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class="vector-toc-link" href="#Definiție_algebrică"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definiție algebrică</span> </div> </a> <ul id="toc-Definiție_algebrică-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Definiție_analitică" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definiție_analitică"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Definiție analitică</span> </div> </a> <ul id="toc-Definiție_analitică-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exemple" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Exemple"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Exemple</span> </div> </a> <ul id="toc-Exemple-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Proprietăți" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Proprietăți"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Proprietăți</span> </div> </a> <ul id="toc-Proprietăți-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografie"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bibliografie</span> </div> </a> <ul id="toc-Bibliografie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lectură_suplimentară" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lectură_suplimentară"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Lectură suplimentară</span> </div> </a> <ul id="toc-Lectură_suplimentară-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legături_externe" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legături_externe"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Legături externe</span> </div> </a> <ul id="toc-Legături_externe-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="Cuprins" 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="Comută cuprinsul" > <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">Comută cuprinsul</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">Număr irațional</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="Mergeți la un articol în altă limbă. Disponibil în 89 limbi" > <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-89" 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">89 limbi</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/Irrasionale_getal" title="Irrasionale getal – afrikaans" lang="af" hreflang="af" data-title="Irrasionale getal" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%BA%D9%8A%D8%B1_%D9%83%D8%B3%D8%B1%D9%8A" title="عدد غير كسري – arabă" lang="ar" hreflang="ar" data-title="عدد غير كسري" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%85%E0%A6%AA%E0%A7%B0%E0%A6%BF%E0%A6%AE%E0%A7%87%E0%A6%AF%E0%A6%BC_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="অপৰিমেয় সংখ্যা – asameză" lang="as" hreflang="as" data-title="অপৰিমেয় সংখ্যা" data-language-autonym="অসমীয়া" data-language-local-name="asameză" 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/N%C3%BAmberu_irracional" title="Númberu irracional – asturiană" lang="ast" hreflang="ast" data-title="Númberu irracional" data-language-autonym="Asturianu" data-language-local-name="asturiană" 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/%C4%B0rrasional_%C9%99d%C9%99dl%C9%99r" title="İrrasional ədədlər – azeră" lang="az" hreflang="az" data-title="İrrasional ədədlər" data-language-autonym="Azərbaycanca" data-language-local-name="azeră" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%98%D1%80%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C_%D2%BB%D0%B0%D0%BD" title="Иррациональ һан – bașkiră" lang="ba" hreflang="ba" data-title="Иррациональ һан" data-language-autonym="Башҡортса" data-language-local-name="bașkiră" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%86%D1%80%D0%B0%D1%86%D1%8B%D1%8F%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Ірацыянальны лік – belarusă" lang="be" hreflang="be" data-title="Ірацыянальны лік" data-language-autonym="Беларуская" data-language-local-name="belarusă" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%BD%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Ирационално число – bulgară" lang="bg" hreflang="bg" data-title="Ирационално число" data-language-autonym="Български" data-language-local-name="bulgară" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%AE%E0%A7%82%E0%A6%B2%E0%A6%A6_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="অমূলদ সংখ্যা – bengaleză" lang="bn" hreflang="bn" data-title="অমূলদ সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="bengaleză" 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/Iracionalan_broj" title="Iracionalan broj – bosniacă" lang="bs" hreflang="bs" data-title="Iracionalan broj" data-language-autonym="Bosanski" data-language-local-name="bosniacă" 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/Nombre_irracional" title="Nombre irracional – catalană" lang="ca" hreflang="ca" data-title="Nombre irracional" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95%DB%8C_%D9%86%D8%A7%DA%95%DB%8E%DA%98%DB%95%DB%8C%DB%8C" title="ژمارەی ناڕێژەیی – kurdă centrală" lang="ckb" hreflang="ckb" data-title="ژمارەی ناڕێژەیی" data-language-autonym="کوردی" data-language-local-name="kurdă centrală" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Iracion%C3%A1ln%C3%AD_%C4%8D%C3%ADslo" title="Iracionální číslo – cehă" lang="cs" hreflang="cs" data-title="Iracionální číslo" data-language-autonym="Čeština" data-language-local-name="cehă" 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%98%D1%80%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%BB%C4%83_%D1%85%D0%B8%D1%81%D0%B5%D0%BF" title="Иррационаллă хисеп – ciuvașă" lang="cv" hreflang="cv" data-title="Иррационаллă хисеп" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhif_anghymarebol" title="Rhif anghymarebol – galeză" lang="cy" hreflang="cy" data-title="Rhif anghymarebol" data-language-autonym="Cymraeg" data-language-local-name="galeză" 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/Irrationale_tal" title="Irrationale tal – daneză" lang="da" hreflang="da" data-title="Irrationale tal" data-language-autonym="Dansk" data-language-local-name="daneză" 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/Irrationale_Zahl" title="Irrationale Zahl – germană" lang="de" hreflang="de" data-title="Irrationale Zahl" data-language-autonym="Deutsch" data-language-local-name="germană" 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%81%CF%81%CE%B7%CF%84%CE%BF%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82" title="Άρρητος αριθμός – greacă" lang="el" hreflang="el" data-title="Άρρητος αριθμός" data-language-autonym="Ελληνικά" data-language-local-name="greacă" 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/Irrational_number" title="Irrational number – engleză" lang="en" hreflang="en" data-title="Irrational number" data-language-autonym="English" data-language-local-name="engleză" 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/Neracionala_nombro" title="Neracionala nombro – esperanto" lang="eo" hreflang="eo" data-title="Neracionala nombro" data-language-autonym="Esperanto" data-language-local-name="esperanto" 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/N%C3%BAmero_irracional" title="Número irracional – spaniolă" lang="es" hreflang="es" data-title="Número irracional" data-language-autonym="Español" data-language-local-name="spaniolă" 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/Irratsionaalarvud" title="Irratsionaalarvud – estonă" lang="et" hreflang="et" data-title="Irratsionaalarvud" data-language-autonym="Eesti" data-language-local-name="estonă" 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/Zenbaki_irrazional" title="Zenbaki irrazional – bască" lang="eu" hreflang="eu" data-title="Zenbaki irrazional" data-language-autonym="Euskara" data-language-local-name="bască" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%DA%AF%D9%86%DA%AF" title="عدد گنگ – persană" lang="fa" hreflang="fa" data-title="عدد گنگ" data-language-autonym="فارسی" data-language-local-name="persană" 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/Irrationaaliluku" title="Irrationaaliluku – finlandeză" lang="fi" hreflang="fi" data-title="Irrationaaliluku" data-language-autonym="Suomi" data-language-local-name="finlandeză" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Irratsionaalarv" title="Irratsionaalarv – Võro" lang="vro" hreflang="vro" data-title="Irratsionaalarv" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Irrationell_t%C3%B8l" title="Irrationell tøl – feroeză" lang="fo" hreflang="fo" data-title="Irrationell tøl" data-language-autonym="Føroyskt" data-language-local-name="feroeză" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr badge-Q17437798 badge-goodarticle mw-list-item" title="articol bun"><a href="https://fr.wikipedia.org/wiki/Nombre_irrationnel" title="Nombre irrationnel – franceză" lang="fr" hreflang="fr" data-title="Nombre irrationnel" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Uimhir_%C3%A9ag%C3%B3imheasta" title="Uimhir éagóimheasta – irlandeză" lang="ga" hreflang="ga" data-title="Uimhir éagóimheasta" data-language-autonym="Gaeilge" data-language-local-name="irlandeză" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%BAmero_irracional" title="Número irracional – galiciană" lang="gl" hreflang="gl" data-title="Número irracional" data-language-autonym="Galego" data-language-local-name="galiciană" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%90%D7%99-%D7%A8%D7%A6%D7%99%D7%95%D7%A0%D7%9C%D7%99" title="מספר אי-רציונלי – ebraică" lang="he" hreflang="he" data-title="מספר אי-רציונלי" data-language-autonym="עברית" data-language-local-name="ebraică" 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%AA%E0%A4%B0%E0%A4%BF%E0%A4%AE%E0%A5%87%E0%A4%AF_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="अपरिमेय संख्या – hindi" lang="hi" hreflang="hi" data-title="अपरिमेय संख्या" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Iracionalni_broj" title="Iracionalni broj – croată" lang="hr" hreflang="hr" data-title="Iracionalni broj" data-language-autonym="Hrvatski" data-language-local-name="croată" 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/Irracion%C3%A1lis_sz%C3%A1mok" title="Irracionális számok – maghiară" lang="hu" hreflang="hu" data-title="Irracionális számok" data-language-autonym="Magyar" data-language-local-name="maghiară" 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%BB%D5%BC%D5%A1%D6%81%D5%AB%D5%B8%D5%B6%D5%A1%D5%AC_%D5%A9%D5%AB%D5%BE" title="Իռացիոնալ թիվ – armeană" lang="hy" hreflang="hy" data-title="Իռացիոնալ թիվ" data-language-autonym="Հայերեն" data-language-local-name="armeană" 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/Bilangan_irasional" title="Bilangan irasional – indoneziană" lang="id" hreflang="id" data-title="Bilangan irasional" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Neracionala_nombro" title="Neracionala nombro – ido" lang="io" hreflang="io" data-title="Neracionala nombro" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%93r%C3%A6%C3%B0ar_t%C3%B6lur" title="Óræðar tölur – islandeză" lang="is" hreflang="is" data-title="Óræðar tölur" data-language-autonym="Íslenska" data-language-local-name="islandeză" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_irrazionale" title="Numero