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id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Initium</div> </a> </li> <li id="toc-De_signo_'"`UNIQ--postMath-0000000D-QINU`"'" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#De_signo_'"`UNIQ--postMath-0000000D-QINU`"'"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>De signo '"`UNIQ--postMath-0000000D-QINU`"'</span> </div> </a> <ul id="toc-De_signo_'"`UNIQ--postMath-0000000D-QINU`"'-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sententiae_de_Infinitate_per_historiam" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Sententiae_de_Infinitate_per_historiam"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Sententiae de Infinitate per historiam</span> </div> </a> <button aria-controls="toc-Sententiae_de_Infinitate_per_historiam-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Sententiae de Infinitate per historiam subsection</span> </button> <ul id="toc-Sententiae_de_Infinitate_per_historiam-sublist" class="vector-toc-list"> <li id="toc-Sententiae_antiquae_Orientales" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sententiae_antiquae_Orientales"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Sententiae antiquae Orientales</span> </div> </a> <ul id="toc-Sententiae_antiquae_Orientales-sublist" class="vector-toc-list"> <li id="toc-Yajurveda" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Yajurveda"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Yajurveda</span> </div> </a> <ul id="toc-Yajurveda-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Genni" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Genni"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Genni</span> </div> </a> <ul id="toc-Genni-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sententiae_priores_Europaeae" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sententiae_priores_Europaeae"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Sententiae priores Europaeae</span> </div> </a> <ul id="toc-Sententiae_priores_Europaeae-sublist" class="vector-toc-list"> <li id="toc-Pythagoras" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Pythagoras"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Pythagoras</span> </div> </a> <ul id="toc-Pythagoras-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Parmenides_et_Zeno_Eleaticus" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Parmenides_et_Zeno_Eleaticus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>Parmenides et Zeno Eleaticus</span> </div> </a> <ul id="toc-Parmenides_et_Zeno_Eleaticus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aristoteles" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Aristoteles"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.3</span> <span>Aristoteles</span> </div> </a> <ul id="toc-Aristoteles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Archimedes_et_Plotinus" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Archimedes_et_Plotinus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.4</span> <span>Archimedes et Plotinus</span> </div> </a> <ul id="toc-Archimedes_et_Plotinus-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sententiae_Mediaevales" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sententiae_Mediaevales"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Sententiae Mediaevales</span> </div> </a> <ul id="toc-Sententiae_Mediaevales-sublist" class="vector-toc-list"> <li id="toc-Guillelmus_de_Ockham" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Guillelmus_de_Ockham"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.1</span> <span>Guillelmus de Ockham</span> </div> </a> <ul id="toc-Guillelmus_de_Ockham-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sententiae_a_Renascentia_usque_ad_hodiernum_diem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sententiae_a_Renascentia_usque_ad_hodiernum_diem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Sententiae a Renascentia usque ad hodiernum diem</span> </div> </a> <ul id="toc-Sententiae_a_Renascentia_usque_ad_hodiernum_diem-sublist" class="vector-toc-list"> <li id="toc-Galilaeus" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Galilaeus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4.1</span> <span>Galilaeus</span> </div> </a> <ul id="toc-Galilaeus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lockius" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Lockius"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4.2</span> <span>Lockius</span> </div> </a> <ul id="toc-Lockius-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sententiae_hodiernae" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sententiae_hodiernae"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Sententiae hodiernae</span> </div> </a> <ul id="toc-Sententiae_hodiernae-sublist" class="vector-toc-list"> <li id="toc-Blake" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Blake"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5.1</span> <span>Blake</span> </div> </a> <ul id="toc-Blake-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cantor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Cantor"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5.2</span> <span>Cantor</span> </div> </a> <ul id="toc-Cantor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wittgenstein" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Wittgenstein"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5.3</span> <span>Wittgenstein</span> </div> </a> <ul id="toc-Wittgenstein-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Infinitas_in_mathematica" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Infinitas_in_mathematica"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Infinitas in mathematica</span> </div> </a> <button aria-controls="toc-Infinitas_in_mathematica-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Infinitas in mathematica subsection</span> </button> <ul id="toc-Infinitas_in_mathematica-sublist" class="vector-toc-list"> <li id="toc-Proprietates_infinitatis_arithmeticae" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Proprietates_infinitatis_arithmeticae"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Proprietates infinitatis arithmeticae</span> </div> </a> <ul id="toc-Proprietates_infinitatis_arithmeticae-sublist" class="vector-toc-list"> <li id="toc-Infinitas_secum" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Infinitas_secum"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Infinitas secum</span> </div> </a> <ul id="toc-Infinitas_secum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aequationes_cum_infinitate_purisque_numeris" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Aequationes_cum_infinitate_purisque_numeris"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>Aequationes cum infinitate purisque numeris</span> </div> </a> <ul id="toc-Aequationes_cum_infinitate_purisque_numeris-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Operationes_indefinitae" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Operationes_indefinitae"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.3</span> <span>Operationes indefinitae</span> </div> </a> <ul id="toc-Operationes_indefinitae-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Alia_notanda" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Alia_notanda"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.4</span> <span>Alia notanda</span> </div> </a> <ul id="toc-Alia_notanda-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Infinitas_in_analysi_reali_et_calculus_infinitesimalis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Infinitas_in_analysi_reali_et_calculus_infinitesimalis"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Infinitas in analysi reali et calculus infinitesimalis</span> </div> </a> <ul id="toc-Infinitas_in_analysi_reali_et_calculus_infinitesimalis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Infinitas_in_geometria" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Infinitas_in_geometria"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Infinitas in geometria</span> </div> </a> <ul id="toc-Infinitas_in_geometria-sublist" class="vector-toc-list"> <li id="toc-Torricellius" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Torricellius"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.1</span> <span>Torricellius</span> </div> </a> <ul id="toc-Torricellius-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Simiae_infinitae" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Simiae_infinitae"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Simiae infinitae</span> </div> </a> <ul id="toc-Simiae_infinitae-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Infinitas_in_fictione_scientiae" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Infinitas_in_fictione_scientiae"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Infinitas in fictione scientiae</span> </div> </a> <ul id="toc-Infinitas_in_fictione_scientiae-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nexus_interni" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Nexus_interni"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Nexus interni</span> </div> </a> <ul id="toc-Nexus_interni-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fontes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Fontes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Fontes</span> </div> </a> <button aria-controls="toc-Fontes-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Fontes subsection</span> </button> <ul id="toc-Fontes-sublist" class="vector-toc-list"> <li id="toc-Bibliographia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliographia"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Bibliographia</span> </div> </a> <ul id="toc-Bibliographia-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Nexus_externi" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Nexus_externi"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Nexus externi</span> </div> </a> <ul id="toc-Nexus_externi-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="Index" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Infinitas</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 112 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-112" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">112 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Oneindigheid" title="Oneindigheid – Africana" lang="af" hreflang="af" data-title="Oneindigheid" data-language-autonym="Afrikaans" data-language-local-name="Africana" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Unendlichkeit" title="Unendlichkeit – Alemannic" lang="gsw" hreflang="gsw" data-title="Unendlichkeit" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%8B%95%E1%88%8B%E1%8D%8D" title="አዕላፍ – Amharica" lang="am" hreflang="am" data-title="አዕላፍ" data-language-autonym="አማርኛ" data-language-local-name="Amharica" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Infinito" title="Infinito – Aragonensis" lang="an" hreflang="an" data-title="Infinito" data-language-autonym="Aragonés" data-language-local-name="Aragonensis" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%84%D8%A7%D9%86%D9%87%D8%A7%D9%8A%D8%A9" title="لانهاية – Arabica" lang="ar" hreflang="ar" data-title="لانهاية" data-language-autonym="العربية" data-language-local-name="Arabica" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%84%D8%A7%D9%85%D8%B3%D8%A7%D9%84%D9%8A%D8%A9" title="لامسالية – Moroccan Arabic" lang="ary" hreflang="ary" data-title="لامسالية" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D9%84%D9%87%D8%A7%D8%B4_%D9%86%D9%87%D8%A7%D9%8A%D9%87" title="ملهاش نهايه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ملهاش نهايه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%85%E0%A6%B8%E0%A7%80%E0%A6%AE" title="অসীম – Assamica" lang="as" hreflang="as" data-title="অসীম" data-language-autonym="অসমীয়া" data-language-local-name="Assamica" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Infinitu" title="Infinitu – Asturian" lang="ast" hreflang="ast" data-title="Infinitu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sonsuzluq" title="Sonsuzluq – Atropatenica" lang="az" hreflang="az" data-title="Sonsuzluq" data-language-autonym="Azərbaycanca" data-language-local-name="Atropatenica" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B3%D9%88%D9%86%D8%B3%D9%88%D8%B2" title="سونسوز – South Azerbaijani" lang="azb" hreflang="azb" data-title="سونسوز" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D0%B8%D0%BA%D2%BB%D0%B5%D2%99%D0%BB%D0%B5%D0%BA" title="Сикһеҙлек – Bashkir" lang="ba" hreflang="ba" data-title="Сикһеҙлек" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Begal%C4%ABb%C4%97" title="Begalībė – Samogitian" lang="sgs" hreflang="sgs" data-title="Begalībė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%B0%D0%BD%D0%B5%D1%87%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Бесканечнасць – Ruthenica Alba" lang="be" hreflang="be" data-title="Бесканечнасць" data-language-autonym="Беларуская" data-language-local-name="Ruthenica Alba" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%91%D1%8F%D1%81%D0%BA%D0%BE%D0%BD%D1%86%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Бясконцасьць – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Бясконцасьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B5%D0%B7%D0%BA%D1%80%D0%B0%D0%B9%D0%BD%D0%BE%D1%81%D1%82" title="Безкрайност – Bulgarica" lang="bg" hreflang="bg" data-title="Безкрайност" data-language-autonym="Български" data-language-local-name="Bulgarica" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/Infinity" title="Infinity – Banjar" lang="bjn" hreflang="bjn" data-title="Infinity" data-language-autonym="Banjar" data-language-local-name="Banjar" class="interlanguage-link-target"><span>Banjar</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%B8%E0%A7%80%E0%A6%AE" title="অসীম – Bengalica" lang="bn" hreflang="bn" data-title="অসীম" data-language-autonym="বাংলা" data-language-local-name="Bengalica" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Beskona%C4%8Dnost" title="Beskonačnost – Bosnica" lang="bs" hreflang="bs" data-title="Beskonačnost" data-language-autonym="Bosanski" data-language-local-name="Bosnica" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Infinit" title="Infinit – Catalana" lang="ca" hreflang="ca" data-title="Infinit" data-language-autonym="Català" data-language-local-name="Catalana" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%8E%DA%A9%DB%86%D8%AA%D8%A7%DB%8C%DB%8C" title="بێکۆتایی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بێکۆتایی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Infinitu" title="Infinitu – Corsa" lang="co" hreflang="co" data-title="Infinitu" data-language-autonym="Corsu" data-language-local-name="Corsa" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Nekone%C4%8Dno" title="Nekonečno – Bohemica" lang="cs" hreflang="cs" data-title="Nekonečno" data-language-autonym="Čeština" data-language-local-name="Bohemica" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%92%C4%95%C3%A7%D1%81%C4%95%D1%80%D0%BB%C4%95%D1%85" title="Вĕçсĕрлĕх – Chuvassica" lang="cv" hreflang="cv" data-title="Вĕçсĕрлĕх" data-language-autonym="Чӑвашла" data-language-local-name="Chuvassica" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Anfeidredd" title="Anfeidredd – Cambrica" lang="cy" hreflang="cy" data-title="Anfeidredd" data-language-autonym="Cymraeg" data-language-local-name="Cambrica" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Uendelighed" title="Uendelighed – Danica" lang="da" hreflang="da" data-title="Uendelighed" data-language-autonym="Dansk" data-language-local-name="Danica" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Unendlich_(Mathematik)" title="Unendlich (Mathematik) – Germanica" lang="de" hreflang="de" data-title="Unendlich (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="Germanica" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%86%CF%80%CE%B5%CE%B9%CF%81%CE%BF" title="Άπειρο – Graeca" lang="el" hreflang="el" data-title="Άπειρο" data-language-autonym="Ελληνικά" data-language-local-name="Graeca" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Infinity" title="Infinity – Anglica" lang="en" hreflang="en" data-title="Infinity" data-language-autonym="English" data-language-local-name="Anglica" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Senfineco" title="Senfineco – Esperantica" lang="eo" hreflang="eo" data-title="Senfineco" data-language-autonym="Esperanto" data-language-local-name="Esperantica" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Infinito" title="Infinito – Hispanica" lang="es" hreflang="es" data-title="Infinito" data-language-autonym="Español" data-language-local-name="Hispanica" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/L%C3%B5pmatus" title="Lõpmatus – Estonica" lang="et" hreflang="et" data-title="Lõpmatus" data-language-autonym="Eesti" data-language-local-name="Estonica" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Infinitu" title="Infinitu – Vasconica" lang="eu" hreflang="eu" data-title="Infinitu" data-language-autonym="Euskara" data-language-local-name="Vasconica" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%DB%8C%E2%80%8C%D9%86%D9%87%D8%A7%DB%8C%D8%AA" title="بی‌نهایت – Persica" lang="fa" hreflang="fa" data-title="بی‌نهایت" data-language-autonym="فارسی" data-language-local-name="Persica" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/%C3%84%C3%A4rett%C3%B6myys" title="Äärettömyys – Finnica" lang="fi" hreflang="fi" data-title="Äärettömyys" data-language-autonym="Suomi" data-language-local-name="Finnica" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Infini" title="Infini – Francogallica" lang="fr" hreflang="fr" data-title="Infini" data-language-autonym="Français" data-language-local-name="Francogallica" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/%C3%9Cnentelkhaid" title="Ünentelkhaid – Northern Frisian" lang="frr" hreflang="frr" data-title="Ünentelkhaid" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/%C3%89igr%C3%ADoch" title="Éigríoch – Hibernica" lang="ga" hreflang="ga" data-title="Éigríoch" data-language-autonym="Gaeilge" data-language-local-name="Hibernica" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%84%A1%E9%99%90" title="無限 – Gan" lang="gan" hreflang="gan" data-title="無限" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Enfini" title="Enfini – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Enfini" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Infinito" title="Infinito – Gallaica" lang="gl" hreflang="gl" data-title="Infinito" data-language-autonym="Galego" data-language-local-name="Gallaica" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%85%E0%AA%A8%E0%AA%82%E0%AA%A4" title="અનંત – Gujaratensis" lang="gu" hreflang="gu" data-title="અનંત" data-language-autonym="ગુજરાતી" data-language-local-name="Gujaratensis" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%99%D7%A0%D7%A1%D7%95%D7%A3" title="אינסוף – Hebrew" lang="he" hreflang="he" data-title="אינסוף" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A4%82%E0%A4%A4" title="अनंत – Hindica" lang="hi" hreflang="hi" data-title="अनंत" data-language-autonym="हिन्दी" data-language-local-name="Hindica" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Anant" title="Anant – Fiji Hindi" lang="hif" hreflang="hif" data-title="Anant" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Beskona%C4%8Dnost" title="Beskonačnost – Croatica" lang="hr" hreflang="hr" data-title="Beskonačnost" data-language-autonym="Hrvatski" data-language-local-name="Croatica" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/V%C3%A9gtelen" title="Végtelen – Hungarica" lang="hu" hreflang="hu" data-title="Végtelen" data-language-autonym="Magyar" data-language-local-name="Hungarica" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B6%D5%BE%D5%A5%D6%80%D5%BB%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6_(%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1)" title="Անվերջություն (մաթեմատիկա) – Armenica" lang="hy" hreflang="hy" data-title="Անվերջություն (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="Armenica" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Takhingga" title="Takhingga – Indonesian" lang="id" hreflang="id" data-title="Takhingga" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Awan_inggana" title="Awan inggana – Iloko" lang="ilo" hreflang="ilo" data-title="Awan inggana" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%93endanleiki" title="Óendanleiki – Islandica" lang="is" hreflang="is" data-title="Óendanleiki" data-language-autonym="Íslenska" data-language-local-name="Islandica" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Infinito_(matematica)" title="Infinito (matematica) – Italiana" lang="it" hreflang="it" data-title="Infinito (matematica)" data-language-autonym="Italiano" data-language-local-name="Italiana" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%84%A1%E9%99%90" title="無限 – Iaponica" lang="ja" hreflang="ja" data-title="無限" data-language-autonym="日本語" data-language-local-name="Iaponica" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Infiniti" title="Infiniti – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Infiniti" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/li_ci%27i" title="li ci'i – Lojban" lang="jbo" hreflang="jbo" data-title="li ci'i" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A3%E1%83%A1%E1%83%90%E1%83%A1%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%9D%E1%83%91%E1%83%90" title="უსასრულობა – Georgiana" lang="ka" hreflang="ka" data-title="უსასრულობა" data-language-autonym="ქართული" data-language-local-name="Georgiana" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A8%D0%B5%D0%BA%D1%81%D1%96%D0%B7%D0%B4%D1%96%D0%BA" title="Шексіздік – Cazachica" lang="kk" hreflang="kk" data-title="Шексіздік" data-language-autonym="Қазақша" data-language-local-name="Cazachica" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%A8%E0%B2%82%E0%B2%A4" title="ಅನಂತ – Cannadica" lang="kn" hreflang="kn" data-title="ಅನಂತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Cannadica" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AC%B4%ED%95%9C" title="무한 – Coreana" lang="ko" hreflang="ko" data-title="무한" data-language-autonym="한국어" data-language-local-name="Coreana" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/B%C3%AAdaw%C3%AE" title="Bêdawî – Curdica" lang="ku" hreflang="ku" data-title="Bêdawî" data-language-autonym="Kurdî" data-language-local-name="Curdica" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Didhiwedhter" title="Didhiwedhter – Cornubica" lang="kw" hreflang="kw" data-title="Didhiwedhter" data-language-autonym="Kernowek" data-language-local-name="Cornubica" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A7%D0%B5%D0%BA%D1%81%D0%B8%D0%B7%D0%B4%D0%B8%D0%BA" title="Чексиздик – Chirgisica" lang="ky" hreflang="ky" data-title="Чексиздик" data-language-autonym="Кыргызча" data-language-local-name="Chirgisica" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Begalyb%C4%97" title="Begalybė – Lithuanica" lang="lt" hreflang="lt" data-title="Begalybė" data-language-autonym="Lietuvių" data-language-local-name="Lithuanica" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bezgal%C4%ABba" title="Bezgalība – Lettonica" lang="lv" hreflang="lv" data-title="Bezgalība" data-language-autonym="Latviešu" data-language-local-name="Lettonica" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tsiefa" title="Tsiefa – Malagasiana" lang="mg" hreflang="mg" data-title="Tsiefa" data-language-autonym="Malagasy" data-language-local-name="Malagasiana" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Бесконечност – Macedonica" lang="mk" hreflang="mk" data-title="Бесконечност" data-language-autonym="Македонски" data-language-local-name="Macedonica" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%A8%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%A4" title="അനന്തത – Malabarica" lang="ml" hreflang="ml" data-title="അനന്തത" data-language-autonym="മലയാളം" data-language-local-name="Malabarica" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D1%8F%D0%B7%D0%B3%D0%B0%D0%B0%D1%80%D0%B3%D2%AF%D0%B9" title="Хязгааргүй – Mongolica" lang="mn" hreflang="mn" data-title="Хязгааргүй" data-language-autonym="Монгол" data-language-local-name="Mongolica" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A4%82%E0%A4%A4" title="अनंत – Marathica" lang="mr" hreflang="mr" data-title="अनंत" data-language-autonym="मराठी" data-language-local-name="Marathica" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ketakterhinggaan" title="Ketakterhinggaan – Malayana" lang="ms" hreflang="ms" data-title="Ketakterhinggaan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malayana" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%94%E1%80%94%E1%80%B9%E1%80%90" title="အနန္တ – Birmanica" lang="my" hreflang="my" data-title="အနန္တ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Birmanica" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Unendlichkeid" title="Unendlichkeid – Low German" lang="nds" hreflang="nds" data-title="Unendlichkeid" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Oneindigheid" title="Oneindigheid – Batava" lang="nl" hreflang="nl" data-title="Oneindigheid" data-language-autonym="Nederlands" data-language-local-name="Batava" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Uendeleg" title="Uendeleg – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Uendeleg" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Uendelig" title="Uendelig – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Uendelig" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Infinit" title="Infinit – Occitana" lang="oc" hreflang="oc" data-title="Infinit" data-language-autonym="Occitan" data-language-local-name="Occitana" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%A8%E0%A9%B0%E0%A8%A4" title="ਅਨੰਤ – Panjabica" lang="pa" hreflang="pa" data-title="ਅਨੰਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Panjabica" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Niesko%C5%84czono%C5%9B%C4%87" title="Nieskończoność – Polonica" lang="pl" hreflang="pl" data-title="Nieskończoność" data-language-autonym="Polski" data-language-local-name="Polonica" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%86%D8%A7%D9%86%D8%AA%DB%8C" title="انانتی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انانتی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Infinito" title="Infinito – Lusitana" lang="pt" hreflang="pt" data-title="Infinito" data-language-autonym="Português" data-language-local-name="Lusitana" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Infinit" title="Infinit – Dacoromanica" lang="ro" hreflang="ro" data-title="Infinit" data-language-autonym="Română" data-language-local-name="Dacoromanica" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Бесконечность – Russica" lang="ru" hreflang="ru" data-title="Бесконечность" data-language-autonym="Русский" data-language-local-name="Russica" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Бесконечность – Rusyn" lang="rue" hreflang="rue" data-title="Бесконечность" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Nfinitu_(matim%C3%A0tica)" title="Nfinitu (matimàtica) – Sicilian" lang="scn" hreflang="scn" data-title="Nfinitu (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Infinity" title="Infinity – Scots" lang="sco" hreflang="sco" data-title="Infinity" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Beskona%C4%8Dnost_(matematika)" title="Beskonačnost (matematika) – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Beskonačnost (matematika)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%85%E0%B6%B1%E0%B6%B1%E0%B7%8A%E0%B6%AD%E0%B6%BA" title="අනන්තය – Singhalensis" lang="si" hreflang="si" data-title="අනන්තය" data-language-autonym="සිංහල" data-language-local-name="Singhalensis" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Infinity" title="Infinity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Infinity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Nekone%C4%8Dno" title="Nekonečno – Slovaca" lang="sk" hreflang="sk" data-title="Nekonečno" data-language-autonym="Slovenčina" data-language-local-name="Slovaca" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Neskon%C4%8Dnost" title="Neskončnost – Slovena" lang="sl" hreflang="sl" data-title="Neskončnost" data-language-autonym="Slovenščina" data-language-local-name="Slovena" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Kusingaperi" title="Kusingaperi – Shona" lang="sn" hreflang="sn" data-title="Kusingaperi" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Pafund%C3%ABsia" title="Pafundësia – Albanica" lang="sq" hreflang="sq" data-title="Pafundësia" data-language-autonym="Shqip" data-language-local-name="Albanica" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B0%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Бесконачност – Serbica" lang="sr" hreflang="sr" data-title="Бесконачност" data-language-autonym="Српски / srpski" data-language-local-name="Serbica" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/O%C3%A4ndlighet" title="Oändlighet – Suecica" lang="sv" hreflang="sv" data-title="Oändlighet" data-language-autonym="Svenska" data-language-local-name="Suecica" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AE%BF" title="முடிவிலி – Tamulica" lang="ta" hreflang="ta" data-title="முடிவிலி" data-language-autonym="தமிழ்" data-language-local-name="Tamulica" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%91%D0%B5%D0%B8%D0%BD%D1%82%D0%B8%D2%B3%D0%BE%D3%A3" title="Беинтиҳоӣ – Tadzikica" lang="tg" hreflang="tg" data-title="Беинтиҳоӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="Tadzikica" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%99%E0%B8%B1%E0%B8%99%E0%B8%95%E0%B9%8C" title="อนันต์ – Thai" lang="th" hreflang="th" data-title="อนันต์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kawalang-hanggan" title="Kawalang-hanggan – Tagalog" lang="tl" hreflang="tl" data-title="Kawalang-hanggan" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sonsuz" title="Sonsuz – Turcica" lang="tr" hreflang="tr" data-title="Sonsuz" data-language-autonym="Türkçe" data-language-local-name="Turcica" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A7%D0%B8%D0%BA%D1%81%D0%B5%D0%B7%D0%BB%D0%B5%D0%BA" title="Чиксезлек – Tatarica" lang="tt" hreflang="tt" data-title="Чиксезлек" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatarica" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9D%D0%B5%D1%81%D0%BA%D1%96%D0%BD%D1%87%D0%B5%D0%BD%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Нескінченність – Ucrainica" lang="uk" hreflang="uk" data-title="Нескінченність" data-language-autonym="Українська" data-language-local-name="Ucrainica" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%AA%D9%86%D8%A7%DB%81%DB%8C_%D8%A7%D9%88%D8%B1_%D9%84%D8%A7%D9%85%D8%AA%D9%86%D8%A7%DB%81%DB%8C" title="متناہی اور لامتناہی – Urdu" lang="ur" hreflang="ur" data-title="متناہی اور لامتناہی" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Cheksizlik" title="Cheksizlik – Uzbecica" lang="uz" hreflang="uz" data-title="Cheksizlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbecica" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Lopm%C3%A4tomuz" title="Lopmätomuz – Veps" lang="vep" hreflang="vep" data-title="Lopmätomuz" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%C3%B4_t%E1%BA%ADn" title="Vô tận – Vietnamica" lang="vi" hreflang="vi" data-title="Vô tận" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamica" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Infinidad" title="Infinidad – Waray" lang="war" hreflang="war" data-title="Infinidad" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%97%A0%E7%A9%B7" title="无穷 – Wu" lang="wuu" hreflang="wuu" data-title="无穷" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%95%D7%9E%D7%A2%D7%A0%D7%93%D7%9C%D7%A2%D7%9B%D7%A7%D7%99%D7%99%D7%98" title="אומענדלעכקייט – Yiddish" lang="yi" hreflang="yi" data-title="אומענדלעכקייט" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%97%A0%E7%A9%B7" title="无穷 – Sinica" lang="zh" hreflang="zh" data-title="无穷" data-language-autonym="中文" data-language-local-name="Sinica" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%84%A1%E9%99%90" title="無限 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="無限" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/B%C3%BB-h%C4%81n" title="Bû-hān – Minnan" lang="nan" hreflang="nan" data-title="Bû-hān" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%84%A1%E7%AA%AE%E7%9B%A1" title="無窮盡 – Cantonese" lang="yue" hreflang="yue" data-title="無窮盡" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q205#sitelinks-wikipedia" title="Nexus inter linguas recensere" class="wbc-editpage">Nexus recensere</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Spatia nominalia"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Infinitas" title="Videre paginam [c]" accesskey="c"><span>Res</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Disputatio:Infinitas" rel="discussion" title="Disputatio de hac pagina [t]" accesskey="t"><span>Disputatio</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" 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title="Fontem huius paginae recensere [e]" accesskey="e"><span>Fontem recensere</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Infinitas&action=history" title="Superiores huius paginae versiones [h]" accesskey="h"><span>Historiam inspicere</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Instrumenta" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Instrumenta</span> 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Vicipaedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="la" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:Lemniscate_Building_2.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lemniscate_Building_2.gif/220px-Lemniscate_Building_2.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/65/Lemniscate_Building_2.gif 1.5x" data-file-width="250" data-file-height="250" /></a><figcaption><a href="/wiki/Lemniscus_(mathematica)" title="Lemniscus (mathematica)">Lemniscus</a> <a href="/wiki/Iacobus_Bernoulli" class="mw-redirect" title="Iacobus Bernoulli">Iacobi Bernoulli</a>, una ex figuris lemniscatis quae adhibetur ad infinitatem significandam.</figcaption></figure> <p><dfn style="font-style:inherit;font-weight:bold;">Infinitas</dfn> (<style data-mw-deduplicate="TemplateStyles:r3826701">.mw-parser-output i i.pns-genus{font-style:normal}</style><a href="https://la.wiktionary.org/wiki/infinitas" class="extiw" title="wikt:infinitas">-atis, <i class="pns-genus">f</i>.</a>), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> notata, est notio quasi <a href="/wiki/Numerus" title="Numerus">numerica</a> quae adhibetur ad multas <a href="/wiki/Sententia" class="mw-disambig" title="Sententia">sententias</a> <a href="/wiki/Mathematica" title="Mathematica">mathematicas</a>, <a href="/wiki/Philosophia" title="Philosophia">philosophicas</a>, et <a href="/wiki/Theologia" title="Theologia">theologicas</a> explicandas, quibus omnibus absentia finium aut termini modis variis intellegitur. </p><p>Nonnumquam <a href="/wiki/Homo" class="mw-redirect mw-disambig" title="Homo">homines</a>, in locutione vulgari, loquuntur de infinitate in rebus finitis sed diu perennibus; ita <i>hora,</i> si quid invitus facere cogaris, videatur <i>infinita.