Vesica piscis">the measure of the fish</a> or Theodorus' constant. Length of the <a href="/wiki/Space_diagonal" title="Space diagonal">space diagonal</a> of a <a href="/wiki/Cube" title="Cube">cube</a> with edge length 1. <a href="/wiki/Altitude_(triangle)" title="Altitude (triangle)">Altitude</a> of an <a href="/wiki/Equilateral_triangle" title="Equilateral triangle">equilateral triangle</a> with side length 2. Altitude of a <a href="/wiki/Hexagon" title="Hexagon">regular hexagon</a> with side length 1 and diagonal length 2. </td></tr> <tr> <td><a href="/wiki/Tribonacci_numbers" class="mw-redirect" title="Tribonacci numbers">Tribonacci constant</a> </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {3\cdot 11}}}}+{\sqrt[{3}]{19-3{\sqrt {3\cdot 11}}}}}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mn>19</mn> <mo>+</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> <mo>⋅</mo> <mn>11</mn> </msqrt> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mn>19</mn> <mo>−</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> <mo>⋅</mo> <mn>11</mn> </msqrt> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {3\cdot 11}}}}+{\sqrt[{3}]{19-3{\sqrt {3\cdot 11}}}}}{3}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e505f93d0dfc9d9ff812306a79c9a2034c0b20e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:39.187ex; height:7.676ex;" alt="{\displaystyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {3\cdot 11}}}}+{\sqrt[{3}]{19-3{\sqrt {3\cdot 11}}}}}{3}}}"> </td> <td>1.839286755214161132551852564653 </td> <td>The only real solution of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{3}=x^{2}+x+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}=x^{2}+x+1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1b8b2a75ab4e25a7081cec607ab2ece9818d99a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:16.039ex; height:2.843ex;" alt="{\displaystyle x^{3}=x^{2}+x+1}">.(<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A058265" class="extiw" title="oeis:A058265">A058265</a>) The limit ratio between subsequent numbers in the <a href="/wiki/Generalizations_of_Fibonacci_numbers#Tribonacci_numbers" title="Generalizations of Fibonacci numbers">Tribonacci sequence</a>.(<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A000073" class="extiw" title="oeis:A000073">A000073</a>) Appears in the volume and coordinates of the <a href="/wiki/Snub_cube" title="Snub cube">snub cube</a> and some related polyhedra. </td></tr> <tr> <td><a href="/wiki/Supersilver_ratio" title="Supersilver ratio">Supersilver ratio</a> </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dfrac {2+{\sqrt[{3}]{\dfrac {43+3{\sqrt {3\cdot 59}}}{2}}}+{\sqrt[{3}]{\dfrac {43-3{\sqrt {3\cdot 59}}}{2}}}}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>2</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>43</mn> <mo>+</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> <mo>⋅</mo> <mn>59</mn> </msqrt> </mrow> </mrow> <mn>2</mn> </mfrac> </mstyle> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>43</mn> <mo>−</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> <mo>⋅</mo> <mn>59</mn> </msqrt> </mrow> </mrow> <mn>2</mn> </mfrac> </mstyle> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> </mrow> <mn>3</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dfrac {2+{\sqrt[{3}]{\dfrac {43+3{\sqrt {3\cdot 59}}}{2}}}+{\sqrt[{3}]{\dfrac {43-3{\sqrt {3\cdot 59}}}{2}}}}{3}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b72b3fda21fb58c4de7c97e7c643a1c16d91b238" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:40.859ex; height:10.343ex;" alt="{\displaystyle {\dfrac {2+{\sqrt[{3}]{\dfrac {43+3{\sqrt {3\cdot 59}}}{2}}}+{\sqrt[{3}]{\dfrac {43-3{\sqrt {3\cdot 59}}}{2}}}}{3}}}"> </td> <td>2.20556943040059031170202861778 </td> <td>The only real solution of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{3}=2x^{2}+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}=2x^{2}+1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0542beb2e75e872e0742ab14d5787b33ae1a755" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.032ex; height:2.843ex;" alt="{\displaystyle x^{3}=2x^{2}+1}">.(<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A356035" class="extiw" title="oeis:A356035">A356035</a>) The limit ratio between subsequent numbers in the <a href="/wiki/Supersilver_ratio#Third-order_Pell_sequences" title="Supersilver ratio">third-order Pell sequence</a>. (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A008998" class="extiw" title="oeis:A008998">A008998</a>) </td></tr> <tr> <td><a href="/wiki/Square_root_of_five" class="mw-redirect" title="Square root of five">Square root of five</a> </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {5}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {5}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b78ccdb7e18e02d4fc567c66aac99bf524acb5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.843ex;" alt="{\displaystyle {\sqrt {5}}}"> </td> <td>2.236067977499789696409173668731 </td> <td>Length of the <a href="/wiki/Diagonal" title="Diagonal">diagonal</a> of a 1 × 2 <a href="/wiki/Rectangle" title="Rectangle">rectangle</a>. </td></tr> <tr> <td><a href="/wiki/Silver_ratio" title="Silver ratio">Silver ratio</a> (δS) </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}+1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc755e5f8f11e001e5c0f194683023266dac3aba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.101ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}+1}"> </td> <td>2.414213562373095048801688724210 </td> <td>The larger of the two real roots of x2 = 2x + 1. Altitude of a <a href="/wiki/Octagon" title="Octagon">regular octagon</a> with side length 1. </td></tr> <tr> <td><a href="/wiki/Bronze_ratio" class="mw-redirect" title="Bronze ratio">Bronze ratio</a> (S3) </td> <td style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {{\sqrt {13}}+3}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>13</mn> </msqrt> </mrow> <mo>+</mo> <mn>3</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {{\sqrt {13}}+3}{2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/924681808eaa098b42860342be7e3b57d08832bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.1ex; height:5.843ex;" alt="{\displaystyle {\frac {{\sqrt {13}}+3}{2}}}"> </td> <td>3.302775637731994646559610633735 </td> <td>The larger of the two real roots of x2 = 3x + 1. </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Transcendental_numbers">Transcendental numbers</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=13" title="Edit section: Transcendental numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Transcendental_number" title="Transcendental number">Transcendental number</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1253789634"> <table class="wikitable sortable sticky-header"> <tbody><tr> <th>Name </th> <th>Symbol or Formula </th> <th>Decimal expansion </th> <th>Notes and notability </th></tr> <tr> <td><a href="/wiki/Gelfond%27s_constant" title="Gelfond's constant">Gelfond's constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{\pi }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{\pi }}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eefb10ad1f3612be16a802dd913a9edfb5b9d823" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.258ex; height:2.343ex;" alt="{\displaystyle e^{\pi }}"> </td> <td>23.14069263277925... </td> <td> </td></tr> <tr> <td><a href="/wiki/Ramanujan%27s_constant" class="mw-redirect" title="Ramanujan's constant">Ramanujan's constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{\pi {\sqrt {163}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>163</mn> </msqrt> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{\pi {\sqrt {163}}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74fd61cac30067a5b97427918bbc23b1f310115f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.092ex; height:3.009ex;" alt="{\displaystyle e^{\pi {\sqrt {163}}}}"> </td> <td>262537412640768743.99999999999925... </td> <td> </td></tr> <tr> <td><a href="/wiki/Gaussian_integral" title="Gaussian integral">Gaussian integral</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>π</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {\pi }}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae18ec124928c74818b516e6350ca9610966c6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.268ex; height:3.009ex;" alt="{\displaystyle {\sqrt {\pi }}}"> </td> <td>1.772453850905516... </td> <td> </td></tr> <tr> <td><a href="/wiki/Komornik%E2%80%93Loreti_constant" title="Komornik–Loreti constant">Komornik–Loreti constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"> </td> <td>1.787231650... </td> <td> </td></tr> <tr> <td><a href="/wiki/Universal_parabolic_constant" title="Universal parabolic constant">Universal parabolic constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{2}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87858df7457aa93caaef5a316db87a7240cc8c29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.547ex; height:2.509ex;" alt="{\displaystyle P_{2}}"> </td> <td>2.29558714939... </td> <td> </td></tr> <tr> <td><a href="/wiki/Gelfond%E2%80%93Schneider_constant" title="Gelfond–Schneider constant">Gelfond–Schneider constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{\sqrt {2}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fe00689bdab9da3d6cd6015ca5e26c5702eaf22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.586ex; height:3.009ex;" alt="{\displaystyle 2^{\sqrt {2}}}"> </td> <td>2.665144143... </td> <td> </td></tr> <tr> <td><a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">Euler's number</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"> </td> <td>2.718281828459045235360287471352662497757247... </td> <td>Raising e to the power of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}">π will result in <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -1}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/704fb0427140d054dd267925495e78164fee9aac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.971ex; height:2.343ex;" alt="{\displaystyle -1}">. </td></tr> <tr> <td><a href="/wiki/Pi" title="Pi">Pi</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"> </td> <td>3.141592653589793238462643383279502884197169399375... </td> <td>Pi is a constant irrational number that is the result of dividing the circumference of a circle by its diameter. </td></tr> <tr> <td><a href="/wiki/Super_Root" class="mw-redirect" title="Super Root">Super square-root</a> of 2 </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\sqrt {2}}_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\sqrt {2}}_{s}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cbb09d4cb4c4fb66a0c13c8058f8dc0b85ac1fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.102ex; height:3.009ex;" alt="{\textstyle {\sqrt {2}}_{s}}"><a href="#cite_note-7">[7]</a> </td> <td>1.559610469...<a href="#cite_note-8">[8]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Liouville_constant" class="mw-redirect" title="Liouville constant">Liouville constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle L}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fb88de7e4d31737dae8f02575033272f29e6720" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\textstyle L}"> </td> <td>0.110001000000000000000001000... </td> <td> </td></tr> <tr> <td><a href="/wiki/Champernowne_constant" title="Champernowne constant">Champernowne constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle C_{10}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle C_{10}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a97a416629b352b1853f78026d15f44f24eef2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.538ex; height:2.509ex;" alt="{\textstyle C_{10}}"> </td> <td>0.12345678910111213141516... </td> <td>This constant contains every number string inside it, as its decimals are just every number in order. (1,2,3,etc.) </td></tr> <tr> <td><a href="/wiki/Prouhet%E2%80%93Thue%E2%80%93Morse_constant" title="Prouhet–Thue–Morse constant">Prouhet–Thue–Morse constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \tau }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d590a3e8735feb2d65c6fa0c4bc71ff946cd8bec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\textstyle \tau }"> </td> <td>0.412454033640... </td> <td> </td></tr> <tr> <td><a href="/wiki/Omega_constant" title="Omega constant">Omega constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" 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 \Omega }"> </td> <td>0.5671432904097838729999686622... </td> <td> </td></tr> <tr> <td><a href="/wiki/Cahen%27s_constant" title="Cahen's constant">Cahen's constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle C}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca76d9ff4b48256b6a4a99bcb234b64b2fa72b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\textstyle C}"> </td> <td>0.64341054629... </td> <td> </td></tr> <tr> <td><a href="/wiki/Natural_logarithm_of_2" title="Natural logarithm of 2">Natural logarithm of 2</a> </td> <td>ln 2 </td> <td>0.693147180559945309417232121458 </td> <td> </td></tr> <tr> <td><a href="/wiki/Lemniscate_constant" title="Lemniscate constant">Lemniscate constant</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \varpi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>ϖ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \varpi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c07216609a178d8e1105c0565555657e3a72b251" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:1.676ex;" alt="{\textstyle \varpi }"> </td> <td>2.622057554292119810464839589891... </td> <td>The ratio of the perimeter of <a href="/wiki/Lemniscate_of_Bernoulli" title="Lemniscate of Bernoulli">Bernoulli's lemniscate</a> to its diameter. </td></tr> <tr> <td><a href="/wiki/Tau_(mathematical_constant)" class="mw-redirect" title="Tau (mathematical constant)">Tau</a> </td> <td><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau =2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau =2\pi }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f794342a98efabf8935e897a1c4af6b7a0526d72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.795ex; height:2.176ex;" alt="{\displaystyle \tau =2\pi }"> </td> <td>6.283185307179586476925286766559... </td> <td>The ratio of the <a href="/wiki/Circumference" title="Circumference">circumference</a> to a <a href="/wiki/Radius" title="Radius">radius</a>, and the number of <a href="/wiki/Radian" title="Radian">radians</a> in a complete circle;<a href="#cite_note-9">[9]</a><a href="#cite_note-10">[10]</a> 2 <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"> π </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Irrational_but_not_known_to_be_transcendental">Irrational but not known to be transcendental</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=14" title="Edit section: Irrational but not known to be transcendental">edit</a>]</div> Some numbers are known to be <a href="/wiki/Irrational_number" title="Irrational number">irrational numbers</a>, but have not been proven to be transcendental. This differs from the algebraic numbers, which are known not to be transcendental. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1253789634"> <table class="wikitable sortable sticky-header"> <tbody><tr> <th>Name </th> <th>Decimal expansion </th> <th>Proof of irrationality </th> <th>Reference of unknown transcendentality </th></tr> <tr> <td><a href="/wiki/Riemann_zeta_function" title="Riemann zeta function">ζ</a>(3), also known as <a href="/wiki/Ap%C3%A9ry%27s_constant" title="Apéry's constant">Apéry's constant</a> </td> <td>1.202056903159594285399738161511449990764986292 </td> <td><a href="#cite_note-Apery-1979-11">[11]</a> </td> <td><a href="#cite_note-12">[12]</a> </td></tr> <tr> <td><a href="/wiki/Erd%C5%91s%E2%80%93Borwein_constant" title="Erdős–Borwein constant">Erdős–Borwein constant</a>, E </td> <td>1.606695152415291763... </td> <td><a href="#cite_note-13">[13]</a><a href="#cite_note-14">[14]</a> </td> <td>[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] </td></tr> <tr> <td><a href="/wiki/Copeland%E2%80%93Erd%C5%91s_constant" title="Copeland–Erdős constant">Copeland–Erdős constant</a> </td> <td>0.235711131719232931374143... </td> <td>Can be proven with <a href="/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions" title="Dirichlet's theorem on arithmetic progressions">Dirichlet's theorem on arithmetic progressions</a> or <a href="/wiki/Bertrand%27s_postulate" title="Bertrand's postulate">Bertrand's postulate</a> (Hardy and Wright, p. 113) or <a href="/wiki/Olivier_Ramar%C3%A9" title="Olivier Ramaré">Ramare's theorem</a> that every even integer is a sum of at most six primes. It also follows directly from its normality. </td> <td>[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] </td></tr> <tr> <td><a href="/wiki/Prime_constant" title="Prime constant">Prime constant</a>, ρ </td> <td>0.414682509851111660248109622... </td> <td>Proof of the number's irrationality is given at <a href="/wiki/Prime_constant" title="Prime constant">prime constant</a>. </td> <td>[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] </td></tr> <tr> <td><a href="/wiki/Reciprocal_Fibonacci_constant" title="Reciprocal Fibonacci constant">Reciprocal Fibonacci constant</a>, ψ </td> <td>3.359885666243177553172011302918927179688905133731... </td> <td><a href="#cite_note-15">[15]</a><a href="#cite_note-16">[16]</a> </td> <td><a href="#cite_note-17">[17]</a> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Real_but_not_known_to_be_irrational,_nor_transcendental">Real but not known to be irrational, nor transcendental</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=15" title="Edit section: Real but not known to be irrational, nor transcendental">edit</a>]</div> For some numbers, it is not known whether they are algebraic or transcendental. The following list includes real numbers that have not been proved to be irrational, nor transcendental. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1253789634"> <table class="wikitable sortable sticky-header"> <tbody><tr> <th>Name and symbol </th> <th>Decimal expansion </th> <th>Notes </th></tr> <tr> <td><a href="/wiki/Euler%E2%80%93Mascheroni_constant" class="mw-redirect" title="Euler–Mascheroni constant">Euler–Mascheroni constant</a>, γ </td> <td>0.577215664901532860606512090082...<a href="#cite_note-18">[18]</a> </td> <td>Believed to be transcendental but not proven to be so. However, it was shown that at least one of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"> and the Euler-Gompertz constant <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }"> is transcendental.<a href="#cite_note-:4-19">[19]</a><a href="#cite_note-:5-20">[20]</a> It was also shown that all but at most one number in an infinite list containing <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\gamma }{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>γ</mi> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\gamma }{4}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46b39e27cf65562ed6cb3d4fccf657192676a6f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.098ex; height:4.843ex;" alt="{\displaystyle {\frac {\gamma }{4}}}"> have to be transcendental.<a href="#cite_note-21">[21]</a><a href="#cite_note-22">[22]</a> </td></tr> <tr> <td><a href="/wiki/Gompertz_constant" title="Gompertz constant">Euler–Gompertz constant</a>, δ </td> <td>0.596 347 362 323 194 074 341 078 499 369...<a href="#cite_note-23">[23]</a> </td> <td>It was shown that at least one of the Euler-Mascheroni constant <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"> and the Euler-Gompertz constant <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }"> is transcendental.<a href="#cite_note-:4-19">[19]</a><a href="#cite_note-:5-20">[20]</a> </td></tr> <tr> <td><a href="/wiki/Catalan%27s_constant" title="Catalan's constant">Catalan's constant</a>, G </td> <td>0.915965594177219015054603514932384110774... </td> <td>It is not known whether this number is irrational.<a href="#cite_note-24">[24]</a> </td></tr> <tr> <td><a href="/wiki/Khinchin%27s_constant" title="Khinchin's constant">Khinchin's constant</a>, K0 </td> <td>2.685452001...<a href="#cite_note-:1-25">[25]</a> </td> <td>It is not known whether this number is irrational.<a href="#cite_note-26">[26]</a> </td></tr> <tr> <td>1st <a href="/wiki/Feigenbaum_constant" class="mw-redirect" title="Feigenbaum constant">Feigenbaum constant</a>, δ </td> <td>4.6692... </td> <td>Both Feigenbaum constants are believed to be <a href="/wiki/Transcendental_number" title="Transcendental number">transcendental</a>, although they have not been proven to be so.<a href="#cite_note-Briggs-27">[27]</a> </td></tr> <tr> <td>2nd <a href="/wiki/Feigenbaum_constant" class="mw-redirect" title="Feigenbaum constant">Feigenbaum constant</a>, α </td> <td>2.5029... </td> <td>Both Feigenbaum constants are believed to be <a href="/wiki/Transcendental_number" title="Transcendental number">transcendental</a>, although they have not been proven to be so.<a href="#cite_note-Briggs-27">[27]</a> </td></tr> <tr> <td><a href="/wiki/Glaisher%E2%80%93Kinkelin_constant" title="Glaisher–Kinkelin constant">Glaisher–Kinkelin constant</a>, A </td> <td>1.28242712... </td> <td> </td></tr> <tr> <td><a href="/wiki/Backhouse%27s_constant" title="Backhouse's constant">Backhouse's constant</a> </td> <td>1.456074948... </td> <td> </td></tr> <tr> <td><a href="/wiki/Frans%C3%A9n%E2%80%93Robinson_constant" title="Fransén–Robinson constant">Fransén–Robinson constant</a>, F </td> <td>2.8077702420... </td> <td> </td></tr> <tr> <td><a href="/wiki/L%C3%A9vy%27s_constant" title="Lévy's constant">Lévy's constant</a>,β </td> <td>1.18656 91104 15625 45282... </td> <td> </td></tr> <tr> <td><a href="/wiki/Mills%27_constant" title="Mills' constant">Mills' constant</a>, A </td> <td>1.30637788386308069046... </td> <td>It is not known whether this number is irrational.(<a href="#CITEREFFinch2003">Finch 2003</a>) </td></tr> <tr> <td><a href="/wiki/Ramanujan%E2%80%93Soldner_constant" title="Ramanujan–Soldner constant">Ramanujan–Soldner constant</a>, μ </td> <td>1.451369234883381050283968485892027449493... </td> <td> </td></tr> <tr> <td><a href="/wiki/Sierpi%C5%84ski%27s_constant" title="Sierpiński's constant">Sierpiński's constant</a>, K </td> <td>2.5849817595792532170658936... </td> <td> </td></tr> <tr> <td><a href="/wiki/Totient_summatory_constant" class="mw-redirect" title="Totient summatory constant">Totient summatory constant</a> </td> <td>1.339784...<a href="#cite_note-28">[28]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Double_exponential_function#Doubly_exponential_sequences" title="Double exponential function">Vardi's constant</a>, E </td> <td>1.264084735305... </td> <td> </td></tr> <tr> <td><a href="/wiki/Somos%27_quadratic_recurrence_constant" title="Somos' quadratic recurrence constant">Somos' quadratic recurrence constant</a>, σ </td> <td>1.661687949633594121296... </td> <td> </td></tr> <tr> <td><a href="/wiki/Niven%27s_constant" title="Niven's constant">Niven's constant</a>, C </td> <td>1.705211... </td> <td> </td></tr> <tr> <td><a href="/wiki/Brun%27s_constant" class="mw-redirect" title="Brun's constant">Brun's constant</a>, B2 </td> <td>1.902160583104... </td> <td>The irrationality of this number would be a consequence of the truth of the infinitude of <a href="/wiki/Twin_prime" title="Twin prime">twin primes</a>. </td></tr> <tr> <td><a href="/wiki/Landau%27s_totient_constant" class="mw-redirect" title="Landau's totient constant">Landau's totient constant</a> </td> <td>1.943596...