irrazionale – italiană" lang="it" hreflang="it" data-title="Numero irrazionale" data-language-autonym="Italiano" data-language-local-name="italiană" 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%E7%90%86%E6%95%B0" title="無理数 – japoneză" lang="ja" hreflang="ja" data-title="無理数" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%98%E1%83%A0%E1%83%90%E1%83%AA%E1%83%98%E1%83%9D%E1%83%9C%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%98" title="ირაციონალური რიცხვი – georgiană" lang="ka" hreflang="ka" data-title="ირაციონალური რიცხვი" data-language-autonym="ქართული" data-language-local-name="georgiană" 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%A0%D0%B0%D0%B1%D0%B0%D0%B9%D1%81%D1%8B%D0%B7_%D1%81%D0%B0%D0%BD" title="Рабайсыз сан – kazahă" lang="kk" hreflang="kk" data-title="Рабайсыз сан" data-language-autonym="Қазақша" data-language-local-name="kazahă" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AC%B4%EB%A6%AC%EC%88%98" title="무리수 – coreeană" lang="ko" hreflang="ko" data-title="무리수" data-language-autonym="한국어" data-language-local-name="coreeană" 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/Hejmar%C3%AAn_na_aql%C3%AE" title="Hejmarên na aqlî – kurdă" lang="ku" hreflang="ku" data-title="Hejmarên na aqlî" data-language-autonym="Kurdî" data-language-local-name="kurdă" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%98%D1%80%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%B4%D1%8B%D0%BA_%D1%81%D0%B0%D0%BD" title="Иррационалдык сан – kârgâză" lang="ky" hreflang="ky" data-title="Иррационалдык сан" data-language-autonym="Кыргызча" data-language-local-name="kârgâză" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numerus_irrationalis" title="Numerus irrationalis – latină" lang="la" hreflang="la" data-title="Numerus irrationalis" data-language-autonym="Latina" data-language-local-name="latină" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/N%C3%BCmar_irazziunaal" title="Nümar irazziunaal – Lombard" lang="lmo" hreflang="lmo" data-title="Nümar irazziunaal" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%88%E0%BA%B3%E0%BA%99%E0%BA%A7%E0%BA%99%E0%BA%AD%E0%BA%B0%E0%BA%9B%E0%BA%BB%E0%BA%81%E0%BA%81%E0%BA%B0%E0%BA%95%E0%BA%B4" title="ຈຳນວນອະປົກກະຕິ – laoțiană" lang="lo" hreflang="lo" data-title="ຈຳນວນອະປົກກະຕິ" data-language-autonym="ລາວ" data-language-local-name="laoțiană" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Iracionalusis_skai%C4%8Dius" title="Iracionalusis skaičius – lituaniană" lang="lt" hreflang="lt" data-title="Iracionalusis skaičius" data-language-autonym="Lietuvių" data-language-local-name="lituaniană" 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/Iracion%C4%81ls_skaitlis" title="Iracionāls skaitlis – letonă" lang="lv" hreflang="lv" data-title="Iracionāls skaitlis" data-language-autonym="Latviešu" data-language-local-name="letonă" 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/Isa_tsivoasaina" title="Isa tsivoasaina – malgașă" lang="mg" hreflang="mg" data-title="Isa tsivoasaina" data-language-autonym="Malagasy" data-language-local-name="malgașă" 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%98%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%B5%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Ирационален број – macedoneană" lang="mk" hreflang="mk" data-title="Ирационален број" data-language-autonym="Македонски" data-language-local-name="macedoneană" 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%AD%E0%B4%BF%E0%B4%A8%E0%B5%8D%E0%B4%A8%E0%B4%95%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF" title="അഭിന്നകസംഖ്യ – malayalam" lang="ml" hreflang="ml" data-title="അഭിന്നകസംഖ്യ" data-language-autonym="മലയാളം" data-language-local-name="malayalam" 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%98%D1%80%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE" title="Иррационал тоо – mongolă" lang="mn" hreflang="mn" data-title="Иррационал тоо" data-language-autonym="Монгол" data-language-local-name="mongolă" 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%AA%E0%A4%B0%E0%A4%BF%E0%A4%AE%E0%A5%87%E0%A4%AF_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="अपरिमेय संख्या – marathi" lang="mr" hreflang="mr" data-title="अपरिमेय संख्या" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Nombor_bukan_nisbah" title="Nombor bukan nisbah – malaeză" lang="ms" hreflang="ms" data-title="Nombor bukan nisbah" data-language-autonym="Bahasa Melayu" data-language-local-name="malaeză" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Numru_irrazzjonali" title="Numru irrazzjonali – malteză" lang="mt" hreflang="mt" data-title="Numru irrazzjonali" data-language-autonym="Malti" data-language-local-name="malteză" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Irrationaal_getal" title="Irrationaal getal – neerlandeză" lang="nl" hreflang="nl" data-title="Irrationaal getal" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" 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/Irrasjonale_tal" title="Irrasjonale tal – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Irrasjonale tal" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană 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/Irrasjonalt_tall" title="Irrasjonalt tall – norvegiană bokmål" lang="nb" hreflang="nb" data-title="Irrasjonalt tall" data-language-autonym="Norsk bokmål" data-language-local-name="norvegiană bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%85%E0%AC%AA%E0%AC%B0%E0%AC%BF%E0%AC%AE%E0%AD%87%E0%AD%9F_%E0%AC%B8%E0%AC%82%E0%AC%96%E0%AD%8D%E0%AD%9F%E0%AC%BE" title="ଅପରିମେୟ ସଂଖ୍ୟା – odia" lang="or" hreflang="or" data-title="ଅପରିମେୟ ସଂଖ୍ୟା" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A8%BC%E0%A9%88%E0%A8%B0-%E0%A8%AC%E0%A8%9F%E0%A9%87%E0%A8%A8%E0%A9%81%E0%A8%AE%E0%A8%BE_%E0%A8%B8%E0%A9%B0%E0%A8%96%E0%A8%BF%E0%A8%86" title="ਗ਼ੈਰ-ਬਟੇਨੁਮਾ ਸੰਖਿਆ – punjabi" lang="pa" hreflang="pa" data-title="ਗ਼ੈਰ-ਬਟੇਨੁਮਾ ਸੰਖਿਆ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" 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/Liczby_niewymierne" title="Liczby niewymierne – poloneză" lang="pl" hreflang="pl" data-title="Liczby niewymierne" data-language-autonym="Polski" data-language-local-name="poloneză" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero_irracional" title="Número irracional – portugheză" lang="pt" hreflang="pt" data-title="Número irracional" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D1%80%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Иррациональное число – rusă" lang="ru" hreflang="ru" data-title="Иррациональное число" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/N%C3%B9mmuru_irrazziunali" title="Nùmmuru irrazziunali – siciliană" lang="scn" hreflang="scn" data-title="Nùmmuru irrazziunali" data-language-autonym="Sicilianu" data-language-local-name="siciliană" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Iracionalni_broj" title="Iracionalni broj – sârbo-croată" lang="sh" hreflang="sh" data-title="Iracionalni broj" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="sârbo-croată" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Irrational_number" title="Irrational number – Simple English" lang="en-simple" hreflang="en-simple" data-title="Irrational number" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Iracion%C3%A1lne_%C4%8D%C3%ADslo" title="Iracionálne číslo – slovacă" lang="sk" hreflang="sk" data-title="Iracionálne číslo" data-language-autonym="Slovenčina" data-language-local-name="slovacă" 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/Iracionalno_%C5%A1tevilo" title="Iracionalno število – slovenă" lang="sl" hreflang="sl" data-title="Iracionalno število" data-language-autonym="Slovenščina" data-language-local-name="slovenă" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-smn mw-list-item"><a href="https://smn.wikipedia.org/wiki/Irrationaalloho" title="Irrationaalloho – sami inari" lang="smn" hreflang="smn" data-title="Irrationaalloho" data-language-autonym="Anarâškielâ" data-language-local-name="sami inari" class="interlanguage-link-target"><span>Anarâškielâ</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Numrat_irracional%C3%AB" title="Numrat irracionalë – albaneză" lang="sq" hreflang="sq" data-title="Numrat irracionalë" data-language-autonym="Shqip" data-language-local-name="albaneză" 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%98%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%B0%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Ирационалан број – sârbă" lang="sr" hreflang="sr" data-title="Ирационалан број" data-language-autonym="Српски / srpski" data-language-local-name="sârbă" 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/Irrationella_tal" title="Irrationella tal – suedeză" lang="sv" hreflang="sv" data-title="Irrationella tal" data-language-autonym="Svenska" data-language-local-name="suedeză" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Namba_isiyowiana" title="Namba isiyowiana – swahili" lang="sw" hreflang="sw" data-title="Namba isiyowiana" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%BF%E0%AE%95%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%81%E0%AE%B1%E0%AE%BE_%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="விகிதமுறா எண் – tamilă" lang="ta" hreflang="ta" data-title="விகிதமுறா எண்" data-language-autonym="தமிழ்" data-language-local-name="tamilă" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%85%E0%B0%A8%E0%B0%BF%E0%B0%B7%E0%B1%8D%E0%B0%AA_%E0%B0%B8%E0%B0%82%E0%B0%96%E0%B1%8D%E0%B0%AF" title="అనిష్ప సంఖ్య – telugu" lang="te" hreflang="te" data-title="అనిష్ప సంఖ్య" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%B4%D0%B0%D0%B4%D2%B3%D0%BE%D0%B8_%D0%B8%D1%80%D1%80%D0%B0%D1%82%D1%81%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D3%A3" title="Ададҳои ирратсионалӣ – tadjică" lang="tg" hreflang="tg" data-title="Ададҳои ирратсионалӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="tadjică" 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%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%AD%E0%B8%95%E0%B8%A3%E0%B8%A3%E0%B8%81%E0%B8%A2%E0%B8%B0" title="จำนวนอตรรกยะ – thailandeză" lang="th" hreflang="th" data-title="จำนวนอตรรกยะ" data-language-autonym="ไทย" data-language-local-name="thailandeză" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0rrasyonel_say%C4%B1lar" title="İrrasyonel sayılar – turcă" lang="tr" hreflang="tr" data-title="İrrasyonel sayılar" data-language-autonym="Türkçe" data-language-local-name="turcă" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D1%80%D1%80%D0%B0%D1%86%D1%96%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Ірраціональне число – ucraineană" lang="uk" hreflang="uk" data-title="Ірраціональне число" data-language-autonym="Українська" data-language-local-name="ucraineană" 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/%D8%BA%DB%8C%D8%B1%D9%86%D8%A7%D8%B7%D9%82_%D8%B9%D8%AF%D8%AF" title="غیرناطق عدد – urdu" lang="ur" hreflang="ur" data-title="غیرناطق عدد" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Irratsional_sonlar" title="Irratsional sonlar – uzbecă" lang="uz" hreflang="uz" data-title="Irratsional