</i> In aliis talibus casibus, saepe infinitas significat "rem maiorem quam maximam quam excogitari possit". Saepe etiam, homines loquuntur de <a href="/w/index.php?title=Plus_quam_infinitas&action=edit&redlink=1" class="new" title="Plus quam infinitas (non est haec pagina)">plure quam infinitas</a>, vel <a href="/wiki/Infinitas_%2B_1" class="mw-redirect" title="Infinitas + 1">infinitate + 1</a>, quae immo quippe ambae sunt nugae.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Mathematica" title="Mathematica">mathematica</a>, infinitas usurpatur quasi <a href="/wiki/Numerus_realis" title="Numerus realis">numero reali</a>. In quibusdam autem scholis rationis, infinitas e contrario non putatur esse <a href="/wiki/Numerus" title="Numerus">numerus</a>, sed conceptio theoretica. </p><p>In <a href="/wiki/Philosophia" title="Philosophia">philosophia</a>, <a href="/wiki/Tempus" title="Tempus">tempus</a> <a href="/wiki/Spatium" title="Spatium">spatiumque</a> ratione infinitatis explicentur, ut descripsit <a href="/wiki/Antinomia" title="Antinomia">antinomia</a> prima <a href="/wiki/Immanuel_Kantius" title="Immanuel Kantius">Immanuelis Kantii</a>. Infinitum tempus appellatur <i><a href="/wiki/Aeternitas" title="Aeternitas">Aeternitas</a></i>. In <a href="/wiki/Philosophia_Graeca" class="mw-redirect" title="Philosophia Graeca">philosophia Graeca</a>, gratia exempli in eo quod <a href="/wiki/Anaximander" title="Anaximander">Anaximander</a> <i><a href="/wiki/Apiron" title="Apiron">τὸ Ἄπειρον</a></i> appellavit, infinitas est origo et fons omnium. In <a href="/wiki/Religio" title="Religio">rebus theologicis</a>, infinitas fit <a href="/wiki/Deus" title="Deus">Deus</a>. In <a href="/wiki/Theologia" title="Theologia">theologia</a> <a href="/wiki/Religio_Iudaica" title="Religio Iudaica">Iudaeo</a>-<a href="/wiki/Religio_Christiana" title="Religio Christiana">Christiana</a>, sicut in operibus <a href="/wiki/Duns_Scotus" title="Duns Scotus">Ioannes Duns Scoti</a>, notio <a href="/wiki/Deus" title="Deus">deitatis</a> est infinitus non <a href="/wiki/Quantitas" title="Quantitas">quantitate</a>, at potestate. </p><p>Ut legas de spatio infinito, vide <a href="/wiki/Universum" title="Universum">Universum</a>. </p> <style data-mw-deduplicate="TemplateStyles:r3856202">.mw-parser-output table.capsatab{float:right;clear:right;border:1px solid #eaecf0;background-color:#f7f8ff;margin:.25em 0 1em 1em;padding:.3em .25em;max-width:22em;font-size:.88em;border-radius:1em;box-shadow:8px 8px 8px rgba(0,0,0,.2)}.mw-parser-output table.capsatab caption{font-weight:bold;text-align:center}.mw-parser-output table.capsatab th,.mw-parser-output table.capsatab td{margin:0;vertical-align:top;box-sizing:border-box}.mw-parser-output table.capsatab th{min-width:8.8em;padding:.1em .25em .1em .1em;text-align:right}.mw-parser-output table.capsatab td{min-width:11em;padding:.1em .1em .1em .25em;text-align:left}.mw-parser-output table.capsatab th:only-child,.mw-parser-output table.capsatab td:only-child{text-align:center;min-width:0}.mw-parser-output table.capsatab th:only-child{background-color:#e6e6fa;padding:.15em .5em}.mw-parser-output table.capsatab td:only-child{padding:.1em}@media(max-width:768px){.mw-parser-output table.capsatab{float:none;margin:.25em auto 1em auto}}</style> <table class="capsatab"> <caption>Systemata Numerica <a href="/wiki/Mathematica" title="Mathematica">Mathematicae</a> </caption> <tbody><tr> <th>Numeri Elementarii </th></tr> <tr> <td style="text-align: left;"> <p><b><a href="/wiki/Numerus_naturalis" title="Numerus naturalis">Naturales</a></b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf9a96b565ea202d0f4322e9195613fb26a9bed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {N} }"></span> {0,1,2,3,...} sive {1,2,3,...}<br /> </p> <ul><li><a href="/wiki/Numerus_primus" title="Numerus primus">Primi</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {P} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">P</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {P} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1053af9e662ceaf56c4455f90e0f67273422eded" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.42ex; height:2.176ex;" alt="{\displaystyle \mathbb {P} }"></span> {2,3,5,7,11,...}</li> <li><a href="/wiki/Numerus_abundans" title="Numerus abundans">Abundantes</a></li> <li><a href="/wiki/Numeri_amicabiles" title="Numeri amicabiles">Amicabiles</a></li> <li><a href="/wiki/Numerus_compositus" title="Numerus compositus">Compositi</a></li> <li><a href="/wiki/Numerus_defectivus" title="Numerus defectivus">Defectivi</a></li> <li><a href="/wiki/Numerus_perfectus" title="Numerus perfectus">Perfecti</a></li> <li><a href="/wiki/Numerus_sociabilis" title="Numerus sociabilis">Sociabiles</a><br /></li></ul> <p><b><a href="/wiki/Numerus_integer" title="Numerus integer">Integri</a></b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" 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 {Z} }"></span> {...,-2,-1,0,+1,+2,...}<br /> </p> <ul><li><a href="/wiki/Numerus_par" class="mw-redirect" title="Numerus par">Pares</a> {...,-2,0,+2,...}</li> <li><a href="/wiki/Numerus_impar" title="Numerus impar">Impares</a> {...,-3,-1,+1,+3,...}<br /></li></ul> <p><b><a href="/wiki/Numerus_rationalis" title="Numerus rationalis">Rationales</a></b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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></span><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} }"></span><br /> <b><a href="/wiki/Numerus_realis" title="Numerus realis">Reales</a></b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" 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 {R} }"></span> </p> <ul><li><a href="/wiki/Numerus_irrationalis" title="Numerus irrationalis">Irrationales</a></li></ul> <p><b><a href="/wiki/Numerus_complexus" title="Numerus complexus">Complexi</a></b> ℂ </p> <ul><li><a href="/wiki/Numerus_algebraicus" title="Numerus algebraicus">Algebraici</a></li> <li><a href="/wiki/Numerus_transcendens" title="Numerus transcendens">Transcendentes</a> <ul><li><a href="/wiki/Numerus_pi" title="Numerus pi">Numerus pi</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi =3.14159265358979\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo>=</mo> <mn>3.14159265358979</mn> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi =3.14159265358979\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6de554f9fba9eb9849cf9f5ed6d193922b0dc765" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:25.624ex; height:2.176ex;" alt="{\displaystyle \pi =3.14159265358979\ldots }"></span></li> <li><a href="/wiki/Numerus_Euleri" class="mw-redirect" title="Numerus Euleri">Numerus Euleri</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e=2.718281828459045\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mn>2.718281828459045</mn> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e=2.718281828459045\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35593d7fb535e89fb9f2bf15e7941e84977c0741" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:26.538ex; height:2.176ex;" alt="{\displaystyle e=2.718281828459045\ldots }"></span></li></ul></li> <li><a href="/wiki/Numerus_imaginarius" class="mw-redirect" title="Numerus imaginarius">Numerus imaginarius</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i={\sqrt {-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" 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">{\displaystyle i={\sqrt {-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/370c8cebe9634fbfc84c29ea61680b0ad4a1ae0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.807ex; height:3.009ex;" alt="{\displaystyle i={\sqrt {-1}}}"></span><br /></li></ul> <p><b><a href="/wiki/Numerus_quaternus" title="Numerus quaternus">Quaterni</a></b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {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></span><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} }"></span><br /> <b><a href="/wiki/Numerus_octonus" title="Numerus octonus">Octoni</a></b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {O} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">O</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {O} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1ed2664a4fe515e6fbed25a7193ce663b82920c" 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 {O} }"></span><br /> <a class="mw-selflink selflink">Infinitas</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> </p> </td></tr> <tr> <th>Variae radices </th></tr> <tr> <td style="text-align: left;"> <ul><li><a href="/wiki/Systema_numericum_binarium" title="Systema numericum binarium">Radix binaria(2)</a></li> <li><a href="/wiki/Systema_numericum_octale" title="Systema numericum octale">Radix octalis(8)</a></li> <li><a href="/wiki/Systema_numericum_decimale" title="Systema numericum decimale">Radix decimalis(10)</a></li> <li><a href="/wiki/Systema_numericum_sedecimale" title="Systema numericum sedecimale">Radix sedecimalis(16)</a></li></ul> </td></tr></tbody></table> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="De_signo_'"`UNIQ--postMath-0000000D-QINU`"'"><span id="De_signo_.7F.27.22.60UNIQ--postMath-0000000D-QINU.60.22.27.7F"></span>De signo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=1" title="Recensere partem: De signo '"`UNIQ--postMath-0000000D-QINU`"'" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=1" title="Edit section's source code: De signo '"`UNIQ--postMath-0000000D-QINU`"'"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:John_Wallis_by_Sir_Godfrey_Kneller,_Bt.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/John_Wallis_by_Sir_Godfrey_Kneller%2C_Bt.jpg/200px-John_Wallis_by_Sir_Godfrey_Kneller%2C_Bt.jpg" decoding="async" width="200" height="242" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/John_Wallis_by_Sir_Godfrey_Kneller%2C_Bt.jpg/300px-John_Wallis_by_Sir_Godfrey_Kneller%2C_Bt.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/John_Wallis_by_Sir_Godfrey_Kneller%2C_Bt.jpg/400px-John_Wallis_by_Sir_Godfrey_Kneller%2C_Bt.jpg 2x" data-file-width="2400" data-file-height="2900" /></a><figcaption><a href="/w/index.php?title=Iohannes_Wallis&action=edit&redlink=1" class="new" title="Iohannes Wallis (non est haec pagina)">Iohannes Wallis</a> fuit primus qui lemniscum quasi symbolum infinitatis in litteratura mathematica introduxit.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:Ouroboros_1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Ouroboros_1.jpg/200px-Ouroboros_1.jpg" decoding="async" width="200" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Ouroboros_1.jpg/300px-Ouroboros_1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Ouroboros_1.jpg/400px-Ouroboros_1.jpg 2x" data-file-width="815" data-file-height="832" /></a><figcaption>Imago <a href="/wiki/Uroborus" title="Uroborus">urobori</a>, qui saepe est pictus in forma lemniscata. De <i><a href="/w/index.php?title=De_Lapide_Philisophico&action=edit&redlink=1" class="new" title="De Lapide Philisophico (non est haec pagina)">De Lapide Philisophico</a></i>, a <a href="/w/index.php?title=Lucas_Iennisius&action=edit&redlink=1" class="new" title="Lucas Iennisius (non est haec pagina)">Luca Iennisio</a>.</figcaption></figure> <p>Origines signi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> non clare cognoscuntur. Figura ipsa appellatur <i><b><a href="/wiki/Lemniscus_(mathematica)" title="Lemniscus (mathematica)">lemniscus</a></b></i>, et in animo concipi potest modum quo iter trans <a href="/w/index.php?title=Curvum_simplex&action=edit&redlink=1" class="new" title="Curvum simplex (non est haec pagina)">curvum simplicem</a> a lemnisco factum numquam finiret. </p><p><a href="/wiki/Aequatio" title="Aequatio">Aequatio</a> <a href="/wiki/Renatus_Cartesius" title="Renatus Cartesius">Cartesiana</a> quae lemniscum reddit est: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x^{2}+y^{2})^{2}=2a^{2}(x^{2}-y^{2})\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x^{2}+y^{2})^{2}=2a^{2}(x^{2}-y^{2})\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2260ffc45643e3d6874791594524d7fe82b8c9bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.483ex; height:3.176ex;" alt="{\displaystyle (x^{2}+y^{2})^{2}=2a^{2}(x^{2}-y^{2})\,}"></span></dd></dl> <p>Vulgo fama est <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> signum derivatum esse a <a href="/wiki/Moebii_taenia" class="mw-redirect" title="Moebii taenia">Moebii taenia</a>. Item, in animo potest iter concipi aeternum trans faciem sine finibus. Haec autem explicatio haud sufficit, quoniam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> scribebatur ad infinitatem significandam fere ducentos annos prius quam <a href="/wiki/Augustus_Ferdinandus_Moebius" title="Augustus Ferdinandus Moebius">Augustus Ferdinandus Moebius</a> et <a href="/w/index.php?title=Iohannes_Benedictus_Listing&action=edit&redlink=1" class="new" title="Iohannes Benedictus Listing (non est haec pagina)">Iohannes Benedictus Listing</a> invenerint Moebii taeniam anno <a href="/wiki/1858" title="1858">1858</a>. </p><p><a href="/w/index.php?title=Iohannes_Wallis&action=edit&redlink=1" class="new" title="Iohannes Wallis (non est haec pagina)">Iohannes Wallis</a> saepissime fertur instituisse <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> ad infinitatem scribendam anno <a href="/wiki/1655" title="1655">1655</a>, in suo libro <i><a href="/w/index.php?title=De_sectionibus_conicis&action=edit&redlink=1" class="new" title="De sectionibus conicis (non est haec pagina)">De sectionibus conicis</a>.</i><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Coniectatur hoc signum a <a href="/wiki/Numerus#Numeri_Latini" title="Numerus">numero Romano</a> pro 1000 derivatum esse, ipsum a <a href="/w/index.php?title=Numeri_Etrusci&action=edit&redlink=1" class="new" title="Numeri Etrusci (non est haec pagina)">numero Etrusco</a> pro 1000, quod est specie CIƆ, et interdum significabat Romanis modo "plurima". Propositum etiam derivatum esse a <a href="/wiki/Littera" title="Littera">littera</a> <a href="/wiki/Lingua_Graeca_antiqua" title="Lingua Graeca antiqua">Graeca</a> ω (<a href="/wiki/Omega" title="Omega">omega</a>), littera ultima <a href="/wiki/Abecedarium#Abecedarium_Graecum" title="Abecedarium">abecedarii Graeci</a>.<sup id="cite_ref-histmath_3-0" class="reference"><a href="#cite_note-histmath-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Etiam symbolum inventum est in <a href="/wiki/Ars" title="Ars">arte</a> vulgari, et in symbolis religiosis antiquis. Gratia exempli, <i><a href="/wiki/Uroborus" title="Uroborus">οὐροβóρος</a></i> saepe est pictus in forma lemnisci. </p><p>In <a href="/wiki/Unicodex" title="Unicodex">Unicodice</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> designatur a <b><span style="font-size:20pt">∞</span></b> , codice (U+221E) (&#8734;). </p> <div class="mw-heading mw-heading2"><h2 id="Sententiae_de_Infinitate_per_historiam">Sententiae de Infinitate per historiam</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=2" title="Recensere partem: Sententiae de Infinitate per historiam" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=2" title="Edit section's source code: Sententiae de Infinitate per historiam"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Per saecula, homines in <a href="/wiki/Nox" title="Nox">noctis</a> <a href="/wiki/Caelum" title="Caelum">caelum</a> intuebantur, universi fines coniectantes. Etiam enumerabant de finibus numerorum mirantes. <a href="/wiki/Natura" title="Natura">Natura</a> ergo infinitatem vel eius rationem petebant. Textus antiquissimi nobis noti sunt de <a href="/wiki/Philosophus" class="mw-redirect" title="Philosophus">philosophis</a> <a href="/wiki/India" title="India">Indicis</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Sententiae_antiquae_Orientales">Sententiae antiquae Orientales</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=3" title="Recensere partem: Sententiae antiquae Orientales" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=3" title="Edit section's source code: Sententiae antiquae Orientales"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Yajurveda"><a href="/wiki/Yajurveda" title="Yajurveda">Yajurveda</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=4" title="Recensere partem: Yajurveda" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=4" title="Edit section's source code: Yajurveda"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Inter primas sententias infinitatis notas reperitur in libro <a href="/wiki/India" title="India">Indico</a> <i><a href="/wiki/Yajurveda" title="Yajurveda">Yajurveda</a></i><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> ("scientia precum orationis solutae") c. <a href="/w/index.php?title=1200_a.C.n.&action=edit&redlink=1" class="new" title="1200 a.C.n. (non est haec pagina)">1200</a>–<a href="/wiki/900_a.C.n." title="900 a.C.n.">900</a> <a href="/wiki/Aera_vulgaris" title="Aera vulgaris">ante aer. vulg.</a>) qui continet hanc sententiam: "si ex infinitate removeas, vel infinitati addas, infinitas etiam remanet." Verbis exactis Sanscriticis: </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio"><table style="background-color:inherit;"><tbody><tr><td> <dl><dd><dl><dd> </dd></dl></dd> <dd>Pūrṇam adaḥ pūrṇam idam</dd> <dd>pūrṇāt pūrṇam udacyate</dd> <dd>pūrṇasya pūrṇam ādāya</dd> <dd>pūrṇam evāvasiṣyate</dd></dl> </td><td>    </td><td> <dl><dd><dl><dd>Quae est <a href="/wiki/Latine" class="mw-redirect" title="Latine">Latine</a> conversa:</dd></dl></dd> <dd>Plenum illud, plenum hoc ;</dd> <dd>ex pleno plenum tollitur.</dd> <dd>Cum pleni plenum aufertur</dd> <dd>plenum quidem manebit.