<a href="#cite_note-29">[29]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Brun%27s_constant" class="mw-redirect" title="Brun's constant">Brun's constant for prime quadruplets</a>, B4 </td> <td>0.8705883800... </td> <td> </td></tr> <tr> <td><a href="/wiki/Random_Fibonacci_sequence" title="Random Fibonacci sequence">Viswanath's constant</a> </td> <td>1.1319882487943... </td> <td> </td></tr> <tr> <td><a href="/wiki/Khinchin%E2%80%93L%C3%A9vy_constant" class="mw-redirect" title="Khinchin–Lévy constant">Khinchin–Lévy constant</a> </td> <td>1.1865691104...<a href="#cite_note-30">[30]</a> </td> <td>This number represents the probability that three random numbers have no <a href="/wiki/Common_factor" class="mw-redirect" title="Common factor">common factor</a> greater than 1.<a href="#cite_note-David_Wells_page_29-31">[31]</a> </td></tr> <tr> <td><a href="/wiki/Landau%E2%80%93Ramanujan_constant" title="Landau–Ramanujan constant">Landau–Ramanujan constant</a> </td> <td>0.76422365358922066299069873125... </td> <td> </td></tr> <tr> <td><a href="/wiki/Fresnel_integral" title="Fresnel integral">C(1)</a> </td> <td>0.77989340037682282947420641365... </td> <td> </td></tr> <tr> <td><a href="/wiki/Riemann%E2%80%93Siegel_formula" title="Riemann–Siegel formula">Z(1)</a> </td> <td>−0.736305462867317734677899828925614672... </td> <td> </td></tr> <tr> <td><a href="/wiki/Heath-Brown%E2%80%93Moroz_constant" title="Heath-Brown–Moroz constant">Heath-Brown–Moroz constant</a>, C </td> <td>0.001317641... </td> <td> </td></tr> <tr> <td><a href="/wiki/Kepler%E2%80%93Bouwkamp_constant" title="Kepler–Bouwkamp constant">Kepler–Bouwkamp constant</a>,K' </td> <td>0.1149420448... </td> <td> </td></tr> <tr> <td><a href="/wiki/MRB_constant" title="MRB constant">MRB constant</a>,S </td> <td>0.187859... </td> <td>It is not known whether this number is irrational. </td></tr> <tr> <td><a href="/wiki/Meissel%E2%80%93Mertens_constant" title="Meissel–Mertens constant">Meissel–Mertens constant</a>, M </td> <td>0.2614972128476427837554268386086958590516... </td> <td> </td></tr> <tr> <td><a href="/wiki/Bernstein%27s_constant" title="Bernstein's constant">Bernstein's constant</a>, β </td> <td>0.2801694990... </td> <td> </td></tr> <tr> <td><a href="/wiki/Gauss%E2%80%93Kuzmin%E2%80%93Wirsing_constant" class="mw-redirect" title="Gauss–Kuzmin–Wirsing constant">Gauss–Kuzmin–Wirsing constant</a>, λ1 </td> <td>0.3036630029...<a href="#cite_note-32">[32]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Hafner%E2%80%93Sarnak%E2%80%93McCurley_constant" title="Hafner–Sarnak–McCurley constant">Hafner–Sarnak–McCurley constant</a>,σ </td> <td>0.3532363719... </td> <td> </td></tr> <tr> <td><a href="/wiki/Artin%27s_conjecture_on_primitive_roots" title="Artin's conjecture on primitive roots">Artin's constant</a>,CArtin </td> <td>0.3739558136... </td> <td> </td></tr> <tr> <td><a href="/wiki/Fresnel_integral" title="Fresnel integral">S(1)</a> </td> <td>0.438259147390354766076756696625152... </td> <td> </td></tr> <tr> <td><a href="/wiki/Dawson_integral" class="mw-redirect" title="Dawson integral">F(1)</a> </td> <td>0.538079506912768419136387420407556... </td> <td> </td></tr> <tr> <td><a href="/wiki/Stephens%27_constant" title="Stephens' constant">Stephens' constant</a> </td> <td>0.575959...<a href="#cite_note-33">[33]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Golomb%E2%80%93Dickman_constant" title="Golomb–Dickman constant">Golomb–Dickman constant</a>, λ </td> <td>0.62432998854355087099293638310083724... </td> <td> </td></tr> <tr> <td><a href="/wiki/Twin_prime_conjecture#First_Hardy–Littlewood_conjecture" class="mw-redirect" title="Twin prime conjecture">Twin prime constant</a>, C2 </td> <td>0.660161815846869573927812110014... </td> <td> </td></tr> <tr> <td><a href="/wiki/Feller%E2%80%93Tornier_constant" title="Feller–Tornier constant">Feller–Tornier constant</a> </td> <td>0.661317...<a href="#cite_note-34">[34]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Laplace_limit" title="Laplace limit">Laplace limit</a>, ε </td> <td>0.6627434193...<a href="#cite_note-35">[35]</a> </td> <td> </td></tr> <tr> <td><a href="/wiki/Embree%E2%80%93Trefethen_constant" class="mw-redirect" title="Embree–Trefethen constant">Embree–Trefethen constant</a> </td> <td>0.70258... </td> <td> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Numbers_not_known_with_high_precision">Numbers not known with high precision</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=16" title="Edit section: Numbers not known with high precision">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Normal_number" title="Normal number">Normal number</a> and <a href="/wiki/Uncomputable_number" class="mw-redirect" title="Uncomputable number">Uncomputable number</a></div> Some real numbers, including transcendental numbers, are not known with high precision. <ul><li>The constant in the <a href="/wiki/Berry%E2%80%93Esseen_theorem" title="Berry–Esseen theorem">Berry–Esseen Theorem</a>: 0.4097 < C < 0.4748</li> <li><a href="/wiki/De_Bruijn%E2%80%93Newman_constant" title="De Bruijn–Newman constant">De Bruijn–Newman constant</a>: 0 ≤ Λ ≤ 0.2</li> <li><a href="/wiki/Chaitin%27s_constant" title="Chaitin's constant">Chaitin's constants</a> Ω, which are transcendental and provably impossible to compute.</li> <li><a href="/wiki/Bloch%27s_theorem_(complex_variables)#Bloch's_constant" class="mw-redirect" title="Bloch's theorem (complex variables)">Bloch's constant</a> (also <a href="/wiki/Landau%27s_constants" class="mw-redirect" title="Landau's constants">2nd Landau's constant</a>): 0.4332 < B < 0.4719</li> <li><a href="/wiki/Landau%27s_constants" class="mw-redirect" title="Landau's constants">1st Landau's constant</a>: 0.5 < L < 0.5433</li> <li><a href="/wiki/Landau%27s_constants" class="mw-redirect" title="Landau's constants">3rd Landau's constant</a>: 0.5 < A ≤ 0.7853</li> <li><a href="/wiki/Grothendieck_constant" class="mw-redirect" title="Grothendieck constant">Grothendieck constant</a>: 1.67 < k < 1.79</li> <li>Romanov's constant in <a href="/wiki/Romanov%27s_theorem" title="Romanov's theorem">Romanov's theorem</a>: 0.107648 < d < 0.49094093, Romanov conjectured that it is 0.434</li></ul> <div class="mw-heading mw-heading2"><h2 id="Hypercomplex_numbers">Hypercomplex numbers</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=17" title="Edit section: Hypercomplex numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Hypercomplex_number" title="Hypercomplex number">Hypercomplex number</a></div> <a href="/wiki/Hypercomplex_number" title="Hypercomplex number">Hypercomplex number</a> is a term for an <a href="/wiki/Element_(mathematics)" title="Element (mathematics)">element</a> of a unital <a href="/wiki/Algebra_over_a_field" title="Algebra over a field">algebra</a> over the <a href="/wiki/Field_(mathematics)" title="Field (mathematics)">field</a> of <a href="/wiki/Real_number" title="Real number">real numbers</a>. The <a href="/wiki/Complex_number" title="Complex number">complex numbers</a> are often symbolised by a boldface C (or <a href="/wiki/Blackboard_bold" title="Blackboard bold">blackboard bold</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {\mathbb {C} } }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {\mathbb {C} } }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22cef13d33664b41eac040e05c2c2485d043e04b" 