sonlar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecă" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91_v%C3%B4_t%E1%BB%89" title="Số vô tỉ – vietnameză" lang="vi" hreflang="vi" data-title="Số vô tỉ" data-language-autonym="Tiếng Việt" data-language-local-name="vietnameză" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Irrationoale_getalln" title="Irrationoale getalln – West Flemish" lang="vls" hreflang="vls" data-title="Irrationoale getalln" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/N%E1%BB%8D%CC%81mb%C3%A0_al%C3%A1%C3%ACn%C3%AD%C3%ACp%C3%ADn" title="Nọ́mbà aláìníìpín – yoruba" lang="yo" hreflang="yo" data-title="Nọ́mbà aláìníìpín" data-language-autonym="Yorùbá" data-language-local-name="yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%84%A1%E7%90%86%E6%95%B8" title="無理數 – chineză" lang="zh" hreflang="zh" data-title="無理數" data-language-autonym="中文" data-language-local-name="chineză" class="interlanguage-link-target"><span>中文</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-l%C3%AD-s%C3%B2%CD%98" title="Bû-lí-sò͘ – chineză min nan" lang="nan" hreflang="nan" data-title="Bû-lí-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="chineză min nan" 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%90%86%E6%95%B8" title="無理數 – cantoneză" lang="yue" hreflang="yue" data-title="無理數" data-language-autonym="粵語" data-language-local-name="cantoneză" 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/Q607728#sitelinks-wikipedia" title="Modifică legăturile interlinguale" class="wbc-editpage">Modifică legăturile</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="Spații de nume"> <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 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versiune a acestei pagini"><span>Legătură permanentă</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&action=info" title="Mai multe informații despre această pagină"><span>Informații despre pagină</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:Citeaz%C4%83&page=Num%C4%83r_ira%C8%9Bional&id=16442406&wpFormIdentifier=titleform" title="Informații cu privire la modul de citare a acestei pagini"><span>Citează acest articol</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fro.wikipedia.org%2Fwiki%2FNum%25C4%2583r_ira%25C8%259Bional"><span>Obține URL scurtat</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fro.wikipedia.org%2Fwiki%2FNum%25C4%2583r_ira%25C8%259Bional"><span>Descărcați codul QR</span></a></li> </ul> </div> </div> <div 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<div id="siteSub" class="noprint">De la Wikipedia, enciclopedia liberă</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="ro" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r16501920">.mw-parser-output .ambox{margin:0px 10%;border:1px solid #aaa;border-left:10px solid #1e90ff;background:#fbfbfb}.mw-parser-output table.ambox-notice{border-left:10px solid #1e90ff}.mw-parser-output table.ambox-speedy{border-left:10px solid #b22222;background:#fee}.mw-parser-output table.ambox-delete{border-left:10px solid #b22222}.mw-parser-output table.ambox-content{border-left:10px solid #f28500}.mw-parser-output table.ambox-style{border-left:10px solid #f4c430}.mw-parser-output table.ambox-move{border-left:10px solid #9932cc}.mw-parser-output table.ambox-protection{border-left:10px solid #bba}@media screen{html.skin-theme-clientpref-night .mw-parser-output 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.ambox-content,html.skin-theme-clientpref-night .mw-parser-output .ambox-style,html.skin-theme-clientpref-night .mw-parser-output .ambox-move,html.skin-theme-clientpref-night .mw-parser-output .ambox-protection{background-color:#202122!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ambox,html.skin-theme-clientpref-os .mw-parser-output .ambox-notice{border-left:10px solid #000f1e!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy{background-color:#310402!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete{border-left:10px solid #070101!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-content{border-left:10px solid #261500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left:10px solid #544004!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left:10px solid #1e0a28!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left:10px solid #bba!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-notice,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete,html.skin-theme-clientpref-os .mw-parser-output .ambox-content,html.skin-theme-clientpref-os .mw-parser-output .ambox-style,html.skin-theme-clientpref-os .mw-parser-output .ambox-move,html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{background-color:#202122!important}}</style><table class="metadata plainlinks ambox ambox ambox-content ambox-content" style=""> <tbody><tr><td class="mbox-image"><div style="width: 52px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Question_book-4.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/50px-Question_book-4.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/75px-Question_book-4.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Question_book-4.svg/100px-Question_book-4.svg.png 2x" data-file-width="262" data-file-height="204" /></a></span></div></td><td class="mbox-text" style=""><span class="mbox-text-span"><b>Acest articol sau această secțiune are <a href="/wiki/Wikipedia:Citarea_surselor" title="Wikipedia:Citarea surselor">bibliografia</a> incompletă sau inexistentă.</b><br /> Puteți contribui prin adăugarea de referințe în vederea <a href="/wiki/Wikipedia:Verificabilitate" title="Wikipedia:Verificabilitate">susținerii bibliografice</a> a afirmațiilor pe care le conține.