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></dd></dl></td></tr></tbody></table></div><div style="text-align:right;"><cite style="font-style:normal;">– Philosophi Hindici, <i><a href="/wiki/Yajurveda" title="Yajurveda">Yajurveda</a></i></cite></div><div><i></i></div><div style="text-align:right;">― convertit <a href="/wiki/Usor:CriticusFortuitus" title="Usor:CriticusFortuitus">CriticusFortuitus</a></div></blockquote> <div class="mw-heading mw-heading4"><h4 id="Genni">Genni</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=5" title="Recensere partem: Genni" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=5" title="Edit section's source code: Genni"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:HinduSwastika.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/HinduSwastika.svg/200px-HinduSwastika.svg.png" decoding="async" width="200" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/HinduSwastika.svg/300px-HinduSwastika.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/HinduSwastika.svg/400px-HinduSwastika.svg.png 2x" data-file-width="142" data-file-height="145" /></a><figcaption><a href="/wiki/Crux_gammata" title="Crux gammata">Crux gammata</a>, symbolum Gennorum.</figcaption></figure> <p><a href="/w/index.php?title=Gennismus&action=edit&redlink=1" class="new" title="Gennismus (non est haec pagina)">Genni</a>,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> in opere mathematico <i><a href="/w/index.php?title=Surya_Prajnapti&action=edit&redlink=1" class="new" title="Surya Prajnapti (non est haec pagina)">Surya Prajnapti</a></i> (c. <a href="/wiki/400_a.C.n." title="400 a.C.n.">400</a> <a href="/wiki/Aera_vulgaris" title="Aera vulgaris">ante aer. vulg.</a>) omnibus numeris tres categorias attribuerunt. Quisque categoria ultra divisa est in tribus ordinibus: </p> <ul><li><b>Enumerabiles</b> : minores, medii, maiores.</li> <li><b>Innumerabiles</b> : fere innumerabiles, vere innumerabiles, infinite innumerabiles.</li> <li><b>Infiniti</b> : fere infiniti, vere infiniti, infinite infiniti.</li></ul> <p>Genni primi fuerunt qui dixerunt omnes infinitates non esse aequas. Infinitates dissimiles agnoverant quattuor, quae sunt: <a href="/wiki/Linea" class="mw-redirect" title="Linea">recta</a> infinitas in una <a href="/wiki/Dimensio" class="mw-disambig" title="Dimensio">dimensione</a>, <a href="/wiki/Quadrum" title="Quadrum">quadrata</a> infinitas in duabus dimensionibus, <a href="/wiki/Cubus" title="Cubus">cubica</a> infinitas in tribus dimensionibus, et infinita infinitas in dimensionibus infinitis. </p><p>Secundum Singh (1987), Joseph (2000), et Agrawal (2000), maximus numerus enumerablis <i>N</i> <a href="/wiki/Iainismus" title="Iainismus">hominum Ianorum</a> est hodierna <a href="/w/index.php?title=Numerus_Aleph&action=edit&redlink=1" class="new" title="Numerus Aleph (non est haec pagina)">aleph-null</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \aleph _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">ℵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \aleph _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721cd7f8c15a2e72ad162bdfa5baea8eef98aab1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.475ex; height:2.509ex;" alt="{\displaystyle \aleph _{0}}"></span> (<a href="/w/index.php?title=Numerus_cardinalis&action=edit&redlink=1" class="new" title="Numerus cardinalis (non est haec pagina)">numeri cardinalis</a> notio copiae iinfinitae integrorum 1, 2, . . . .), minimi <a href="/w/index.php?title=Numerus_transfinitus&action=edit&redlink=1" class="new" title="Numerus transfinitus (non est haec pagina)">transfiniti</a> numeri cardinalis. </p> <div class="mw-heading mw-heading3"><h3 id="Sententiae_priores_Europaeae">Sententiae priores Europaeae</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=6" title="Recensere partem: Sententiae priores Europaeae" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=6" title="Edit section's source code: Sententiae priores Europaeae"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Europa" title="Europa">Europa</a>, primi <a href="/wiki/Graecia" title="Graecia">Graeci</a> de infinitate finxerunt. </p> <div class="mw-heading mw-heading4"><h4 id="Pythagoras"><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=7" title="Recensere partem: Pythagoras" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=7" title="Edit section's source code: Pythagoras"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pyhtagoras docebat <a href="/w/index.php?title=Unum&action=edit&redlink=1" class="new" title="Unum (non est haec pagina)">unitatem</a> esse numerum maximae gravitatis; fontem omnium numerorum, ut facile numeremus ad infinitatem, modo unum addentes ad numerum priorem.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Parmenides_et_Zeno_Eleaticus"><a href="/wiki/Parmenides" title="Parmenides">Parmenides</a> et <a href="/wiki/Zeno_Eleaticus" class="mw-redirect" title="Zeno Eleaticus">Zeno Eleaticus</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=8" title="Recensere partem: Parmenides et Zeno Eleaticus" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=8" title="Edit section's source code: Parmenides et Zeno Eleaticus"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:Zeno_Paradox.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Zeno_Paradox.svg/300px-Zeno_Paradox.svg.png" decoding="async" width="300" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Zeno_Paradox.svg/450px-Zeno_Paradox.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Zeno_Paradox.svg/600px-Zeno_Paradox.svg.png 2x" data-file-width="450" data-file-height="350" /></a><figcaption>Paradoxum Zenonis, de Achille et Testudine.</figcaption></figure> <p><a href="/wiki/Parmenides" title="Parmenides">Parmenides</a> docebat praecepta Pythagoreis similia: dixit unum esse omnia, quod unus in partibus infinitis dividi posset. </p><p><a href="/wiki/Zeno_Eleaticus" class="mw-redirect" title="Zeno Eleaticus">Zeno Eleaticus</a> diversa <a href="/w/index.php?title=Paradoxa_Zenonis_Eleatae&action=edit&redlink=1" class="new" title="Paradoxa Zenonis Eleatae (non est haec pagina)">paradoxa</a> proposuit ut theorias Parmenidis illustraret (circiter <a href="/wiki/460_a.C.n." title="460 a.C.n.">460</a> <a href="/wiki/Aera_vulgaris" title="Aera vulgaris">ante aer. vulg.</a>). In uno ex his, quod est servatum et explicatum in <a href="/wiki/Aristoteles" title="Aristoteles">Aristotelis</a> <i><a href="/wiki/Physica_(Aristoteles)" class="mw-redirect" title="Physica (Aristoteles)">Physicis</a></i>, Achilles cursu Testudinem persequitur, at numquam potest praeterire, quod Achille ad locum Testudinis assecuto, iam Testudo ultra moverit. Ita hoc modo continuant ad infinitum: </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio"><span title="Graece scriptum"><span lang="grc">"...ἔστιν δὲ καὶ οὗτος ὁ αὐτὸς λόγος τῷ διχοτομεῖν, διαφέρει δ’ ἐν τῷ διαιρεῖν μὴ δίχα τὸ προσλαμβανόμενον μέγεθος. τὸ μὲν οὖν μὴ καταλαμβάνεσθαι τὸ βραδύτερον συμβέβηκεν ἐκ τοῦ λόγου, γίγνεται δὲ παρὰ ταὐτὸ τῇ διχοτομίᾳ..."<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></span></span> <p><br /> <br /> </p> <dl><dd>Quae est <a href="/wiki/Latine" class="mw-redirect" title="Latine">Latine</a> conversa:</dd></dl> <p><br /> </p> ...est autem et huius rationis eadem vis quae in partes aequales sectionis; sed hoc differt, quod magnitudinem quae accipitur non in dimidia dividit...<sup id="cite_ref-argyropylus_9-0" class="reference"><a href="#cite_note-argyropylus-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Zeno_Eleaticus" class="mw-redirect" title="Zeno Eleaticus">Zeno</a>, <i>in <a href="/wiki/Aristoteles" title="Aristoteles">Aristotelis</a> <a href="/w/index.php?title=Physica_(Aristotelis)&action=edit&redlink=1" class="new" title="Physica (Aristotelis) (non est haec pagina)">Physicis</a></i></cite></div><div><i></i></div><div style="text-align:right;">― convertit <a href="/wiki/Ioannes_Argyropylus_Byzantius" title="Ioannes Argyropylus Byzantius">Argyropolus</a></div></blockquote> <div class="mw-collapsible mw-collapsed" style="margin: 1.5em auto; border: none; border-collapse: collapse; font-size: 95%; clear: both; border-radius: .25em; background-color: rgba(0, 32, 255, .01666); padding: 0 .25em;"><div style="text-align: center; font-weight: bold; font-size: 100%; padding: .1em; background-color: rgba(0, 32, 255, .01666);">Integer paradoxorum textus</div><div class="mw-collapsible-content" style="padding: .5em;"> <div align="center"><b>Paradoxa Zenonis</b></div> <p><span title="Graece scriptum"><span lang="grc">"Ζήνων δὲ παραλογίζεται· εἰ γὰρ αἰεί, φησίν, ἠρεμεῖ πᾶν [ἢ κινεῖται] ὅταν ᾖ κατὰ τὸ ἴσον, ἔστιν δ’ αἰεὶ τὸ φερόμενον ἐν τῷ νῦν, ἀκίνητον τὴν φερομένην εἶναι ὀϊστόν. τοῦτο δ’ ἐστὶ ψεῦδος· οὐ γὰρ σύγκειται ὁ χρόνος ἐκ τῶν νῦν τῶν ἀδιαιρέτων, ὥσπερ οὐδ’ ἄλλο μέγεθος οὐδέν. τέτταρες δ’ εἰσὶν οἱ λόγοι περὶ κινήσεως Ζήνωνος οἱ παρέχοντες τὰς δυσκολίας τοῖς λύουσιν, πρῶτος μὲν ὁ περὶ τοῦ μὴ κινεῖσθαι διὰ τὸ πρότερον εἰς τὸ ἥμισυ δεῖν ἀφικέσθαι τὸ φερόμενον ἢ πρὸς τὸ τέλος, περὶ οὗ διείλομεν ἐν τοῖς πρότερον λόγοις. δεύτερος δ’ ὁ καλούμενος Ἀχιλλεύς· ἔστι δ’ οὗτος, ὅτι τὸ βραδύτατον οὐδέποτε καταληφθήσεται θέον ὑπὸ τοῦ ταχίστου· ἔμπροσθεν γὰρ ἀναγκαῖον ἐλθεῖν τὸ διῶκον ὅθεν ὥρμησεν τὸ φεῦγον, ὥστε ἀεί τι προέχειν ἀναγκαῖον τὸ βραδύτερον. ἔστιν δὲ καὶ οὗτος ὁ αὐτὸς λόγος τῷ διχοτομεῖν, διαφέρει δ’ ἐν τῷ διαιρεῖν μὴ δίχα τὸ προσλαμβανόμενον μέγεθος. τὸ μὲν οὖν μὴ καταλαμβάνεσθαι τὸ βραδύτερον συμβέβηκεν ἐκ τοῦ λόγου, γίγνεται δὲ παρὰ ταὐτὸ τῇ διχοτομίᾳ (ἐν ἀμφοτέροις γὰρ συμβαίνει μὴ ἀφικνεῖσθαι πρὸς τὸ πέρας διαιρουμένου πως τοῦ μεγέθους· ἀλλὰ πρόσκειται ἐν τούτῳ ὅτι οὐδὲ τὸ τάχιστον τετραγῳδημένον ἐν τῷ διώκειν τὸ βραδύτατον), ὥστ’ ἀνάγκη καὶ τὴν λύσιν εἶναι τὴν αὐτήν. τὸ δ’ ἀξιοῦν ὅτι τὸ προέχον οὐ καταλαμβάνεται, ψεῦδος· ὅτε γὰρ προέχει, οὐ καταλαμβάνεται· ἀλλ’ ὅμως καταλαμβάνεται, εἴπερ δώσει διεξιέναι τὴν πεπερασμένην. οὗτοι μὲν οὖν οἱ δύο λόγοι, τρίτος δ’ ὁ νῦν ῥηθείς, ὅτι ἡ ὀϊστὸς φερομένη ἕστηκεν. συμβαίνει δὲ παρὰ τὸ λαμβάνειν τὸν χρόνον συγκεῖσθαι ἐκ τῶν νῦν· μὴ διδομένου γὰρ τούτου οὐκ ἔσται ὁ συλλογισμός.</span></span> </p><p><span title="Graece scriptum"><span lang="grc">"τέταρτος δ’ ὁ περὶ τῶν ἐν τῷ σταδίῳ κινουμένων ἐξ ἐναντίας ἴσων ὄγκων παρ’ ἴσους, τῶν μὲν ἀπὸ τέλους τοῦ σταδίου τῶν δ’ ἀπὸ μέσου, ἴσῳ τάχει, ἐν ᾧ συμβαίνειν οἴεται ἴσον εἶναι χρόνον τῷ διπλασίῳ τὸν ἥμισυν. ἔστι δ’ ὁ παραλογισμὸς ἐν τῷ τὸ μὲν παρὰ κινούμενον τὸ δὲ παρ’ ἠρεμοῦν τὸ ἴσον μέγεθος ἀξιοῦν τῷ ἴσῳ τάχει τὸν ἴσον φέρεσθαι χρόνον· τοῦτο δ’ ἐστὶ ψεῦδος. οἷον ἔστωσαν οἱ ἑστῶτες ἴσοι ὄγκοι ἐφ’ ὧν τὰ ΑΑ, οἱ δ’ ἐφ’ ὧν τὰ ΒΒ ἀρχόμενοι ἀπὸ τοῦ μέσου, ἴσοι τὸν ἀριθμὸν τούτοις ὄντες καὶ τὸ μέγεθος, οἱ δ’ ἐφ’ ὧν τὰ ΓΓ ἀπὸ τοῦ ἐσχάτου, ἴσοι τὸν ἀριθμὸν ὄντες τούτοις καὶ τὸ μέγεθος, καὶ ἰσοταχεῖς τοῖς Β. συμβαίνει δὴ τὸ πρῶτον Β ἅμα ἐπὶ τῷ ἐσχάτῳ εἶναι καὶ τὸ πρῶτον Γ, παρ’ ἄλληλα κινουμένων. συμβαίνει δὲ τὸ Γ παρὰ πάντα [τὰ Β] διεξεληλυθέναι, τὸ δὲ Β παρὰ τὰ ἡμίση· ὥστε ἥμισυν εἶναι τὸν χρόνον· ἴσον γὰρ ἑκάτερόν ἐστιν παρ’ ἕκαστον. ἅμα δὲ συμβαίνει τὸ πρῶτον Β παρὰ πάντα τὰ Γ παρεληλυθέναι· ἅμα γὰρ ἔσται τὸ πρῶτον Γ καὶ τὸ πρῶτον Β ἐπὶ τοῖς ἐναντίοις ἐσχάτοις, [ἴσον χρόνον παρ’ ἕκαστον γιγνόμενον τῶν Β ὅσον περ τῶν Α, ὥς φησιν,] διὰ τὸ ἀμφότερα ἴσον χρόνον παρὰ τὰ Α γίγνεσθαι. ὁ μὲν οὖν λόγος οὗτός ἐστιν, συμβαίνει δὲ παρὰ τὸ εἰρημένον ψεῦδος."<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></span></span> </p><p>(conversus ab <a href="/wiki/Ioannes_Argyropylus_Byzantius" title="Ioannes Argyropylus Byzantius">Argyropylo</a>)<br /> Zeno vero prave ratiocinatur. dicit enim, si semper omne quiescit aut movetur, cum est in sibi aequali, id autem quod fertur, est sibi aequali spatio, in ipso nunc semper, immobilem eam esse sagittam quae fertur. hoc autem est falsum: tempus enim non ex ipsis nunc indivisibilibus constat, quemadmodum nec ulla alia magnitudo. quattuor autem Zenonis de motu sunt rationes, quae difficultatem solventibus afferunt. at prima quidem est ea qua motus ex eo tollitur, quia prius ad medium quam ad finem id quod fertur pervenire oportet: de qua distinximus antea. secunda vero est ea quae nuncupatur Achilles, qua motus rursus ex eo tollitur, quia nunquam id quod celerrime currit, id consequetur quod tardius currit: id enim quod persequitur eo perveniat ante necesse est, unde id quod fugit fugam arripuit; quare tardius ipsum semper aliquo spatio praecedat necesse est. est autem et huius rationis eadem vis quae in partes aequales sectionis; sed hoc differt, quod magnitudinem quae accipitur non in dimidia dividit. accidit igitur ut tardius ipsum non attingatur ex ratione nimirum ipsa. fit autem ob divisionem, qua quidem et antecedens utitur ratio. in utrisque namque fit ut non perveniatur ad finem magnitudine subeuntem et si non eodem modo, divisionem. sed in hac additur tamquam tragice decantatum, ne celerrimum quidem unquam tardissimum attingere persequendo. quare solutionem utriusque eandem esse necesse est. id vero, quod censet nunquam id attingi quod antecedit, falsum est: nam cum antecedit, non attingitur, attamen attingitur tandem, si dabit magnitudinem finitam id quod movetur transire. hae igitur duae sunt rationes Zenonis. tertia vero est ea quae quiescere dicit sagittam, cum fertur; de qua paulo ante diximus. Accidit autem id ex eo quia tempus sumitur ex suis punctis constare; quod si non dederis, ratio continuo exspirabit. </p><p>Quarta est ea quae de iis est aequalibus molibus, quae propter aequales alias moles aequali celeritate partim e calce stadii, partim e medio contra moventur; ubi fieri putat ut duplo tempori dimidium sit aequale. rationis autem fallacia in existimatione illa consistit. ea namque quorum alterum fertur propter quescens, alterum propter id quod movetur, aequalem magnitudinem celeritate aequali transire in aequali tempore censet. hoc autem falsum est. sint quiescentes quidem aequales moles <i>a a a a;</i> super has autem moveantur <i>b b b b,</i> incipiendo a medio ipsarum molium <i>a,</i> numero et magnitudine aequales; <i>c c c c</i> vero his aequales modo eodem et aeque celeres super ipsas, incipiendo a prima, quae est in medio ipsarum <i>a,</i> motu contrario moveantur. accidit igitur primam <i>b</i> atque <i>c</i> molem simul in ipsis esse extremis, et <i>c</i> quidem universas <i>b</i> moles, <i>b</i> vero dimidium ipsarum <i>a</i> pertransivisse. quare fit ut sit dimidium tempus: utraque enim aequali tempore molium unamquanque transivit. et insuper accidit <i>b</i> per omnes moles <i>c</i> transivisse. prima namque <i>c</i> et <i>b </i> moles in contrariis sunt extremis, tanto in tempore per unamquanque <i>b</i> molium mota quanto quanque molium <i>a</i> transivit, ut dicit, propterea quod utraque aequali in tempore per <i>a</i> moles est mota. ratio igitur haec est. fit autem ob id quod diximus falsum.<sup id="cite_ref-argyropylus_9-1" class="reference"><a href="#cite_note-argyropylus-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> </div></div> <div class="mw-heading mw-heading4"><h4 id="Aristoteles"><a href="/wiki/Aristoteles" title="Aristoteles">Aristoteles</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=9" title="Recensere partem: Aristoteles" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=9" title="Edit section's source code: Aristoteles"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:(Venice)_Aristide_-_Francesco_Hayez_-_gallerie_Accademia_Venice.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/%28Venice%29_Aristide_-_Francesco_Hayez_-_gallerie_Accademia_Venice.jpg/200px-%28Venice%29_Aristide_-_Francesco_Hayez_-_gallerie_Accademia_Venice.jpg" decoding="async" width="200" height="259" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/%28Venice%29_Aristide_-_Francesco_Hayez_-_gallerie_Accademia_Venice.jpg/300px-%28Venice%29_Aristide_-_Francesco_Hayez_-_gallerie_Accademia_Venice.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/%28Venice%29_Aristide_-_Francesco_Hayez_-_gallerie_Accademia_Venice.jpg/400px-%28Venice%29_Aristide_-_Francesco_Hayez_-_gallerie_Accademia_Venice.jpg 2x" data-file-width="6786" data-file-height="8772" /></a><figcaption><a href="/wiki/Aristoteles" title="Aristoteles">Aristoteles</a> a <a href="/wiki/Franciscus_Hayez" title="Franciscus Hayez">Francisco Hayez</a> depictus, <a href="/wiki/1811" title="1811">1811</a>.</figcaption></figure> <p>In <a href="/wiki/Europa" title="Europa">Europa</a> et scholis rationis Europaeis hodiernis, theoria solita ab <a href="/wiki/Aristoteles" title="Aristoteles">Aristotele</a> data est (circa <a href="/wiki/350_a.C.n." title="350 a.C.n.">350</a> <a href="/wiki/Aera_vulgaris" title="Aera vulgaris">ante aer. vulg.</a>): </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio"><span title="Graece scriptum"><span lang="grc">"... ἐπὶ δὲ τὸ πλεῖον ἀεὶ ἔστι νοῆσαι· ἄπειροι γὰρ αἱ διχοτομίαι τοῦ μεγέθους. ὥστε δυνάμει μὲν ἔστιν, ἐνεργείᾳ δ’ οὔ· ἀλλ’ ἀεὶ ὑπερβάλλει τὸ λαμβανόμενον παντὸς ὡρισμένου πλήθους."</span></span><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <p><br /> <br /> </p> <dl><dd>Quae est Latine conversa:</dd></dl> <p><br /> </p> "... versus plus autem fit ut semper intelligatur. divisiones enim magnitudinis duas in partes aequales sunt infinitae. quare potentia quidem est, actu non est : sed semper id quod accipitur, multitudinem omnem exsuperat definitam."