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 {\mathbb {C} } }">, Unicode <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734">U+2102 ℂ DOUBLE-STRUCK CAPITAL C), while the set of <a href="/wiki/Quaternion" title="Quaternion">quaternions</a> is denoted by a boldface H (or <a href="/wiki/Blackboard_bold" title="Blackboard bold">blackboard bold</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {H} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">H</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {H} }</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e050965453c42bcc6bd544546703c836bdafeac9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \mathbb {H} }">, Unicode <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734">U+210D ℍ DOUBLE-STRUCK CAPITAL H). <div class="mw-heading mw-heading3"><h3 id="Algebraic_complex_numbers">Algebraic complex numbers</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=18" title="Edit section: Algebraic complex numbers">edit</a>]</div> <ul><li><a href="/wiki/Imaginary_unit" title="Imaginary unit">Imaginary unit</a>: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle i={\sqrt {-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle i={\sqrt {-1}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535867ece56ad7df382c23f0861a71caa41aa920" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.807ex; height:2.843ex;" alt="{\textstyle i={\sqrt {-1}}}"></li> <li>nth <a href="/wiki/Roots_of_unity" class="mw-redirect" title="Roots of unity">roots of unity</a>: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \xi _{n}^{k}=\cos {\bigl (}2\pi {\frac {k}{n}}{\bigr )}+i\sin {\bigl (}2\pi {\frac {k}{n}}{\bigr )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msubsup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msubsup> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>k</mi> <mi>n</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> <mo>+</mo> <mi>i</mi> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>k</mi> <mi>n</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \xi _{n}^{k}=\cos {\bigl (}2\pi {\frac {k}{n}}{\bigr )}+i\sin {\bigl (}2\pi {\frac {k}{n}}{\bigr )}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc656c84ef2736ce75033847f189ae1bb4632228" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29ex; height:3.509ex;" alt="{\textstyle \xi _{n}^{k}=\cos {\bigl (}2\pi {\frac {k}{n}}{\bigr )}+i\sin {\bigl (}2\pi {\frac {k}{n}}{\bigr )}}">, while <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle 0\leq k\leq n-10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mn>0</mn> <mo>≤</mo> <mi>k</mi> <mo>≤</mo> <mi>n</mi> <mo>−</mo> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle 0\leq k\leq n-10}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18bc48a2bb4eb93be9ba34f5ca781e800a260b07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:15.131ex; height:2.343ex;" alt="{\textstyle 0\leq k\leq n-10}">, <a href="/wiki/Greatest_common_divisor" title="Greatest common divisor">GCD</a>(k, n) = 1</li></ul> <div class="mw-heading mw-heading3"><h3 id="Other_hypercomplex_numbers">Other hypercomplex numbers</h3>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=19" title="Edit section: Other hypercomplex numbers">edit</a>]</div> <ul><li>The <a href="/wiki/Quaternion" title="Quaternion">quaternions</a></li> <li>The <a href="/wiki/Octonion" title="Octonion">octonions</a></li> <li>The <a href="/wiki/Sedenion" title="Sedenion">sedenions</a></li> <li>The <a href="/wiki/Trigintaduonion" title="Trigintaduonion">trigintaduonions</a></li> <li>The <a href="/wiki/Dual_number" title="Dual number">dual numbers</a> (with an <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimal</a>)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Transfinite_numbers">Transfinite numbers</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=20" title="Edit section: Transfinite numbers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Transfinite_number" title="Transfinite number">Transfinite number</a></div> <a href="/wiki/Transfinite_numbers" class="mw-redirect" title="Transfinite numbers">Transfinite numbers</a> are numbers that are "<a href="/wiki/Infinity" title="Infinity">infinite</a>" in the sense that they are larger than all <a href="/wiki/Finite_set" title="Finite set">finite</a> numbers, yet not necessarily <a href="/wiki/Absolutely_infinite" class="mw-redirect" title="Absolutely infinite">absolutely infinite</a>. <ul><li><a href="/wiki/Aleph-null" class="mw-redirect" title="Aleph-null">Aleph-null</a>: ℵ0: the smallest infinite cardinal, and the cardinality of <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><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} }">, the set of <a href="/wiki/Natural_number" title="Natural number">natural numbers</a></li> <li><a href="/wiki/Aleph-one" class="mw-redirect" title="Aleph-one">Aleph-one</a>: ℵ1: the cardinality of ω1, the set of all countable ordinal numbers</li> <li><a href="/wiki/Beth-one" class="mw-redirect" title="Beth-one">Beth-one</a>: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beth _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ℶ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beth _{1}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb3462a86543187911778e6ff64ed1dc27b19f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.05ex; width:2.655ex; height:2.676ex;" alt="{\displaystyle \beth _{1}}">: the <a href="/wiki/Cardinality_of_the_continuum" title="Cardinality of the continuum">cardinality of the continuum</a> 2ℵ0</li> <li>ℭ or <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">c</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {c}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21924b960341255be18e538e51404718f29cbc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.905ex; height:1.676ex;" alt="{\displaystyle {\mathfrak {c}}}">: the <a href="/wiki/Cardinality_of_the_continuum" title="Cardinality of the continuum">cardinality of the continuum</a> 2ℵ0</li> <li><a href="/wiki/First_infinite_ordinal" class="mw-redirect" title="First infinite ordinal">Omega</a>: ω, the smallest <a href="/wiki/Infinite_ordinal" class="mw-redirect" title="Infinite ordinal">infinite ordinal</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Numbers_representing_physical_quantities">Numbers representing physical quantities</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=21" title="Edit section: Numbers representing physical quantities">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Physical_constant" title="Physical constant">Physical constant</a> and <a href="/wiki/List_of_physical_constants" title="List of physical constants">List of physical constants</a></div> Physical quantities that appear in the universe are often described using <a href="/wiki/Physical_constant" title="Physical constant">physical constants</a>. <ul><li><a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a>: NA = 6.02214076×1023 mol−1‍<a href="#cite_note-physconst-NA-36">[36]</a></li> <li><a href="/wiki/Mass_of_the_electron" class="mw-redirect" title="Mass of the electron">Electron mass</a>: me = 9.1093837139(28)×10−31 kg‍<a href="#cite_note-physconst-me-37">[37]</a></li> <li><a href="/wiki/Fine-structure_constant" title="Fine-structure constant">Fine-structure constant</a>: α = 0.0072973525643(11)‍<a href="#cite_note-physconst-alpha-38">[38]</a></li> <li><a href="/wiki/Gravitational_constant" title="Gravitational constant">Gravitational constant</a>: G = 6.67430(15)×10−11 m3⋅kg−1⋅s−2‍<a href="#cite_note-physconst-G-39">[39]</a></li> <li><a href="/wiki/Molar_mass_constant" title="Molar mass constant">Molar mass constant</a>: Mu = 1.00000000105(31)×10−3 kg⋅mol−1‍<a href="#cite_note-physconst-Mu-40">[40]</a></li> <li><a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a>: h = 6.62607015×10−34 J⋅Hz−1‍<a href="#cite_note-physconst-h-41">[41]</a></li> <li><a href="/wiki/Rydberg_constant" title="Rydberg constant">Rydberg constant</a>: R∞ = 10973731.568157(12) m−1‍<a href="#cite_note-physconst-Rinf-42">[42]</a></li> <li><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light in vacuum</a>: c = 299792458 m⋅s−1‍<a href="#cite_note-physconst-c-43">[43]</a></li> <li><a href="/wiki/Vacuum_electric_permittivity" class="mw-redirect" title="Vacuum electric permittivity">Vacuum electric permittivity</a>: ε0 = 8.8541878188(14)×10−12 F⋅m−1‍<a href="#cite_note-physconst-eps0-44">[44]</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Numbers_representing_geographical_and_astronomical_distances">Numbers representing geographical and astronomical distances</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=22" title="Edit section: Numbers representing geographical and astronomical distances">edit</a>]</div> <ul><li><a href="/wiki/Equator#Exact_length" title="Equator">6378.137</a>, the average equatorial radius of Earth in <a href="/wiki/Kilometers" class="mw-redirect" title="Kilometers">kilometers</a> (following <a href="/wiki/GRS_80" class="mw-redirect" title="GRS 80">GRS 80</a> and <a href="/wiki/WGS_84" class="mw-redirect" title="WGS 84">WGS 84</a> standards).</li> <li><a href="/wiki/Equator#Exact_length" title="Equator">40075.0167</a>, the length of the <a href="/wiki/Equator" title="Equator">Equator</a> in kilometers (following GRS 80 and WGS 84 standards).</li> <li><a href="/wiki/Lunar_distance_(astronomy)" class="mw-redirect" title="Lunar distance (astronomy)">384399</a>, the semi-major axis of the <a href="/wiki/Orbit_of_the_Moon" title="Orbit of the Moon">orbit of the Moon</a>, in kilometers, roughly the distance between the center of Earth and that of the Moon.</li> <li><a href="/wiki/Astronomical_Unit" class="mw-redirect" title="Astronomical Unit">149597870700</a>, the average distance between the Earth and the Sun or <a href="/wiki/Astronomical_Unit" class="mw-redirect" title="Astronomical Unit">Astronomical Unit</a> (AU), in meters.</li> <li><a href="/wiki/Light-year" title="Light-year">9460730472580800</a>, one <a href="/wiki/Light-year" title="Light-year">light-year</a>, the distance travelled by light in one <a href="/wiki/Julian_year_(astronomy)" title="Julian year (astronomy)">Julian year</a>, in meters.</li> <li><a href="/wiki/Parsec" title="Parsec">30856775814913673</a>, the distance of one <a href="/wiki/Parsec" title="Parsec">parsec</a>, another astronomical unit, in whole meters.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Numbers_without_specific_values">Numbers without specific values</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=23" title="Edit section: Numbers without specific values">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Indefinite_and_fictitious_numbers" title="Indefinite and fictitious numbers">Indefinite and fictitious numbers</a></div> Many languages have words expressing <a href="/wiki/Indefinite_and_fictitious_numbers" title="Indefinite and fictitious numbers">indefinite and fictitious numbers</a>—inexact terms of indefinite size, used for comic effect, for exaggeration, as <a href="/wiki/Placeholder_name" title="Placeholder name">placeholder names</a>, or when precision is unnecessary or undesirable. One technical term for such words is "non-numerical vague quantifier".<a href="#cite_note-45">[45]</a> Such words designed to indicate large quantities can be called "indefinite hyperbolic numerals".<a href="#cite_note-46">[46]</a> <div class="mw-heading mw-heading2"><h2 id="Named_numbers">Named numbers</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=24" title="Edit section: Named numbers">edit</a>]</div> <ul><li><a href="/wiki/Hardy%E2%80%93Ramanujan_number" class="mw-redirect" title="Hardy–Ramanujan number">Hardy–Ramanujan number</a>, <a href="/wiki/1729" title="1729">1729</a></li> <li><a href="/wiki/Kaprekar%27s_constant" class="mw-redirect" title="Kaprekar's constant">Kaprekar's constant</a>, <a href="/wiki/6174" title="6174">6174</a></li> <li><a href="/wiki/Eddington_number" title="Eddington number">Eddington number</a>, ~1080</li> <li><a href="/wiki/Googol" title="Googol">Googol</a>, 10100</li> <li><a href="/wiki/Shannon_number" title="Shannon number">Shannon number</a></li> <li><a href="/wiki/Centillion" class="mw-redirect" title="Centillion">Centillion</a>, 10303</li> <li><a href="/wiki/Skewes%27s_number" title="Skewes's number">Skewes's number</a></li> <li><a href="/wiki/Googolplex" title="Googolplex">Googolplex</a>, 10(10100)</li> <li><a href="/wiki/Mega_(number)" class="mw-redirect" title="Mega (number)">Mega</a>/Circle(2)</li> <li><a href="/wiki/Moser%27s_number" class="mw-redirect" title="Moser's number">Moser's number</a></li> <li><a href="/wiki/Graham%27s_number" title="Graham's number">Graham's number</a></li> <li><a href="/wiki/Kruskal%27s_tree_theorem#TREE_function" title="Kruskal's tree theorem">TREE(3)</a></li> <li><a href="/wiki/Friedman%27s_SSCG_function" title="Friedman's SSCG function">SSCG(3)</a></li> <li><a href="/wiki/Rayo%27s_number" title="Rayo's number">Rayo's number</a></li> <li>Kanahiya's Constant, <a href="/w/index.php?title=2592&action=edit&redlink=1" class="new" title="2592 (page does not exist)">2592</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=25" title="Edit section: See also">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1259569809">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col div-col-small" style="column-width: 20em;"> <ul><li><a href="/wiki/Absolute_infinite" title="Absolute infinite">Absolute infinite</a></li> <li><a href="/wiki/English_numerals" title="English numerals">English numerals</a></li> <li><a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">Floating-point arithmetic</a></li> <li><a href="/wiki/Fraction" title="Fraction">Fraction</a></li> <li><a href="/wiki/Integer_sequence" title="Integer sequence">Integer sequence</a></li> <li><a href="/wiki/Interesting_number_paradox" title="Interesting number paradox">Interesting number paradox</a></li> <li><a href="/wiki/Large_numbers" title="Large numbers">Large numbers</a></li> <li><a href="/wiki/List_of_mathematical_constants" title="List of mathematical constants">List of mathematical constants</a></li> <li><a href="/wiki/List_of_prime_numbers" title="List of prime numbers">List of prime numbers</a></li> <li><a href="/wiki/List_of_types_of_numbers" title="List of types of numbers">List of types of numbers</a></li> <li><a href="/wiki/Mathematical_constant" title="Mathematical constant">Mathematical constant</a></li> <li><a href="/wiki/Metric_prefix" title="Metric prefix">Metric prefix</a></li> <li><a href="/wiki/Names_of_large_numbers" title="Names of large numbers">Names of large numbers</a></li> <li><a href="/wiki/Names_of_small_numbers" title="Names of small numbers">Names of small numbers</a></li> <li><a href="/wiki/Negative_number" title="Negative number">Negative number</a></li> <li><a href="/wiki/Numeral_(linguistics)" title="Numeral (linguistics)">Numeral (linguistics)</a></li> <li><a href="/wiki/Numeral_prefix" title="Numeral prefix">Numeral prefix</a></li> <li><a href="/wiki/Order_of_magnitude" title="Order of magnitude">Order of magnitude</a></li> <li><a href="/wiki/Orders_of_magnitude_(numbers)" title="Orders of magnitude (numbers)">Orders of magnitude (numbers)</a></li> <li><a href="/wiki/Ordinal_number" title="Ordinal number">Ordinal number</a></li> <li><a href="/wiki/The_Penguin_Dictionary_of_Curious_and_Interesting_Numbers" title="The Penguin Dictionary of Curious and Interesting Numbers">The Penguin Dictionary of Curious and Interesting Numbers</a></li> <li><a href="/wiki/Perfect_numbers" class="mw-redirect" title="Perfect numbers">Perfect numbers</a></li> <li><a href="/wiki/Power_of_two" title="Power of two">Power of two</a></li> <li><a href="/wiki/Power_of_10" title="Power of 10">Power of 10</a></li> <li><a href="/wiki/Surreal_number" title="Surreal number">Surreal number</a></li> <li><a href="/wiki/Table_of_prime_factors" title="Table of prime factors">Table of prime factors</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=26" title="Edit section: References">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFWeisstein" class="citation web cs1">Weisstein, Eric W. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Hardy-RamanujanNumber.html">"Hardy–Ramanujan Number"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20040408221409/http://mathworld.wolfram.com/Hardy-RamanujanNumber.html">Archived</a> from the original on 2004-04-08.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Hardy%E2%80%93Ramanujan+Number&rft.aulast=Weisstein&rft.aufirst=Eric+W.&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FHardy-RamanujanNumber.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAyonrindeStefatosMillerRicher2020" class="citation journal cs1">Ayonrinde, Oyedeji A.; Stefatos, Anthi; Miller, Shadé; Richer, Amanda; Nadkarni, Pallavi; She, Jennifer; Alghofaily, Ahmad; Mngoma, Nomusa (2020-06-12). "The salience and symbolism of numbers across cultural beliefs and practice". International Review of Psychiatry. 33 (1–2): 179–188. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F09540261.2020.1769289">10.1080/09540261.2020.1769289</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0954-0261">0954-0261</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/32527165">32527165</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:219605482">219605482</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Review+of+Psychiatry&rft.atitle=The+salience+and+symbolism+of+numbers+across+cultural+beliefs+and+practice&rft.volume=33&rft.issue=1%E2%80%932&rft.pages=179-188&rft.date=2020-06-12&rft.issn=0954-0261&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A219605482%23id-name%3DS2CID&rft_id=info%3Apmid%2F32527165&rft_id=info%3Adoi%2F10.1080%2F09540261.2020.1769289&rft.aulast=Ayonrinde&rft.aufirst=Oyedeji+A.&rft.au=Stefatos%2C+Anthi&rft.au=Miller%2C+Shad%C3%A9&rft.au=Richer%2C+Amanda&rft.au=Nadkarni%2C+Pallavi&rft.au=She%2C+Jennifer&rft.au=Alghofaily%2C+Ahmad&rft.au=Mngoma%2C+Nomusa&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-3"><a href="#cite_ref-3">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/video/213933/Demystified-why-is-bakers-dozen-thirteen">"Demystified | Why a baker's dozen is thirteen"</a>. www.britannica.com. 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Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/KhinchinsConstant.html">"Khinchin's constant"</a>. <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Khinchin%27s+constant&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FKhinchinsConstant.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-Briggs-27">^ <a href="#cite_ref-Briggs_27-0">a</a> <a href="#cite_ref-Briggs_27-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBriggs1997" class="citation thesis cs1">Briggs, Keith (1997). <a rel="nofollow" class="external text" href="http://keithbriggs.info/documents/Keith_Briggs_PhD.pdf">Feigenbaum scaling in discrete dynamical systems</a> (PDF) (PhD thesis). <a href="/wiki/University_of_Melbourne" title="University of Melbourne">University of Melbourne</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Feigenbaum+scaling+in+discrete+dynamical+systems&rft.degree=PhD&rft.inst=University+of+Melbourne&rft.date=1997&rft.aulast=Briggs&rft.aufirst=Keith&rft_id=http%3A%2F%2Fkeithbriggs.info%2Fdocuments%2FKeith_Briggs_PhD.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-28"><a href="#cite_ref-28">^</a> <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A065483" class="extiw" title="oeis:A065483">A065483</a> </li> <li id="cite_note-29"><a href="#cite_ref-29">^</a> <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A082695" class="extiw" title="oeis:A082695">A082695</a> </li> <li id="cite_note-30"><a href="#cite_ref-30">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/LevyConstant.html">"Lévy Constant"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=L%C3%A9vy+Constant&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FLevyConstant.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-David_Wells_page_29-31"><a href="#cite_ref-David_Wells_page_29_31-0">^</a> "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 29. </li> <li id="cite_note-32"><a href="#cite_ref-32">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Gauss-Kuzmin-WirsingConstant.html">"Gauss–Kuzmin–Wirsing Constant"</a>. <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Gauss%E2%80%93Kuzmin%E2%80%93Wirsing+Constant&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FGauss-Kuzmin-WirsingConstant.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-33"><a href="#cite_ref-33">^</a> <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A065478" class="extiw" title="oeis:A065478">A065478</a> </li> <li id="cite_note-34"><a href="#cite_ref-34">^</a> <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A065493" class="extiw" title="oeis:A065493">A065493</a> </li> <li id="cite_note-35"><a href="#cite_ref-35">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/LaplaceLimit.html">"Laplace Limit"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Laplace+Limit&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FLaplaceLimit.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-NA-36"><a href="#cite_ref-physconst-NA_36-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?na">"2022 CODATA Value: Avogadro constant"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+Avogadro+constant&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fna&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-me-37"><a href="#cite_ref-physconst-me_37-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?me">"2022 CODATA Value: electron mass"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+electron+mass&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fme&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-alpha-38"><a href="#cite_ref-physconst-alpha_38-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?alph">"2022 CODATA Value: fine-structure constant"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+fine-structure+constant&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Falph&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-G-39"><a href="#cite_ref-physconst-G_39-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?bg">"2022 CODATA Value: Newtonian constant of gravitation"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+Newtonian+constant+of+gravitation&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fbg&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-Mu-40"><a href="#cite_ref-physconst-Mu_40-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?mu">"2022 CODATA Value: molar mass constant"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+molar+mass+constant&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fmu&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-h-41"><a href="#cite_ref-physconst-h_41-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?h">"2022 CODATA Value: Planck constant"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+Planck+constant&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fh&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-Rinf-42"><a