<span class="hide-when-compact"> </span><span class="hide-when-compact"> </span></span></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Square_root_of_2_triangle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Square_root_of_2_triangle.svg/220px-Square_root_of_2_triangle.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Square_root_of_2_triangle.svg/330px-Square_root_of_2_triangle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Square_root_of_2_triangle.svg/440px-Square_root_of_2_triangle.svg.png 2x" data-file-width="500" data-file-height="500" /></a><figcaption><a href="/wiki/Ipotenuz%C4%83" title="Ipotenuză">Ipotenuza</a> unui <a href="/wiki/Triunghi_dreptunghic" title="Triunghi dreptunghic">triunghi dreptunghic</a> <a href="/wiki/Triunghi_isoscel" title="Triunghi isoscel">isoscel</a> cu <a href="/wiki/Catet%C4%83" title="Catetă">catetele</a> egale cu <b>1</b> este un număr irațional, <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 \scriptstyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b6ac02637a190523aa10dde1b52ae41964dfff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.191ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {\sqrt {2}}}"></span>.</figcaption></figure> <p>În <a href="/wiki/Matematic%C4%83" title="Matematică">matematică</a>, un <b>număr irațional</b> este un <a href="/wiki/Num%C4%83r_real" title="Număr real">număr real</a> care <b>nu</b> se poate exprima ca <a href="/wiki/Raport" title="Raport">raportul</a> a două <a href="/wiki/Numere_%C3%AEntregi" class="mw-redirect" title="Numere întregi">numere întregi</a>. Prin contrast, numerele reale care se pot exprima ca raportul (rația) dintre doi întregi se numesc <a href="/wiki/Num%C4%83r_ra%C8%9Bional" title="Număr rațional">numere raționale</a>. Spre deosebire de acestea din urmă, numerele iraționale au un <a href="/wiki/Num%C4%83r_zecimal" title="Număr zecimal">număr infinit de zecimale</a> neperiodice, fiind echivalente cu o sumă infinită de fracții cu <a href="/wiki/Numitor" class="mw-redirect" title="Numitor">numitorul</a> puteri ale numărului 10. Pot apărea prin extragerea <a href="/wiki/Radical_(matematic%C4%83)" title="Radical (matematică)">radicalilor</a> din numere naturale care nu constituie puteri cu <a href="/w/index.php?title=Exponent&action=edit&redlink=1" class="new" title="Exponent — pagină inexistentă">exponent</a> întreg pozitiv (perfecte) ale unei baze oarecare număr natural (<a href="/wiki/Num%C4%83r_algebric" title="Număr algebric">numere algebrice</a>) sau din sume infinite (<a href="/wiki/Num%C4%83r_transcendent" title="Număr transcendent">numere transcendente</a>). Un exemplu de număr rezultat dintr-o sumă infinită este <a href="/wiki/Num%C4%83rul_e" class="mw-redirect" title="Numărul e">numărul e</a> rezultat din suma inverselor <a href="/wiki/Factorial" title="Factorial">factorialelor</a>. </p><p>Aceste numere apar în diferite probleme geometrice ca lungimea diagonalelor unui pătrat funcție de latura sa, latura unui pătrat funcție de aria sa, lungimea laturilor unui triunghi dreptunghic<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> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definiție_algebrică"><span id="Defini.C8.9Bie_algebric.C4.83"></span>Definiție algebrică</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&veaction=edit&section=1" title="Modifică secțiunea: Definiție algebrică" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&action=edit&section=1" title="Edit section's source code: Definiție algebrică"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Considerând <a href="/wiki/Corp_(matematic%C4%83)" title="Corp (matematică)">corpul</a> <a href="/wiki/Num%C4%83r_ra%C8%9Bional" title="Număr rațional">numerelor raționale</a> <span class="Unicode" style="font-family:TITUS Cyberbit Basic, Code2000, Doulos SIL, Chrysanthi Unicode, Bitstream Cyberbit, Bitstream CyberBase, Bitstream Vera, Thryomanes, Gentium, GentiumAlt, Visual Geez Unicode, Lucida Grande, Arial Unicode MS, Microsoft Sans Serif, Lucida Sans Unicode;">ℚ</span>, inclus în corpul <a href="/wiki/Num%C4%83r_real" title="Număr real">numerelor reale</a> <span class="Unicode" style="font-family:TITUS Cyberbit Basic, Code2000, Doulos SIL, Chrysanthi Unicode, Bitstream Cyberbit, Bitstream CyberBase, Bitstream Vera, Thryomanes, Gentium, GentiumAlt, Visual Geez Unicode, Lucida Grande, Arial Unicode MS, Microsoft Sans Serif, Lucida Sans Unicode;">ℝ</span> (<span class="Unicode" style="font-family:TITUS Cyberbit Basic, Code2000, Doulos SIL, Chrysanthi Unicode, Bitstream Cyberbit, Bitstream CyberBase, Bitstream Vera, Thryomanes, Gentium, GentiumAlt, Visual Geez Unicode, Lucida Grande, Arial Unicode MS, Microsoft Sans Serif, Lucida Sans Unicode;">ℚ ⊆ ℝ</span>), mulțimea numerelor iraționale <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 {I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8205f06e0d279689ed04a1ac04a3d9c249c637df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.905ex; height:2.176ex;" alt="{\displaystyle \mathbb {I} }"></span> se poate defini ca diferența dintre mulțimile <span class="Unicode" style="font-family:TITUS Cyberbit Basic, Code2000, Doulos SIL, Chrysanthi Unicode, Bitstream Cyberbit, Bitstream CyberBase, Bitstream Vera, Thryomanes, Gentium, GentiumAlt, Visual Geez Unicode, Lucida Grande, Arial Unicode MS, Microsoft Sans Serif, Lucida Sans Unicode;">ℝ</span> și <span class="Unicode" style="font-family:TITUS Cyberbit Basic, Code2000, Doulos SIL, Chrysanthi