<sup id="cite_ref-argyropylus_9-2" class="reference"><a href="#cite_note-argyropylus-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Aristoteles" title="Aristoteles">Aristoteles</a>, <i><a href="/wiki/Physica_(Aristoteles)" class="mw-redirect" title="Physica (Aristoteles)">Physica</a></i></cite></div><div><i></i></div><div style="text-align:right;">― convertit <a href="/wiki/Ioannes_Argyropylus_Byzantius" title="Ioannes Argyropylus Byzantius">Argyropylus</a> etiam</div></blockquote> <p>Hoc discrimen inter "infinitum potentia" et "infinitum actu" diu magni momenti erat inter philosophos Europaeos. Attamen duae sententiae in loco citato complicantur, quarum altera est numerari semper posse praeter quemlibet <i>numerum</i>, etiamsi tot tantaeve <i>res</i> non existent. Altera est posse quantificare super series infinitas absque impeditione. Exempli gratia, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall n\in \mathbb {Z} (\exists m\in \mathbb {Z} [m>n\wedge P(m)])}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>n</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">∃</mi> <mi>m</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo stretchy="false">[</mo> <mi>m</mi> <mo>></mo> <mi>n</mi> <mo>∧</mo> <mi>P</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall n\in \mathbb {Z} (\exists m\in \mathbb {Z} [m>n\wedge P(m)])}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04e20e41222c6fdc572c167e7b2b8e2a112e4ef5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.616ex; height:2.843ex;" alt="{\displaystyle \forall n\in \mathbb {Z} (\exists m\in \mathbb {Z} [m>n\wedge P(m)])}"></span>, id est: "dato <a href="/wiki/Integer" class="mw-redirect" title="Integer">integro</a> ullo n, est integer m > n ut P(m)". </p> <div class="mw-heading mw-heading4"><h4 id="Archimedes_et_Plotinus"><a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> et <a href="/wiki/Plotinus" title="Plotinus">Plotinus</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=10" title="Recensere partem: Archimedes et Plotinus" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=10" title="Edit section's source code: Archimedes et Plotinus"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> usurpavit infinitatem in eodem modo <a href="/wiki/Calculus_infinitessimalis" class="mw-redirect" title="Calculus infinitessimalis">calculi integralis</a>. Clarissimum exemplum fuit inventio valoris <i><b><a href="/wiki/Pi" class="mw-disambig" title="Pi">π</a></b></i>. Circa <a href="/wiki/250_a.C.n." title="250 a.C.n.">250</a> <a href="/wiki/Aera_vulgaris" title="Aera vulgaris">ante aer. vulg.</a>, et in maxime parte ad sapientiam <a href="/wiki/Eudoxus_Cnidius" class="mw-redirect" title="Eudoxus Cnidius">Eudoxi Cnidii</a>, Archimedes propulsit progressum ad infinitatem intelligendam, rationem <a href="/wiki/Limes" class="mw-disambig" title="Limes">limitum</a> investigans. Circumscripsit circum <a href="/wiki/Circulus" title="Circulus">circulum</a> <a href="/wiki/Polygonum" title="Polygonum">polygonum</a>, cuius latera omnia circuli circumitum tectigit, et scripsit intra circulum polygonum, cuius anguli omnes tectigerunt. Si latera polygonorum augescunt, differentia inter suas areas areae circuli appropinquat. Ubi Archimedes inscribit et circumscribit polygona 96 laterum, approximavit valorem <i><b>π</b></i> est inter 3 + 1/7 (~3.1429) et 3 + 10/71 (~3.1408). Ut late noscetur, <i><b>π</b></i> est <a href="/wiki/Numerus_irrationalis" title="Numerus irrationalis">numerus irrationalis</a>, cuius inventio valde Pythagoreanos vexavit. Archimedes scripsit <i><b>π</b></i> numeros praeter punctum decimalem infinitos continere, et suam approximationem numquam eius valorem totum advenituram esse. At etiam sciit suam approximationem valori toto <i>approprinquaturam</i> esse, dum latera polygonorum ad infinitatem augescunt. Hoc modo viam struxit ad caclculum cum <a href="/wiki/Limes" class="mw-disambig" title="Limes">limitibus</a>. </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:Archimedes_pi.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Archimedes_pi.svg/300px-Archimedes_pi.svg.png" decoding="async" width="300" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Archimedes_pi.svg/450px-Archimedes_pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Archimedes_pi.svg/600px-Archimedes_pi.svg.png 2x" data-file-width="750" data-file-height="250" /></a><figcaption>Ratio Archimedei approximationis <i><b>π</b></i></figcaption></figure> <p>In alio opere, Archimedes temptavit numerum harenularum quae <a href="/wiki/Universum" title="Universum">Universum</a> impleat calculare, rationem quae dicit multitudines maximas infinitam esse dimittens. </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio"><span title="Graece scriptum"><span lang="grc">"Οἴονταί τινες, βασιλεῦ Γέλων, τοῦ ψάμμου τὸν ἀριθμὸν ἄπειρον εἶμεν τῷ πλήθει· λέγω δὲ οὐ μόνον τοῦ περὶ Συρακούσας τε καὶ τὰν ἄλλαν Σικελίαν ὑπάρχοντος, ἀλλὰ καὶ τοῦ κατὰ πᾶσαν χώραν τάν τε οἰκημέναν καὶ τὰν ἀοίκητον."</span></span><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> <p><br /> <br /> </p> <dl><dd>Quae est Latine conversa:</dd></dl> <p><br /> "Sunt, qui existement, rex Gelon, numerum arenae infinitum esse magnitudine<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>; dico autem, non solum eius, quae circa Syracusas et reliquam Siciliam est, sed etiam quae in qualibet regione siue culta siue inculta."<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> <br /> <br /> </p> <dl><dd>Commentatio interpretis:</dd></dl> <p><br /> </p> Probatio eius systema numerandi adhibebat in <i>μυριάδος</i> (ex <i>μύριος</i>, "infinitus") fundatum. Haud numerum rectum Archimedes invenit, at eius defensio finitatis utilis fuit in conceptiones aliorum de infinitate mutando.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a>, <i><a href="/w/index.php?title=Arenarius&action=edit&redlink=1" class="new" title="Arenarius (non est haec pagina)">Arenarius</a></i></cite></div><div><i></i></div><div style="text-align:right;">― convertit <a href="/w/index.php?title=Iohannes_Ludovicus_Heiberg&action=edit&redlink=1" class="new" title="Iohannes Ludovicus Heiberg (non est haec pagina)">Iohannes Ludovicus Heiberg</a></div></blockquote> <div class="mw-heading mw-heading3"><h3 id="Sententiae_Mediaevales">Sententiae <a href="/wiki/Medium_Aevum" class="mw-redirect" title="Medium Aevum">Mediaevales</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=11" title="Recensere partem: Sententiae Mediaevales" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=11" title="Edit section's source code: Sententiae Mediaevales"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Guillelmus_de_Ockham"><a href="/wiki/Guillelmus_de_Ockham" title="Guillelmus de Ockham">Guillelmus de Ockham</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=12" title="Recensere partem: Guillelmus de Ockham" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=12" title="Edit section's source code: Guillelmus de Ockham"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Parmenidis Aristotelisque sententias simplicius scripserunt auctores mediaevales, sicut <a href="/wiki/Guillelmus_de_Ockham" title="Guillelmus de Ockham">Guillelmus de Ockham</a> (<a href="/wiki/1327" title="1327">1327</a>): </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio">"Sed omne continuum est actualiter existens. Igitur quaelibet pars sua est vere existens in rerum natura. Sed partes continui sunt infinitae quia non tot quin plures, igitur partes infinitae sunt actualiter existentes."<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Guillelmus_de_Ockham" title="Guillelmus de Ockham">Guillelmus de Ockham</a>, <i><a href="/w/index.php?title=Opera_Philosophica_et_Theologica&action=edit&redlink=1" class="new" title="Opera Philosophica et Theologica (non est haec pagina)">Opera Philosophica et Theologica</a></i></cite></div><div><i></i></div></blockquote> <p>Ergo, infinitus non potest esse ullus numerus, quod cuilibet numero semper erit numerus maior magnitudine, "quia non tot quin plures." </p><p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Sententiae_a_Renascentia_usque_ad_hodiernum_diem">Sententiae a <a href="/wiki/Aevum_antiquitatis_renascentis" class="mw-redirect" title="Aevum antiquitatis renascentis">Renascentia</a> usque ad hodiernum diem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=13" title="Recensere partem: Sententiae a Renascentia usque ad hodiernum diem" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=13" title="Edit section's source code: Sententiae a Renascentia usque ad hodiernum diem"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Galilaeus"><a href="/wiki/Galilaeus_Galilaei" title="Galilaeus Galilaei">Galilaeus</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=14" title="Recensere partem: Galilaeus" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=14" title="Edit section's source code: Galilaeus"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:Galileo_by_Passignano.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Galileo_by_Passignano.jpg/220px-Galileo_by_Passignano.jpg" decoding="async" width="220" height="274" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Galileo_by_Passignano.jpg/330px-Galileo_by_Passignano.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Galileo_by_Passignano.jpg/440px-Galileo_by_Passignano.jpg 2x" data-file-width="562" data-file-height="699" /></a><figcaption>Galilaeus ab <a href="/w/index.php?title=Dominicus_Passignanus&action=edit&redlink=1" class="new" title="Dominicus Passignanus (non est haec pagina)">Equite Passignano</a>, circiter annum <a href="/wiki/1642" title="1642">1642</a>.</figcaption></figure> <p><a href="/wiki/Galilaeus_Galilaei" title="Galilaeus Galilaei">Galilaeus</a> primus notavit <a href="/w/index.php?title=Biiectio&action=edit&redlink=1" class="new" title="Biiectio (non est haec pagina)">biiectionem</a> serierum infinitorum, cum ullis suorum subserierum. Exempli gratia, series <a href="/wiki/Numeri_quadrati" class="mw-redirect" title="Numeri quadrati">numerorum quadratum</a> {1, 4, 9, 16 . . .} coordinetur cum radicibus suis, nempe numeris naturalibus {1, 2, 3, 4 . . .} in hoc modo (<a href="/wiki/1638" title="1638">1638</a>: </p> <dl><dd>1, 2, 3, 4, . . .</dd> <dd>↓  ↓  ↓  ↓</dd> <dd>1, 4, 9, 16, . . .</dd></dl> <p>Videbatur ab hac dialectica ut series natura minor (ita, quod modo continet aliquot non omnes numeros seriei) quam serie cuius est pars sit, aliquo modo, eadem magnitudine. Hanc dixit Galilaeus esse "ex istis difficultatibus, quae suam ducunt originem ex discursu quem intellectus noster finitus circa infinita instituit".<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> In dialogis <i><a href="/w/index.php?title=De_duabus_novis_scientiis&action=edit&redlink=1" class="new" title="De duabus novis scientiis (non est haec pagina)">De duabus novis scientiis</a>,</i> Salviati, cum Sagredo Simplicioque in elencho colloquens, dicit haec: </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio"><i>"Io non veggo che ad altra decisione si possa venire, che a dire, infiniti essere tutti i numeri, infiniti i quadrati, infinite le loro radici, né la moltitudine de' quadrati esser minore di quella di tutti i numeri, né questa maggior di quella, ed in ultima conclusione, gli attributi di eguale maggiore e minore non aver luogo ne gl'infiniti, ma solo nelle quantità terminate."</i><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> <p><br /> <br /> </p> <dl><dd>Quae est <a href="/wiki/Latine" class="mw-redirect" title="Latine">Latine</a> conversa:</dd></dl> <p><br /> </p> "Non alio modo eum decidi posse video, quam dicendo infinitos esse omnes numeros, infinita quadrata, infinitas eorum radices; quadratorum multitudinem non esse minorem multitudine omnium mimerorum, [<i>sic</i>] nec istam hac maiorem ; et tandem concludendo, aequalitatis, maioritatis et minoritatis attributa in Infinitis nullum habere locum, utpote quae in quantitates terminatas solummodo cadunt."<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Galilaeus_Galilaei" title="Galilaeus Galilaei">Galilaeus</a>, <i><a href="/w/index.php?title=De_duabus_novis_scientiis&action=edit&redlink=1" class="new" title="De duabus novis scientiis (non est haec pagina)">De duabus novis scientiis</a></i></cite></div><div><i></i></div></blockquote> <div class="mw-heading mw-heading4"><h4 id="Lockius"><a href="/wiki/Ioannes_Lockius" title="Ioannes Lockius">Lockius</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=15" title="Recensere partem: Lockius" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=15" title="Edit section's source code: Lockius"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:JohnLocke.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/JohnLocke.png/200px-JohnLocke.png" decoding="async" width="200" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/JohnLocke.png/300px-JohnLocke.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d1/JohnLocke.png/400px-JohnLocke.png 2x" data-file-width="984" data-file-height="1138" /></a><figcaption>Ioannes Lockius, pictus ab <a href="/w/index.php?title=Gotfrey_Kneller&action=edit&redlink=1" class="new" title="Gotfrey Kneller (non est haec pagina)">Gotfrey Kneller</a><sup style="font-size: .75em; font-weight: normal; text-decoration: none;"><a href="/wiki/Disputatio:Infinitas" title="Disputatio:Infinitas">?</a></sup> equite, 1697</figcaption></figure> <p><a href="/wiki/Ioannes_Lockius" title="Ioannes Lockius">Ioannes Lockius</a>, sicut philosophi <a href="/wiki/Empirismus" title="Empirismus">empiristae</a>, homines credidit non posse infinitatem intellegere. Asseruit nostros sensus nobis indicare omnia de mundo quae possimus intellegere, quoniam omnes sensus, et omnia quae possunt sentire sint natura finiti, ergo quippe necessitate nostrae cogitationes esse finitas. Nostra ratio de infinitate esse "negativa" vel "privitiva" (circa <a href="/wiki/1680" title="1680">1680</a>): </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio">Quascumque in animis <i>ideas</i> habemus positivas spatii, durationis, vel numeri, qualitercunque magnae sint e nihilominus sunt finitae ; quando verò supponimus residuum inexhaustum, à quo terminos omnes removermus, et in quo menti indulgemus infinitam cogitationis progressionem, ita ut nunquam consummetur idea ibi nostram infinitatis <i>ideam</i> habemus; quae etiamsi quodammodo clara esse videatur cùm in eâ nihil consideremus praeter finis negationem; attamen cùm in animis nostris spatii, aut durationis infinitae <i>ideam</i> effingere velimus, <i>idea</i> ista valde obscura est, et confusa, quoniam è duabus partibus conflatur, quae valdè inter se diversae sunt, si non planè contradictoriae. Formet quippe in animo sibi quivis spatii cujusvis aut numeri <i>ideam</i> utcunque magnam, manifestum est mentis cogitationem in istà <i>ideâ</i> terminari, quod <i>infinitatis idea</i> repugnat ; ea etenim in <i>imaginariâ progressione infinitâ</i> consistit.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Ioannes_Lockius" title="Ioannes Lockius">Ioannes Lockius</a></cite></div><div><i></i></div></blockquote> <p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Sententiae_hodiernae">Sententiae hodiernae</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=16" title="Recensere partem: Sententiae hodiernae" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=16" title="Edit section's source code: Sententiae hodiernae"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><i>"Duae res tantum sunt infinitae: <a href="/wiki/Universum" title="Universum">universum</a>, et stultitia <a href="/wiki/Homo" class="mw-redirect mw-disambig" title="Homo">hominum</a>. De priore autem haud sum certus."--<a href="/wiki/Albertus_Einstein" title="Albertus Einstein">Albertus Einstein</a></i></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Blake"><a href="/wiki/Gulielmus_Blake" title="Gulielmus Blake">Blake</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=17" title="Recensere partem: Blake" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=17" title="Edit section's source code: Blake"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:William_Blake_by_Thomas_Phillips.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/William_Blake_by_Thomas_Phillips.jpg/200px-William_Blake_by_Thomas_Phillips.jpg" decoding="async" width="200" height="257" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/William_Blake_by_Thomas_Phillips.jpg/300px-William_Blake_by_Thomas_Phillips.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/William_Blake_by_Thomas_Phillips.jpg/400px-William_Blake_by_Thomas_Phillips.jpg 2x" data-file-width="1196" data-file-height="1536" /></a><figcaption>Gulielmus Blake a <a href="/w/index.php?title=Thomas_Phillips&action=edit&redlink=1" class="new" title="Thomas Phillips (non est haec pagina)">Thomas Phillips</a> pictus (<a href="/wiki/1807" title="1807">1807</a>).</figcaption></figure> <p><a href="/wiki/Gulielmus_Blake" title="Gulielmus Blake">Gulielmus Blake</a> autem credidit nostram inopiam perceptionis esse impeditionem primam in infinitatem intelligendam. Dixit (<a href="/wiki/1793" title="1793">1793</a>): </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio">"If the doors of perception were cleansed, every thing would appear to man as it is: infinite."<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> <p><br /> <br /> </p> <dl><dd>Quae est <a href="/wiki/Latine" class="mw-redirect" title="Latine">Latine</a> conversa:</dd></dl> <p><br /> </p> "Si portae perceptionis purgentur, omnia homini videantur ut sunt: infinita."<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Gulielmus_Blake" title="Gulielmus Blake">Gulielmus Blake</a>, <i>The Marriage of Heaven and Hell</i></cite></div><div><i></i></div><div style="text-align:right;">― convertit <a href="/wiki/Usor:Ioscius" title="Usor:Ioscius">Ioscius</a></div></blockquote> <div class="mw-heading mw-heading4"><h4 id="Cantor"><a href="/wiki/Georgius_Cantor" title="Georgius Cantor">Cantor</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=18" title="Recensere partem: Cantor" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=18" title="Edit section's source code: Cantor"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:Matematiker_georg_cantor.