href="#cite_ref-physconst-Rinf_42-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?ryd">"2022 CODATA Value: Rydberg constant"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+Rydberg+constant&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fryd&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-c-43"><a href="#cite_ref-physconst-c_43-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?c">"2022 CODATA Value: speed of light in vacuum"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+speed+of+light+in+vacuum&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fc&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-physconst-eps0-44"><a href="#cite_ref-physconst-eps0_44-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?ep0">"2022 CODATA Value: vacuum electric permittivity"</a>. The NIST Reference on Constants, Units, and Uncertainty. <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>. May 2024. Retrieved 2024-05-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+NIST+Reference+on+Constants%2C+Units%2C+and+Uncertainty&rft.atitle=2022+CODATA+Value%3A+vacuum+electric+permittivity&rft.date=2024-05&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fep0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"> </li> <li id="cite_note-45"><a href="#cite_ref-45">^</a> <a rel="nofollow" class="external text" href="http://versita.metapress.com/content/t98071387u726916/?p=1ad6a085630c432c94528c5548f5c2c4&pi=1">"Bags of Talent, a Touch of Panic, and a Bit of Luck: The Case of Non-Numerical Vague Quantifiers" from Linguista Pragensia, Nov. 2, 2010</a> <a rel="nofollow" class="external text" href="https://archive.today/20120731092211/http://versita.metapress.com/content/t98071387u726916/?p=1ad6a085630c432c94528c5548f5c2c4&pi=1">Archived</a> 2012-07-31 at <a href="/wiki/Archive.today" title="Archive.today">archive.today</a> </li> <li id="cite_note-46"><a href="#cite_ref-46">^</a> <a rel="nofollow" class="external text" href="https://www.bostonglobe.com/ideas/2016/07/13/the-surprising-history-indefinite-hyperbolic-numerals/qYTKpkP9lyWVfItLXuTHdM/story.html">Boston Globe, July 13, 2016: "The surprising history of indefinite hyperbolic numerals"</a> </li> </ol></div></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFinch2003" class="citation cs2">Finch, Steven R. (2003), "Anmol Kumar Singh", <a rel="nofollow" class="external text" href="https://isbnsearch.org/isbn/0521818052">Mathematical Constants (Encyclopedia of Mathematics and its Applications, Series Number 94)</a>, Cambridge University Press, pp. <a rel="nofollow" class="external text" href="https://archive.org/details/mathematicalcons0000finc/page/130">130–133</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0521818052" title="Special:BookSources/0521818052"><bdi>0521818052</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Anmol+Kumar+Singh&rft.btitle=Mathematical+Constants+%28Encyclopedia+of+Mathematics+and+its+Applications%2C+Series+Number+94%29&rft.pages=130-133&rft.pub=Cambridge+University+Press&rft.date=2003&rft.isbn=0521818052&rft.aulast=Finch&rft.aufirst=Steven+R.&rft_id=https%3A%2F%2Fisbnsearch.org%2Fisbn%2F0521818052&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFApéry1979" class="citation cs2">Apéry, Roger (1979), "Irrationalité de <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \zeta (2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ζ</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \zeta (2)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eff246e5aba5259593186618c576a3b7e14bc3c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.067ex; height:2.843ex;" alt="{\displaystyle \zeta (2)}"> et <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \zeta (3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ζ</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \zeta (3)}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3088978098c7b90b2754a9d9b0b994d873e1755c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.067ex; height:2.843ex;" alt="{\displaystyle \zeta (3)}">", Astérisque, 61: 11–13</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ast%C3%A9risque&rft.atitle=Irrationalit%C3%A9+de+MATH+RENDER+ERROR+et+MATH+RENDER+ERROR&rft.volume=61&rft.pages=11-13&rft.date=1979&rft.aulast=Ap%C3%A9ry&rft.aufirst=Roger&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+numbers" class="Z3988">.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=27" title="Edit section: Further reading">edit</a>]</div> <ul><li>Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-4447-3" title="Special:BookSources/0-7167-4447-3">0-7167-4447-3</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=List_of_numbers&action=edit&section=28" title="Edit section: External links">edit</a>]</div> <ul><li><a rel="nofollow" class="external text" href="http://www.archimedes-lab.org/numbers/Num1_69.html">What's Special About This Number? A Zoology of Numbers: from 0 to 500</a></li> <li><a rel="nofollow" class="external text" href="http://www.isthe.com/chongo/tech/math/number/number.html">Name of a Number</a></li> <li><a rel="nofollow" class="external text" href="http://www.mathcats.com/explore/reallybignumbers.html">See how to write big numbers</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20101127194324/http://pages.prodigy.net/jhonig/bignum/indx.html">About big numbers</a> at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (archived 27 November 2010)</li> <li><a rel="nofollow" class="external text" href="http://www.mrob.com/pub/math/largenum.html">Robert P. Munafo's Large Numbers page</a></li> <li><a rel="nofollow" class="external text" href="http://www-users.cs.york.ac.uk/~susan/cyc/b/big.htm">Different notations for big numbers – by Susan Stepney</a></li> <li><a rel="nofollow" class="external text" href="http://www.ibiblio.org/units/large.html">Names for Large Numbers</a>, in How Many? A Dictionary of Units of Measurement by Russ Rowlett</li> <li><a rel="nofollow" class="external text" href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a> (from 0 to 9999)</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=List_of_numbers&oldid=1259914314">https://en.wikipedia.org/w/index.php?title=List_of_numbers&oldid=1259914314</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Number-related_lists" title="Category:Number-related lists">Number-related lists</a></li><li><a href="/wiki/Category:Mathematical_tables" title="Category:Mathematical tables">Mathematical tables</a></li><li><a href="/wiki/Category:Numeral_systems" title="Category:Numeral systems">Numeral systems</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Webarchive_template_archiveis_links" title="Category:Webarchive template archiveis links">Webarchive template archiveis links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Dynamic_lists" title="Category:Dynamic lists">Dynamic lists</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_July_2019" title="Category:Articles with unsourced statements from July 2019">Articles with unsourced statements from July 2019</a></li><li><a href="/wiki/Category:Pages_using_div_col_with_small_parameter" title="Category:Pages using div col with small parameter">Pages using div col with small parameter</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Pages_that_use_a_deprecated_format_of_the_math_tags" title="Category:Pages that use a deprecated format of the math tags">Pages that use a deprecated format of the math tags</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"> This page was last edited on 27 November 2024, at 19:58 (UTC).</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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