Unicode, Bitstream Cyberbit, Bitstream CyberBase, Bitstream Vera, Thryomanes, Gentium, GentiumAlt, Visual Geez Unicode, Lucida Grande, Arial Unicode MS, Microsoft Sans Serif, Lucida Sans Unicode;">ℚ</span>: </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 \mathbb {I} =\mathbb {R} \setminus \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">I</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo class="MJX-variant">∖</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {I} =\mathbb {R} \setminus \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/720d781e3106162ca1f4e2ff351e5714f4308c23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.684ex; height:2.843ex;" alt="{\displaystyle \mathbb {I} =\mathbb {R} \setminus \mathbb {Q} }"></span></dd></dl> <p>adică: </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 \mathbb {I} =\{x|x\in \mathbb {R} ,x\notin \mathbb {Q} \}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">I</mi> </mrow> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>,</mo> <mi>x</mi> <mo>∉</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mo fence="false" stretchy="false">}</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {I} =\{x|x\in \mathbb {R} ,x\notin \mathbb {Q} \}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62c9c07c7ac968b7d7146c95c3e31ee70d0bc619" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.234ex; width:21.012ex; height:2.843ex;" alt="{\displaystyle \mathbb {I} =\{x|x\in \mathbb {R} ,x\notin \mathbb {Q} \}\!}"></span></dd></dl> <p><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 {I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8205f06e0d279689ed04a1ac04a3d9c249c637df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.905ex; height:2.176ex;" alt="{\displaystyle \mathbb {I} }"></span> este o <a href="/wiki/Mul%C8%9Bime_infinit%C4%83" title="Mulțime infinită">mulțime infinită</a> și <a href="/wiki/Mul%C8%9Bime_nenum%C4%83rabil%C4%83" title="Mulțime nenumărabilă">nenumărabilă</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Definiție_analitică"><span id="Defini.C8.9Bie_analitic.C4.83"></span>Definiție analitică</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&veaction=edit&section=2" title="Modifică secțiunea: Definiție analitică" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&action=edit&section=2" title="Edit section's source code: Definiție analitică"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O definiție riguroasă a numerelor iraționale se poate face prin metodele <a href="/wiki/Analiza_matematic%C4%83" title="Analiza matematică">analizei matematice</a>, mai exact prin <a href="/wiki/Construc%C8%9Bia_lui_Dedekind" title="Construcția lui Dedekind">metoda „tăieturilor”</a> a lui <a href="/wiki/Dedekind" class="mw-redirect" title="Dedekind">Dedekind</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Exemple">Exemple</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&veaction=edit&section=3" title="Modifică secțiunea: Exemple" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&action=edit&section=3" title="Edit section's source code: Exemple"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Câteva exemple de numere iraționale, de naturi diferite între ele, algebrice sau transcendente: </p> <ul><li><a href="/wiki/Raportul_de_aur" class="mw-redirect" title="Raportul de aur">Raportul de aur</a>, notat cu litera grecească Φ (<i>phi</i> majuscul) sau cu φ (<i>phi</i> minuscul), care se citesc „fi”, este aproximativ egal cu 1,618033 și poate fi întâlnit în cele mai surprinzătoare împrejurări.</li> <li><a href="/wiki/R%C4%83d%C4%83cin%C4%83_p%C4%83trat%C4%83" title="Rădăcină pătrată">rădăcina pătrată</a> a lui 2, notată <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 \scriptstyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b6ac02637a190523aa10dde1b52ae41964dfff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.191ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {\sqrt {2}}}"></span>, cu <a href="/wiki/Valoare_(matematic%C4%83)" title="Valoare (matematică)">valoarea</a> aproximativă de 1,4142135.</li> <li>numărul <a href="/wiki/Pi" title="Pi"><span class="texhtml mvar" style="font-style:italic;">π</span></a> (pi), cu valoarea aproximativă de 3,141592653.</li> <li>numărul <i><a href="/wiki/E" title="E">e</a></i>, baza <a href="/wiki/Logaritm" title="Logaritm">logaritmilor</a> naturali, cu valoarea aproximativă 2,7182818.</li> <li>sin(1°) (<a href="/wiki/Sinus" title="Sinus">sinusul</a> unghiului de 1 grad).</li> <li><a href="/wiki/Logaritm" title="Logaritm">logaritmii</a> zecimal și natural ai numărului 2, în general logaritmii naturali ai oricărui număr natural mai mare ca 1.</li> <li>soluția <a href="/wiki/Ecua%C8%9Bie_algebric%C4%83" class="mw-redirect" title="Ecuație algebrică">ecuației algebrice</a> x<sup>5</sup> - 3x + 3 = 0. Această soluție este un număr real, irațional, deci care nu se poate exprima ca raport de doi întregi, și care însă, altfel decât s-ar putea crede, nu se poate exprima nici prin rădăcini (radicali), de nici un ordin.