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Matematiker_georg_cantor.jpg/200px-Matematiker_georg_cantor.jpg" decoding="async" width="200" height="239" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/5/5a/Matematiker_georg_cantor.jpg 1.5x" data-file-width="269" data-file-height="322" /></a><figcaption>Georgius Cantor</figcaption></figure> <p><a href="/wiki/Georgius_Cantor" title="Georgius Cantor">Georgius Cantor</a> biiectionis theoriam Galilaei refellit in suo <a href="/w/index.php?title=Argumentum_diagonale&action=edit&redlink=1" class="new" title="Argumentum diagonale (non est haec pagina)">argumento diagonali</a> (<a href="/wiki/1891" title="1891">1891</a>): </p><p>Per indicem serierum ab <a href="/wiki/Cifra" title="Cifra">0is</a> et <a href="/wiki/Unus" title="Unus">1is</a> constructorum infinitum, instruamus novam sequentiam elementorum <i>s</i><sub>0</sub> ut eius elementum primum differat ab elemento primo primae sequentiae in indice, elementum secundum differat ab elemento secundo secundae sequentiae in indice, et cetera in hoc modo, ut <i>n</i><sup>um</sup> elementum diferat ab <i>n</i><sup>o</sup> elemento <i>n</i><sup>ae</sup> sequentiae. Ita, <i>s</i><sub>0,m</sub> erit 0 si <i>s</i><sub>m,m</sub> est 1, et <i>s</i><sub>0,m</sub> erit 1 si <i>s</i><sub>m,m</sub> est 0. </p><p>Exempli gratia: </p> <dl><dd><i>s</i><sub>1</sub> = (<b>0</b>, 0, 0, 0, 0, 0, 0, ...)</dd> <dd><i>s</i><sub>2</sub> = (1, <b>1</b>, 1, 1, 1, 1, 1, ...)</dd> <dd><i>s</i><sub>3</sub> = (0, 1, <b>0</b>, 1, 0, 1, 0, ...)</dd> <dd><i>s</i><sub>4</sub> = (1, 0, 1, <b>0</b>, 1, 0, 1, ...)</dd> <dd><i>s</i><sub>5</sub> = (1, 1, 0, 1, <b>0</b>, 1, 1, ...)</dd> <dd><i>s</i><sub>6</sub> = (0, 0, 1, 1, 0, <b>1</b>, 1, ...)</dd> <dd><i>s</i><sub>7</sub> = (1, 0, 0, 0, 1, 0, <b>0</b>, ...)</dd> <dd>...</dd></dl> <dl><dd><i>s</i><sub>0</sub> = (<b>1</b>, <b>0</b>, <b>1</b>, <b>1</b>, <b>1</b>, <b>0</b>, <b>1</b>, ...)</dd></dl> <p>(Elementa <i>s</i><sub>1,1</sub>, <i>s</i><sub>2,2</sub>, <i>s</i><sub>3,3</sub>, et cetera litteris fortis scribuntur, ut ratio nominis <i><b>diagonalis</b></i> plane videatur.) </p><p>Deinde sequitur ut series <i>T</i>, ab infinitis sequentiis zerorum unorumque non poniatur in indicem <i>s</i><sub>1</sub>, <i>s</i><sub>2</sub>, <i>s</i><sub>3</sub>, ... Nisi, in illo modo instruamus sequentiam <i>s</i><sub>0</sub> qui et sit in indice <i>T</i> (quia est sequentia zerorum unorumque de sequentiis in <i>T</i> <i><b>natura</b></i> est ipsa in <i>T</i>), et simul <b>non</b> est in <i>T</i> (quod eam instruamus ut diferat ab omnibus sequentiis in <i>T</i> aliis). </p><p>Ergo <i>T</i> non conferatur cum numeris naturalibus a biiectione. Brevius: est innumerabilis.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Wittgenstein">Wittgenstein</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=19" title="Recensere partem: Wittgenstein" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=19" title="Edit section's source code: Wittgenstein"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Natura infinitatis etiam disputatur. Aliqui putant esse partem mathematicae, alii philosophiae. Alii ultra ambas coniungunt, sicut <a href="/wiki/Ludovicus_Wittgenstein" title="Ludovicus Wittgenstein">Ludovicus Wittgenstein</a> qui impetum saeve egit in <a href="/w/index.php?title=Theoria_seriei_axiomatica&action=edit&redlink=1" class="new" title="Theoria seriei axiomatica (non est haec pagina)">theoriam seriei axiomaticam</a> (<a href="/wiki/1933" title="1933">1933</a>): </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio">:"... I can see in space the possibility of any finite experience... we recognise [the] essential infinity of space in its smallest part." "[Time] is infinite in the same sense as the three-<a href="/wiki/Dimensio" class="mw-disambig" title="Dimensio">dimensional</a> space of sight and movement is infinite, even if in fact I can only see as far as the walls of my room." <p><br /> "... what is infinite about endlessness is only the endlessness itself."<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> <br /> <br /> </p> <dl><dd>Quae sunt <a href="/wiki/Latine" class="mw-redirect" title="Latine">Latine</a> conversa:</dd></dl> <p><br /> "Possum videre in spatio possibilitatem quamlibet experientiam finitam... essentialem infinitatem agnoscemus spatii in partibus minimis." "[Tempus] est infinitum in eodem modo quo spatium trium dimensionum est infinitum, etiamsi non possim vere spectare praeter parietes mei cubiculi." <br /> </p> "quae sit infinita de infinitate est modo infinitas ipsa."<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Ludovicus_Wittgenstein" title="Ludovicus Wittgenstein">Ludovicus Wittgenstein</a>, <i>Philosophical Remarks</i></cite></div><div><i></i></div><div style="text-align:right;">― convertit <a href="/wiki/Usor:Iustinus" title="Usor:Iustinus">Iustinus</a></div></blockquote> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Infinitas_in_mathematica">Infinitas in <a href="/wiki/Mathematica" title="Mathematica">mathematica</a></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=20" title="Recensere partem: Infinitas in mathematica" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=20" title="Edit section's source code: Infinitas in mathematica"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:MobiusStrip-01.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/MobiusStrip-01.png/240px-MobiusStrip-01.png" decoding="async" width="240" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e7/MobiusStrip-01.png 1.5x" data-file-width="273" data-file-height="216" /></a><figcaption>Via parametrica <a href="/wiki/Moebii_taenia" class="mw-redirect" title="Moebii taenia">Moebii taeniae</a>, quae est symbolum infinitatis mathematicum.</figcaption></figure> <p>Infinitas est numerus maior magnitudine quam omnes <a href="/wiki/Numerus_naturalis" title="Numerus naturalis">numeri naturales</a> vel <a href="/wiki/Numerus_realis" title="Numerus realis">numeri reales</a>. Est tam magna, ut homines vix possint magnitudinem intellegere. Attamen, sicut cum <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ea1ea9ac61e6e1e84ac39130f78143c18865719" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.906ex; height:3.009ex;" alt="{\displaystyle {\sqrt {-1}}}"></span>, quae quoque vix intellegitur, infinitas perfacile tractatur in functionibus mathematicis. </p> <div class="mw-heading mw-heading3"><h3 id="Proprietates_infinitatis_arithmeticae">Proprietates infinitatis <a href="/wiki/Arithmetica" title="Arithmetica">arithmeticae</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=21" title="Recensere partem: Proprietates infinitatis arithmeticae" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=21" title="Edit section's source code: Proprietates infinitatis arithmeticae"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Infinitas <b>non</b> est numerus purum at tamen consideretur pars esse <a href="/w/index.php?title=Linea_numerorum_realium&action=edit&redlink=1" class="new" title="Linea numerorum realium (non est haec pagina)">lineae numerorum realium</a>, in qua arithmetica opera possunt ad infinitatem pertinientes perfaci. Subter sunt multae operationes arithmeticae cum Infinitate et aliis numeris. </p> <div style="clear:both;"></div> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca2608c4b5fd3bffc73585f8c67e379b4e99b6f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle -\infty }"></span> . . . <span class="mw-default-size" typeof="mw:File"><a href="/wiki/Fasciculus:Real_Number_Line.PNG" class="mw-file-description" title="Linea numerorum: omnes numeri reales sunt inter infinitatem negativam et infinitatem positivam"><img alt="Linea numerorum: omnes numeri reales sunt inter infinitatem negativam et infinitatem positivam" src="//upload.wikimedia.org/wikipedia/commons/9/98/Real_Number_Line.PNG" decoding="async" width="540" height="50" class="mw-file-element" data-file-width="540" data-file-height="50" /></a></span> . . . <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bddbb0e4420a7e744cf71bd71216e11b0bf88831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.132ex; height:2.176ex;" alt="{\displaystyle +\infty }"></span></center> <div class="mw-heading mw-heading4"><h4 id="Infinitas_secum">Infinitas secum</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=22" title="Recensere partem: Infinitas secum" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=22" title="Edit section's source code: Infinitas secum"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><dl><dd>1. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty +\infty =\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty +\infty =\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a696353392f6a89d6a355b8809d2b66e8df0761" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.297ex; height:2.176ex;" alt="{\displaystyle \infty +\infty =\infty \,}"></span>, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty +(-\infty )=-\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty +(-\infty )=-\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef7e7b1c8406e4510064a7f6c688b07c25828323" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.531ex; height:2.843ex;" alt="{\displaystyle -\infty +(-\infty )=-\infty \,}"></span></dd> <dd>2. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty \cdot \infty =x\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mi>x</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty \cdot \infty =x\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c429c9c7332498b6aaa1935e1da8bd13873714be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.142ex; height:1.676ex;" alt="{\displaystyle \infty \cdot \infty =x\,}"></span>, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty \cdot (-\infty )=x\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty \cdot (-\infty )=x\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c1dbd03f442b8e13903753dd7f9822910c970fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.567ex; height:2.843ex;" alt="{\displaystyle -\infty \cdot (-\infty )=x\,}"></span>, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty \cdot (-\infty )=-x\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi>x</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty \cdot (-\infty )=-x\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/975fb3ea85ed1f77b3b6c494ecc8ed325dc64c99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.567ex; height:2.843ex;" alt="{\displaystyle \infty \cdot (-\infty )=-x\,}"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Aequationes_cum_infinitate_purisque_numeris"><a href="/wiki/Aequatio" title="Aequatio">Aequationes</a> cum infinitate purisque numeris</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=23" title="Recensere partem: Aequationes cum infinitate purisque numeris" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=23" title="Edit section's source code: Aequationes cum infinitate purisque numeris"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><dl><dd>1. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\infty <x<\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo><</mo> <mi>x</mi> <mo><</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\infty <x<\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a38f9ae421fa14acfb131bc3c4e10a56c8897f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:14.369ex; height:2.176ex;" alt="{\displaystyle -\infty <x<\infty \,}"></span></dd> <dd>2. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x+\infty =\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x+\infty =\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49649911d86392ddb4a4e2a8760b74fed26d9c46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.303ex; height:2.176ex;" alt="{\displaystyle x+\infty =\infty \,}"></span>, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x+(-\infty )=-\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x+(-\infty )=-\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe7aefc67a580afdad1477c94f5f5b72460ffc04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.729ex; height:2.843ex;" alt="{\displaystyle x+(-\infty )=-\infty \,}"></span></dd> <dd>3. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x-\infty =-\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x-\infty =-\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/025e2fb0358f04635481622cddb006b4d0303b67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:14.111ex; height:2.176ex;" alt="{\displaystyle x-\infty =-\infty \,}"></span>, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x-(-\infty )=\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>−</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x-(-\infty )=\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c7a9dececb23c43047072286625c8b832c734f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.921ex; height:2.843ex;" alt="{\displaystyle x-(-\infty )=\infty \,}"></span></dd> <dd>4. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {x \over \infty }=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi mathvariant="normal">∞</mi> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {x \over \infty }=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8a5a2dfea6b82bd675a5e819781c43ae99df842" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.808ex; height:4.676ex;" alt="{\displaystyle {x \over \infty }=0\,}"></span>, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {x \over -\infty }=0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mrow> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {x \over -\infty }=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2af0924f9d125665970b7995a759863c295ad1ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.616ex; height:4.843ex;" alt="{\displaystyle {x \over -\infty }=0\,}"></span></dd> <dd>5. Si <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x>0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>></mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x>0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4bf3dbb12d9694caacbda897b8408618db0c4903" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.978ex; height:2.176ex;" alt="{\displaystyle x>0\,}"></span> deinde <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\cdot \infty =\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\cdot \infty =\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/960838a5db2f066607e0c62eec8e010996c3def6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.755ex; height:1.676ex;" alt="{\displaystyle x\cdot \infty =\infty }"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\cdot (-\infty )=-\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\cdot (-\infty )=-\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/032314101aeffd67526814c7f0a70bc1ebd46d40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.567ex; height:2.843ex;" alt="{\displaystyle x\cdot (-\infty )=-\infty \,}"></span></dd></dl></dd> <dd>6. Quod si <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x<0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo><</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x<0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a42a1043dff028901e1eedc700a9907ffb82acd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.978ex; height:2.176ex;" alt="{\displaystyle x<0\,}"></span> deinde <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\cdot \infty =-\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\cdot \infty =-\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7da0bedcc164654ba4f2bc36278e29dc7c6eafee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.563ex; height:2.176ex;" alt="{\displaystyle x\cdot \infty =-\infty }"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\cdot (-\infty )=\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\cdot (-\infty )=\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b808a1dc944d9e7c8569c7e7f425192d84ccf797" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.759ex; height:2.843ex;" alt="{\displaystyle x\cdot (-\infty )=\infty \,}"></span></dd></dl></dd></dl></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Operationes_indefinitae">Operationes indefinitae</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=24" title="Recensere partem: Operationes indefinitae" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=24" title="Edit section's source code: Operationes indefinitae"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><dl><dd>1. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\cdot \infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\cdot \infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e80877604c550fba11d050cf81b38db55884a82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.552ex; height:2.176ex;" alt="{\displaystyle 0\cdot \infty \,}"></span>, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\cdot (-\infty )\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>⋅</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\cdot (-\infty )\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53d584d1c252f352db3c64aab0e67e287e8f9de0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.17ex; height:2.843ex;" alt="{\displaystyle 0\cdot (-\infty )\,}"></span></dd> <dd>2. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty +(-\infty )\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty +(-\infty )\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2715584306324bb496a2c98245da2c059204c841" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.492ex; height:2.843ex;" alt="{\displaystyle \infty +(-\infty )\,}"></span>, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty -\infty \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty -\infty \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6328ba9c837992782fece04e3c61c178d643cf1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.875ex; height:2.176ex;" alt="{\displaystyle \infty -\infty \,}"></span></dd> <dd>3. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\pm \infty \over \pm \infty }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>±</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow> <mo>±</mo> <mi mathvariant="normal">∞</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\pm \infty \over \pm \infty }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64102d55efdca3327be72119309a8e3e6e005004" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.355ex; height:5.176ex;" alt="{\displaystyle {\pm \infty \over \pm \infty }\,}"></span></dd> <dd>4. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {(\pm \infty )}^{0}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>±</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {(\pm \infty )}^{0}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7587d64d616052a1182bc5690e8fd0ece6f534e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.383ex; height:3.343ex;" alt="{\displaystyle {(\pm \infty )}^{0}\,}"></span></dd> <dd>5. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1^{\pm \infty }\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>±</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1^{\pm \infty }\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b0b838296a35eb1eb4922454059a83abafd5ef9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.703ex; height:2.676ex;" alt="{\displaystyle 1^{\pm \infty }\,}"></span></dd> <dd>6. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty +\infty =\infty \cdot \infty =(-\infty )\cdot (-\infty )=\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mi mathvariant="normal">∞</mi> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty +\infty =\infty \cdot \infty =(-\infty )\cdot (-\infty )=\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34afdf1b9ca1ff4f33df8ddf4825b09ca2d1abc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.995ex; height:2.843ex;" alt="{\displaystyle \infty +\infty =\infty \cdot \infty =(-\infty )\cdot (-\infty )=\infty }"></span></dd> <dd>7. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (-\infty )+(-\infty )=\infty \cdot (-\infty )=(-\infty )\cdot \infty =-\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">∞</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (-\infty )+(-\infty )=\infty \cdot (-\infty )=(-\infty )\cdot \infty =-\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17118a9c0a0b3841d96705e0804e7ac4c5da699f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:48.038ex; height:2.843ex;" alt="{\displaystyle (-\infty )+(-\infty )=\infty \cdot (-\infty )=(-\infty )\cdot \infty =-\infty }"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Alia_notanda">Alia notanda</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=25" title="Recensere partem: Alia notanda" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=25" title="Edit section's source code: Alia notanda"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nota bene <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{x \over \infty }=0]\not \equiv [0\cdot \infty =x]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi mathvariant="normal">∞</mi> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo stretchy="false">]</mo> <mo>≢</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mi>x</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{x \over \infty }=0]\not \equiv [0\cdot \infty =x]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c44d22985b378b6b3385a75c653eaa3deb3a18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:22.701ex; height:4.676ex;" alt="{\displaystyle [{x \over \infty }=0]\not \equiv [0\cdot \infty =x]}"></span>. Hoc est quia zero multiplicatur infinitate non definitur. </p><p>Nota etiam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[{x \over \infty }=0\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi mathvariant="normal">∞</mi> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[{x \over \infty }=0\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/391cc62026d93ce19ed6e74ce689ff45195282ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.616ex; height:4.843ex;" alt="{\displaystyle \left[{x \over \infty }=0\right]}"></span> non aequare <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[0\cdot \infty =x\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> <mo>=</mo> <mi>x</mi> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[0\cdot \infty =x\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e674b4ecc8cc47b5fd8c237c86c5f201c134fde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.887ex; height:2.843ex;" alt="{\displaystyle \left[0\cdot \infty =x\right]}"></span>. Si secunda esset vera, necesse sit vera ess pro <i>omni</i> <i>x</i>, et a transitivitate <i>aequalium</i> relationis, omnes numeri sint aequales. Hoc est significantia indefinitatis sententiae <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\cdot \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\cdot \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4738f1bea788ab349643aa9cd22991c12725615" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.165ex; height:2.176ex;" alt="{\displaystyle 0\cdot \infty }"></span>. </p><p>Etiam per <a href="/wiki/Hospitalii_regula" title="Hospitalii regula">Hospitalii regulam</a>, limes solutionum indefinitarum pro aequatione n inveniantur, si aequatio scribatur forma <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty \over \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> <mi mathvariant="normal">∞</mi> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty \over \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4f428d97dee57b4b0f987fed290926de81a10da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.16ex; height:4.676ex;" alt="{\displaystyle \infty \over \infty }"></span> vel <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0 \over 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> <mn>0</mn> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0 \over 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8b324718dd65509bc4ae7a480a513b3a4afa7f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle 0 \over 0}"></span>, quae saepe solutionem definitam producit. </p> <div class="mw-heading mw-heading3"><h3 id="Infinitas_in_analysi_reali_et_calculus_infinitesimalis">Infinitas in analysi reali et <a href="/wiki/Calculus_infinitesimalis" title="Calculus infinitesimalis">calculus infinitesimalis</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=26" title="Recensere partem: Infinitas in analysi reali et calculus infinitesimalis" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=26" title="Edit section's source code: Infinitas in analysi reali et calculus infinitesimalis"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/w/index.php?title=Analysis_realis&action=edit&redlink=1" class="new" title="Analysis realis (non est haec pagina)">analysi reali</a>, signum <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span>, "infinitas" appellatur, denotat <a href="/wiki/Limes_(mathematica)" title="Limes (mathematica)">limitem</a> infinitam. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\rightarrow \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\rightarrow \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02579e74e2ef1ca0befceba816b311fe5bfd6844" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.268ex; height:1.843ex;" alt="{\displaystyle x\rightarrow \infty }"></span> significat <b>x</b> crescere ultra quemlibet valorem designatum, et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\rightarrow -\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">→</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\rightarrow -\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ad42c280ece91df185e6124b7297036f71d9181" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.076ex; height:2.176ex;" alt="{\displaystyle x\rightarrow -\infty }"></span> significat <b>x</b> tandem aliquando minus fieri quam quilibet valor designatus. </p><p>Infinitas saepe adhibetur non solum ad limitem definiendam, immo etiam in analysi reali quasi numerus realis esset; si <i>f</i>(<i>t</i>) ≥ 0 deinde: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{0}^{1}\,f(t)dt\ =\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mspace width="thinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> <mtext> </mtext> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{0}^{1}\,f(t)dt\ =\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/141bb3a65a99f2d1c511c64ed738a5aaa254b081" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.278ex; height:6.176ex;" alt="{\displaystyle \int _{0}^{1}\,f(t)dt\ =\infty }"></span> significat <i>f</i>(<i>t</i>) non definire aream finitam ab 0 ad 1.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{0}^{\infty }\,f(t)dt\ =\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mspace width="thinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> <mtext> </mtext> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{0}^{\infty }\,f(t)dt\ =\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2079f934d8a78e6030a00ae7c79c9624ec4c7d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.1ex; height:5.843ex;" alt="{\displaystyle \int _{0}^{\infty }\,f(t)dt\ =\infty }"></span> significat aream sub <i>f</i>(<i>t</i>) infinitam esse.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{0}^{\infty }\,f(t)dt\ =1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mspace width="thinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> <mtext> </mtext> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{0}^{\infty }\,f(t)dt\ =1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4684e8cd350c2c94a730216e000009f801dac10f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.938ex; height:5.843ex;" alt="{\displaystyle \int _{0}^{\infty }\,f(t)dt\ =1}"></span> significat aream sub <i>f</i>(<i>t</i>) appropinquere 1</li></ul> <div class="mw-heading mw-heading3"><h3 id="Infinitas_in_geometria">Infinitas in <a href="/wiki/Geometria" title="Geometria">geometria</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=27" title="Recensere partem: Infinitas in geometria" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=27" title="Edit section's source code: Infinitas in geometria"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Partes multarum figurarum <a href="/wiki/Geometria" title="Geometria">geometricarum</a> sunt infinitae. Ex centro <a href="/wiki/Circulus" title="Circulus">circuli</a> inifiniti radii describantur. <a href="/wiki/Linea" class="mw-redirect" title="Linea">Linea</a> in duas partes dimidiatas bipartiatur ad infinitum; semper erit etiam linea ex qua duae sectiones extraheatur. </p> <div class="mw-heading mw-heading4"><h4 id="Torricellius"><a href="/wiki/Evangelista_Torricellius" title="Evangelista Torricellius">Torricellius</a></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=28" title="Recensere partem: Torricellius" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=28" title="Edit section's source code: Torricellius"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:GabrielsHorn.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/GabrielsHorn.png/400px-GabrielsHorn.png" decoding="async" width="400" height="99" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/be/GabrielsHorn.png 1.5x" data-file-width="520" data-file-height="129" /></a><figcaption>Sinistra pars <a href="/wiki/Torricellii_cornu" title="Torricellii cornu">Torricellii cornu</a>.</figcaption></figure> <p>Figura ad dextram inventa est anno <a href="/wiki/1644" title="1644">1644</a> ab <a href="/wiki/Evangelista_Torricellius" title="Evangelista Torricellius">Evangelista Torricellio</a>, appellatur <a href="/wiki/Torricellii_cornu" title="Torricellii cornu">Torricellii cornu</a>. Eius copia est finita, at <a href="/w/index.php?title=Area_superfaciei&action=edit&redlink=1" class="new" title="Area superfaciei (non est haec pagina)">area superfaciei</a> est <i><b>in</b></i>finita. Torricellii verbis: </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio">Incredibile videri potest, cum solidum hoc infinitam longitudinem habeat, nullam tamen ex illis superficiebus cylindricis quas nos consideramus, infinitam longitudinem habere; sed vnamquamq' esse terminatam; vt vnicuiq; patebit, cui vel modicè familiaris sit doctrina Conicorum.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Evangelista_Torricellius" title="Evangelista Torricellius">Evangelista Torricellius</a>, <i><a href="/w/index.php?title=Opera_Geometrica&action=edit&redlink=1" class="new" title="Opera Geometrica (non est haec pagina)">Opera Geometrica</a></i></cite></div><div><i></i></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="Simiae_infinitae"><a href="/wiki/Simiae_infinitae" class="mw-redirect" title="Simiae infinitae">Simiae infinitae</a></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=29" title="Recensere partem: Simiae infinitae" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=29" title="Edit section's source code: Simiae infinitae"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fasciculus:Monkey-typing.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Monkey-typing.jpg/240px-Monkey-typing.jpg" decoding="async" width="240" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Monkey-typing.jpg/360px-Monkey-typing.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Monkey-typing.jpg/480px-Monkey-typing.jpg 2x" data-file-width="633" data-file-height="356" /></a><figcaption>Simia machina dactylographica utitur.</figcaption></figure> <p>Est sententia sensu prisca et forma multiplex quae saepius hodie contexitur a <i><a href="/wiki/Simia" title="Simia">simiis</a> infinitis</i>. Breviter, dicit sortes cuiusdam eventus improbabilis, temptatas per vices infinitas, tandem infinitati appropinquaturas. Elegantius, suasum est si esset infinitus simiarum numerus cum digitis forte cadentibus in superfaciem infinitarum machinarum dactylographicarum, statim corpus integrum <a href="/wiki/Gulielmus_Shakespeare" class="mw-redirect" title="Gulielmus Shakespeare">Gulielmi Shakespeare</a> scriptum fore. </p><p>Ut dictum est, huius sensus sententiae priscus est, et Cicero ipse dedit fontem, at re vera dubitans, <a href="/wiki/Ennius" class="mw-redirect" title="Ennius">Ennio</a> loco Shakespeare: </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio">Hic ego non mirer esse quemquam, qui sibi persuadeat corpora quaedam solida atque individua vi et gravitate ferri mundumque effici ornatissimum et pulcherrimum ex eorum corporum concursione fortuita? Hoc qui existimat fieri potuisse, non intellego, cur non idem putet, si innumerabiles unius et viginti formae litterarum vel aureae vel qualeslibet aliquo coiciantur, posse ex is in terram excussis annales Enni, ut deinceps legi possint, effici; quod nescio an ne in uno quidem versu possit tantum valere fortuna.</div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Cicero" class="mw-redirect" title="Cicero">Cicero</a>, <i><a rel="nofollow" class="external text" href="http://thelatinlibrary.com/cicero/nd2.shtml#93">De Natura Deorum, 2.93</a></i></cite></div><div><i></i></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="Infinitas_in_fictione_scientiae">Infinitas in <a href="/wiki/Mythistoriae_rerum_futurarum" class="mw-redirect" title="Mythistoriae rerum futurarum">fictione scientiae</a></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=30" title="Recensere partem: Infinitas in fictione scientiae" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=30" title="Edit section's source code: Infinitas in fictione scientiae"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <i><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></i> sunt hae definitiones infinitatis: </p> <blockquote class="toccolours" style="float:none; padding:10px 15px 5px 15px; display:table;"><div class="citatio">"Bigger than the biggest thing ever and then some, much bigger than that, in fact really amazingly immense, a totally stunning size, real 'Wow, thats big!' time. Infinity is just so big that by comparison, bigness itself looks really titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we are trying to get across here."<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> <p><br /> "Infinity itself looks flat and uninteresting. Looking up into the night sky is looking into infinity -- distance is incomprehensible and therefore meaningless.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> <br /> <br /> </p> <dl><dd>Quae sunt <a href="/wiki/Latine" class="mw-redirect" title="Latine">Latine</a> conversa:</dd></dl> <p><br /> "Ingentior ingentissima re ullius aevi, praeterque aliquid amplius, multo maior quam hac, re vera profecto immensa omnino miratu, magnitudinis omnino stupefacientis, puri 'Ecce, illudst magnum!' temporis. Infinitas est presse tam ingentissima ut magnitas ipsa in comparatione videatur minima. Pergrandis multiplicatur ab immanissima multiplicatur a titubantitim ingentissimo...tale est modus sententiae quem hic transferre conamur." <br /> </p> "Infinitas ipsa videtur plana et iniucunda. Intui sursum in caelum noctis est in infinitatem pervidere -- distantia non potest intellegi et ergo nullam rationem confert."</div><div style="text-align:right;"><cite style="font-style:normal;">– <a href="/wiki/Duglassius_Adams" title="Duglassius Adams">Duglassius Adams</a>, <i><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></i></cite></div><div><i></i></div><div style="text-align:right;">― convertit <a href="/wiki/Usor:Ioscius" title="Usor:Ioscius">Ioscius</a></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="Nexus_interni">Nexus interni</h2></div> <ul><li><a href="/wiki/Absolutum_(philosophia)" title="Absolutum (philosophia)">Absolutum (philosophia)</a></li> <li><a href="/wiki/Aeternitas" title="Aeternitas">Aeternitas</a></li> <li><a href="/wiki/Apiron" title="Apiron">Apiron</a></li> <li><a href="/wiki/Calculus_infinitesimalis" title="Calculus infinitesimalis">Calculus infinitesimalis</a></li> <li><a href="/wiki/Fragor_Maximus" class="mw-redirect" title="Fragor Maximus">Fragor Maximus</a></li> <li><a href="/wiki/Infinitas_plus_unus" title="Infinitas plus unus">Infinitas plus unus</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Fontes">Fontes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=31" title="Recensere partem: Fontes" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=31" title="Edit section's source code: Fontes"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small"><div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">*John Monaghan, <i>Young Peoples' Ideas of Infinity</i>, Educational Studies in Mathematics, 2001, vol 48, pp 239-257. <ul><li>Polly Shulman, <i>Infinity Plus One, and Other Surreal Numbers</i> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070128184851/http://www.discover.com/issues/dec-95/features/infinityplusonea599/">Discover, vol 16, iss 12, December 1995.</a></li> <li>David Tall, <i>A child thinking about infinity</i> <a rel="nofollow" class="external text" href="http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2001l-childs-infinity.pdf">Journal of Mathematical Behavior, vol 20, iss 1, 2001, pp 7-19</a>.</li></ul> </span></li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><i>De Sectionibus Conicis</i> p. <a rel="nofollow" class="external text" href="http://eebo.chadwyck.com.proxy.uchicago.edu/search/full_rec?EeboId=99833191&ACTION=ByID&SOURCE=pgimages.cfg&ID=V37666&FILE=&SEARCHSCREEN=param%28SEARCHSCREEN%29&VID=37666&PAGENO=39&ZOOM=100&VIEWPORT=&CENTREPOS=&GOTOPAGENO=&ZOOMLIST=100&ZOOMTEXTBOX=&SEARCHCONFIG=param%28SEARCHCONFIG%29">4</a>: "...ex infinitis Prallelogrammis <i>[SIC]</i> æquè altis; quorum quidem singulorum altitudo sit totius altitudinis <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\infty }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi mathvariant="normal">∞</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\infty }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd40fade822de7f56646c7006e7f12744b4a275d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.16ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{\infty }}}"></span>, sive aliquota pars infinite parva ; (esto enim <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> nota numeri infiniti). . . ."</span> </li> <li id="cite_note-histmath-3"><span class="mw-cite-backlink"><a href="#cite_ref-histmath_3-0">↑</a></span> <span class="reference-text">Iulius Cabillon. <a rel="nofollow" class="external text" href="http://sunsite.utk.edu/math_archives/.http/hypermail/historia/jul98/0059.html">Textus</a> citationum de signi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }"></span> originibus compositus. (<a href="/wiki/Anglice" class="mw-redirect" title="Anglice">Anglice</a> scriptus)</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Cf. <a href="/w/index.php?title=Albrechtus_Webber&action=edit&redlink=1" class="new" title="Albrechtus Webber (non est haec pagina)">Albrechti Webber Vratislaviensis</a> <i>Yajurvedae specimen cum commentario</i>, anno 1845</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Translatio ab <a href="/wiki/Usor:CriticusFortuitus" title="Usor:CriticusFortuitus">usore CriticoFortuito</a>. Vide <a href="/wiki/Disputatio:Infinitas#Yajurveda" title="Disputatio:Infinitas">Disputatio:Infinitas#Yajurveda</a> ut explicationem (Anglice) legas.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><a href="/wiki/Hesychius_Alexandrinus" title="Hesychius Alexandrinus">Hesychius</a> γ364: <i>"Γεννοί· οἱ Γυμνοσοφισταί"</i>. Vide <a href="/wiki/Translitteratio_Linguae_Graecae" class="mw-redirect" title="Translitteratio Linguae Graecae">Translitteratio Linguae Graecae</a>.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.washingtonpost.com/wp-srv/style/longterm/books/chap1/mysteryaleph.htm">Commentatio de <i>The Mystery Of The Aleph: Mathematics, the Kabbalah, and the Search for Infinity</i> in <i>the Washington Post</i>, Amir D. Aczel, </a><a href="/wiki/16_Novembris" title="16 Novembris">16 Novembris</a>, <a href="/wiki/2000" title="2000">2000</a>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text"><a href="/wiki/Aristoteles" title="Aristoteles">Aristoteles</a> <i><a href="/wiki/Physica_(Aristoteles)" class="mw-redirect" title="Physica (Aristoteles)">Physica</a></i> VI.ix, 239b15.</span> </li> <li id="cite_note-argyropylus-9"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-argyropylus_9-0">9.0</a></sup> <sup><a href="#cite_ref-argyropylus_9-1">9.1</a></sup> <sup><a href="#cite_ref-argyropylus_9-2">9.2</a></sup></span> <span class="reference-text"><a href="/wiki/Ioannes_Argyropylus_Byzantius" title="Ioannes Argyropylus Byzantius">Ioannes Argyropylus Byzantius</a>, <i><a href="/wiki/Physica_Auscultatio" class="mw-redirect" title="Physica Auscultatio">Physica Auscultatio</a></i>. Textus desumptus de libro <i>Aristotelis opera</i> quem edidit Academia Regia Borussica anno <a href="/wiki/1831" title="1831">1831</a>: PA 3895 .A4 1831 v. 3.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text"><a href="/wiki/Aristoteles" title="Aristoteles">Aristotelis</a> <i><a href="/wiki/Physica_(Aristoteles)" class="mw-redirect" title="Physica (Aristoteles)">Physica</a></i> VI.ix, 239b-240a.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text"><a href="/wiki/Aristoteles" title="Aristoteles">Aristoteles</a> <i><a href="/wiki/Physica_(Aristoteles)" class="mw-redirect" title="Physica (Aristoteles)">Physica</a></i> III.vii</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text"> Archimedes, <i>Arenarius</i>, 2.134.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text">"<i>Hoc tritum prouerbium erat Graecis; Pindarus Ol. II, 98; Paroemiogr. Gr. p. 11, 167, 250 ed. Gaisford</i>"</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><a href="#cite_ref-14">↑</a></span> <span class="reference-text">I.L. Heiberg, PA 3873 .A8 1880 (v. 2 p. 244).</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="http://www.math.uwaterloo.ca/navigation/ideas/reckoner.shtml">http://www.math.uwaterloo.ca/navigation/ideas/reckoner.shtml</a></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text"><a href="/wiki/Guillelmus_de_Ockham" title="Guillelmus de Ockham">Guillelmus de Ockham</a>, Exp. phys. III, 10, Ã‚Â§2</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><a href="#cite_ref-17">↑</a></span> <span class="reference-text"> Interpretis ignoti, <i><a rel="nofollow" class="external text" href="http://math-doc.ujf-grenoble.fr/LiNuM/TM/Gallica/S051264.html">Discursus et Demonstrationes Mathematicae circa duas novas scientias</a></i>, "Dialogus I", p. 29</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><a href="#cite_ref-18">↑</a></span> <span class="reference-text"><a href="/wiki/Galilaeus_Galilaei" title="Galilaeus Galilaei">Galilaeus Galilaei</a>, <i><a rel="nofollow" class="external text" href="http://www.liberliber.it/biblioteca/g/galilei/discorsi_e_dimostrazioni_matematiche_intorno_a_due_nuove_etc/html/index.htm">Discorsi su due nuove scienze</a></i>, <a href="/wiki/1638" title="1638">1638</a>.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><a href="#cite_ref-19">↑</a></span> <span class="reference-text"><i><a rel="nofollow" class="external text" href="http://math-doc.ujf-grenoble.fr/LiNuM/TM/Gallica/S051264.html">Ibid.</a></i>, "Dialogus I", p. 30</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><a href="#cite_ref-20">↑</a></span> <span class="reference-text"><a href="/wiki/Ioannes_Lockius" title="Ioannes Lockius">Ioannes Lockius</a>, Ch. II, xvii, §8.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><a href="#cite_ref-21">↑</a></span> <span class="reference-text"><a href="/wiki/Gulielmus_Blake" title="Gulielmus Blake">Gulielmus Blake</a>, <i><a rel="nofollow" class="external text" href="http://www.gailgastfield.com/mhh/mhh.html">The Marriage of Heaven and Hell</a></i>, <a rel="nofollow" class="external text" href="http://www.gailgastfield.com/mhh/mhh14.jpg">plate 14</a>.</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><a href="#cite_ref-22">↑</a></span> <span class="reference-text">Conversus ab usore <a href="/wiki/Usor:Ioscius" title="Usor:Ioscius">Ioscio</a>, non ab doctioribus. Querellas in eum fer, si sententiae melius convertantur.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><a href="#cite_ref-23">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060423090728/http://uk.geocities.com/frege@btinternet.com/cantor/diagarg.htm">Textus totus de argumento diagonali</a> (<a href="/wiki/Germanice" class="mw-redirect" title="Germanice">Germanice</a>, lingua prima; et <a href="/wiki/Anglice" class="mw-redirect" title="Anglice">Anglice</a>, conversus)</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><a href="#cite_ref-24">↑</a></span> <span class="reference-text"><a href="/wiki/Ludovicus_Wittgenstein" title="Ludovicus Wittgenstein">Ludovicus Wittgenstein</a>, <i>Philosophical Remarks</i> § 141, cf <i>Philosophical Grammar</i>, p. 465.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><a href="#cite_ref-25">↑</a></span> <span class="reference-text">Omnes translationes ab usoribus <a href="/wiki/Usor:Ioscius" title="Usor:Ioscius">Ioscio</a> et <a href="/wiki/Usor:Iustinus" title="Usor:Iustinus">Iustino</a>, non ab doctioribus. Querellas in eos fer, si sententiae melius convertantur.</span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><a href="#cite_ref-26">↑</a></span> <span class="reference-text"><a href="/wiki/Evangelista_Torricellius" title="Evangelista Torricellius">Evangelista Torricellius</a>, <i>De solido Hyperobolico</i>, ex suis <i><a href="/w/index.php?title=Opera_Geometrica&action=edit&redlink=1" class="new" title="Opera Geometrica (non est haec pagina)">Operibus Geometricis</a>, pagina 116a. Imago <a rel="nofollow" class="external text" href="http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.cgi?dir=torri_opera_519_la_1644;step=thumb">362a</a> <a rel="nofollow" class="external text" href="http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.cgi?dir=torri_opera_519_la_1644;step=thumb">Operum Geometricorum</a></i></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><a href="#cite_ref-27">↑</a></span> <span class="reference-text"><a href="/wiki/Duglassius_Adams" title="Duglassius Adams">Duglassius Adams</a>, <i><a href="/wiki/Peregrinatoris_Enchiridion_Galaxiae#Taberna_ad_Fines_Universi" class="mw-redirect" title="Peregrinatoris Enchiridion Galaxiae">Taberna ad Fines Universi</a>,</i> de "The Ultimate Hitchhiker's Guide: Six Stories by Douglas Adams." Wings Books, <a href="/wiki/Novum_Eboracum" title="Novum Eboracum">New York, NY</a>, 1996. De capite 19o, pagina 243a.</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><a href="#cite_ref-28">↑</a></span> <span class="reference-text"><a href="/wiki/Duglassius_Adams" title="Duglassius Adams">Duglassius Adams</a>, <i><a href="/wiki/Peregrinatoris_Enchiridion_Galaxiae" class="mw-redirect" title="Peregrinatoris Enchiridion Galaxiae">Peregrinatoris Enchiridion Galaxiae</a>, de "The Ultimate Hitchhiker's Guide: Six Stories by Douglas Adams." Wings Books, <a href="/wiki/Novum_Eboracum" title="Novum Eboracum">New York, NY</a>, 1996. De capite 24o, pagina 107a.</i></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Bibliographia">Bibliographia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=32" title="Recensere partem: Bibliographia" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=32" title="Edit section's source code: Bibliographia"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small"> <ul><li><span class="citation book">Amir D. Aczel (2001). <i>The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity</i>. Simon & Schuster Adult Publishing Group<span style="display: none;"> </span></span></li> <li>Agrawal, D. P. <a href="/wiki/2000" title="2000">2000</a>. <a rel="nofollow" class="external text" href="http://www.infinityfoundation.com/mandala/t_es/t_es_agraw_jaina.htm"><i>Ancient Jaina Mathematics: an Introduction.</i></a> <a rel="nofollow" class="external text" href="http://infinityfoundation.com">Infinity Foundation</a>.</li> <li><span class="citation book">L. C. Jain (1982). <i>Exact Sciences from Jaina Sources</i><span style="display: none;"> </span></span></li> <li>Jain, L. C. <a href="/wiki/1973" title="1973">1973</a>. Set theory in the Jaina school of mathematics. <i>Indian Journal of History of Science.</i></li> <li><span class="citation book">George G. Joseph (2000). <i>The Crest of the Peacock: Non-European Roots of Mathematics</i> (2nd edition ed.). <a href="/w/index.php?title=Penguin_Books&action=edit&redlink=1" class="new" title="Penguin Books (non est haec pagina)">Penguin Books</a><span style="display: none;"> </span></span></li> <li>O'Connor, John J., et Edmund F. Robertson. <a href="/wiki/1998" title="1998">1998</a>. <a rel="nofollow" class="external text" href="http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Cantor.html">Georg Ferdinand Ludwig Philipp Cantor.</a> <i>MacTutor History of Mathematics archive.</i></li> <li>O'Connor, John J., et Edmund F. Robertson. <a href="/wiki/2000" title="2000">2000</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081220145242/http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Jaina_mathematics.html">Jaina mathematics.</a> <i>MacTutor History of Mathematics archive.</i></li> <li>Pearce, Ian <a href="/wiki/2002" title="2002">2002</a>. <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch5.html">Jainism.</a> <i>MacTutor History of Mathematics archive.</i></li> <li><span class="citation book">Rudy Rucker (1995). <i>Infinity and the Mind: The Science and Philosophy of the Infinite</i>. Princeton University Press<span style="display: none;"> </span></span></li> <li>Singh, N. <a href="/wiki/1988" title="1988">1988</a>. 'Jaina Theory of Actual Infinity and Transfinite Numbers', <i>Journal of Asiatic Society</i>, Vol. 30.</li> <li><span class="citation book">David Foster Wallace (2004). <i>Everything and More: A Compact History of Infinity</i>. W. W. Norton & Company, Inc.<span style="display: none;"> </span></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Nexus_externi">Nexus externi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Infinitas&veaction=edit&section=33" title="Recensere partem: Nexus externi" class="mw-editsection-visualeditor"><span>recensere</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Infinitas&action=edit&section=33" title="Edit section's source code: Nexus externi"><span>fontem recensere</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://scidiv.bcc.ctc.edu/Math/infinity.html">Numerare ad infinitatem</a></li> <li><i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100227033849/http://www.earlham.edu/~peters/writing/infapp.htm">Doctulum in mathematica infinitorum</a></i>, a Peter Suber, de St. John's Review, XLIV, 2 (1998) 1-59.</li> <li><a rel="nofollow" class="external text" href="http://pespmc1.vub.ac.be/INFINITY.html"><i>Infinity</i>, Principia Cybernetica</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20040910082530/http://www.c3.lanl.gov/mega-math/workbk/infinity/infinity.html">Caupona Infinity</a></li> <li><a rel="nofollow" class="external text" href="http://samvak.tripod.com/infinite.html">Sententiae finitatis infinitatisque in philosophia</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060428005158/http://uk.geocities.com/frege@btinternet.com/cantor/Phil-Infinity.htm">Fons medievalium recentumque scriptionum de Infinitate</a></li></ul> <p><br /> </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Receptum de "<a dir="ltr" href="https://la.wikipedia.org/w/index.php?title=Infinitas&oldid=3854134">https://la.wikipedia.org/w/index.php?title=Infinitas&oldid=3854134</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Specialis:Categoriae" title="Specialis:Categoriae">Categoriae</a>: <ul><li><a href="/wiki/Categoria:Paginae_mensis" title="Categoria:Paginae mensis">Paginae mensis</a></li><li><a href="/wiki/Categoria:Numeri" title="Categoria:Numeri">Numeri</a></li><li><a href="/wiki/Categoria:Infinitas" title="Categoria:Infinitas">Infinitas</a></li><li><a href="/wiki/Categoria:Notiones_in_logica" title="Categoria:Notiones in logica">Notiones in logica</a></li><li><a href="/wiki/Categoria:Philosophia_mathematicae" title="Categoria:Philosophia mathematicae">Philosophia mathematicae</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categoriae celatae: <ul><li><a href="/wiki/Categoria:Continetur_textus_Graece_scriptus" title="Categoria:Continetur textus Graece scriptus">Continetur textus Graece scriptus</a></li><li><a href="/wiki/Categoria:Latinitas_dubia_(dubsig)" title="Categoria:Latinitas dubia (dubsig)">Latinitas dubia (dubsig)</a></li><li><a href="/wiki/Categoria:Paginae_cum_sectione_nexuum_internorum" title="Categoria:Paginae cum sectione nexuum internorum">Paginae cum sectione nexuum internorum</a></li><li><a href="/wiki/Categoria:1000_paginae" title="Categoria:1000 paginae">1000 paginae</a></li><li><a href="/wiki/Categoria:Myrias_Mathematica" title="Categoria:Myrias Mathematica">Myrias Mathematica</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"> Novissima mutatio die 24 Septembris 2024 hora 10:46 facta.</li> <li id="footer-info-copyright">Nonobstantibus ceteris condicionibus hunc textum tractare licet secundum <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">"Creative Commons Attribution-ShareAlike License"</a>. 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