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Proprietăți"><span id="Propriet.C4.83.C8.9Bi"></span>Proprietăți</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&veaction=edit&section=4" title="Modifică secțiunea: Proprietăți" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&action=edit&section=4" title="Edit section's source code: Proprietăți"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Există și numere reale despre care nu se știe încă dacă sunt raționale sau iraționale, spre exemplu suma π + e și multe altele. </p><p>Numerele iraționale pot fi <a href="/wiki/Num%C4%83r_transcendent" title="Număr transcendent">transcendente</a>, spre deosebire de numerele raționale care sunt întotdeauna <a href="/wiki/Num%C4%83r_algebric" title="Număr algebric">algebrice</a>. Un număr este numit „algebric” dacă este soluția unei <a href="/wiki/Ecua%C8%9Bie_algebric%C4%83" class="mw-redirect" title="Ecuație algebrică">ecuații algebrice</a> cu coeficienți raționali, de genul x<sup>5</sup>-3x+3=0. Numărul irațional <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 {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b19c09494138b5082459afac7f9a8d99c546fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.843ex;" alt="{\displaystyle {\sqrt {3}}}"></span>, de exemplu, este algebric, în timp ce numerele e și π s-a demonstrat că sunt transcendente. </p><p>Numerele iraționale sunt întotdeauna fracții zecimale cu un număr nesfârșit de zecimale, neperiodice. În scris, zecimalele cele mai puțin semnificative se reprezintă simbolic cu 3 puncte "..."; de exemplu π = 3,1415926... , sau e = 2,7182818... </p><p>Dacă un număr zecimal oarecare are un număr infinit de zecimale, care însă se repetă periodic, eventual în grupuri, atunci el se poate exprima întotdeauna ca raportul a două numere întregi, deci numărul zecimal în discuție este un <a href="/wiki/Numere_ra%C8%9Bionale" class="mw-redirect" title="Numere raționale">număr rațional</a>. Spre exemplu, numărul 4,37295295295... , notat și 4,37(295), este egal cu 4 + 37/100 + 295/99.900 = 436.858/99.900. </p><p>Pot fi aproximate prin numere raționale cu <a href="/wiki/Aproxima%C8%9Bie_diofantic%C4%83" title="Aproximație diofantică">aproximație diofantică</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Bibliografie">Bibliografie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&veaction=edit&section=5" title="Modifică secțiunea: Bibliografie" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&action=edit&section=5" title="Edit section's source code: Bibliografie"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Miron_Nicolescu" title="Miron Nicolescu">Miron Nicolescu</a>, <i>Analiză matematică</i>, vol. I, Editura Tehnică, București, 1957, pp. 69-94.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Lectură_suplimentară"><span id="Lectur.C4.83_suplimentar.C4.83"></span>Lectură suplimentară</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&veaction=edit&section=6" title="Modifică secțiunea: Lectură suplimentară" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&action=edit&section=6" title="Edit section's source code: Lectură suplimentară"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Mario_Livio" title="Mario Livio">Mario Livio</a>, <i>Secțiunea de aur - Povestea lui </i>phi<i>, cel mai uimitor număr</i>, <a href="/wiki/Editura_Humanitas" title="Editura Humanitas">Editura Humanitas</a>, 2016</li></ul> <div class="mw-heading mw-heading2"><h2 id="Legături_externe"><span id="Leg.C4.83turi_externe"></span>Legături externe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&veaction=edit&section=7" title="Modifică secțiunea: Legături externe" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Num%C4%83r_ira%C8%9Bional&action=edit&section=7" title="Edit section's source code: Legături externe"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Commons-logo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Materiale media legate de <span class="plainlinks"><b><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Irrational_numbers?uselang=ro">număr irațional</a></b></span> la <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a></li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="http://www.dm.uniba.it/~psiche/bas2/node5.html">Zeno's Paradoxes and Incommensurability</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160513063302/http://www.dm.uniba.it/~psiche/bas2/node5.html">Arhivat</a> în <time datetime="2016-05-13">13 mai 2016</time>, la <a href="/wiki/Wayback_Machine" class="mw-redirect" title="Wayback Machine">Wayback Machine</a>.</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="Reference-Mathworld-Irrational_Number"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Eric W. Weisstein</a>, <i><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/IrrationalNumber.html">Irrational Number</a></i> la <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>.</cite></li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="http://www.cut-the-knot.org/proofs/sq_root.shtml">Square root of 2 is irrational</a></li></ul> <p><br clear="all" /> </p> <table class="toc noprint" cellpadding="0" width="95%" cellspacing="2" style="align:center; text-align:center;clear:all;"> <tbody><tr> <th rowspan="2"><span style="display:inline;vertical-align:baseline"><span style="display:inline-block;margin:2px 0px;vertical-align:baseline;border:solid 1px #AAAAAA;border-collapse:collapse;padding:0px"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Ulam_1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Ulam_1.png/80px-Ulam_1.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Ulam_1.png/120px-Ulam_1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Ulam_1.png/160px-Ulam_1.png 2x" data-file-width="400" data-file-height="400" /></a></span></span></span> </th> <th bgcolor="#EEE8DD"><a href="/wiki/Matematic%C4%83" title="Matematică"><font color="#080808">Matematică</font></a> – <a href="/wiki/Teoria_numerelor" title="Teoria numerelor">Teoria numerelor</a> --- <a href="/wiki/Categorie:Matematic%C4%83_discret%C4%83" title="Categorie:Matematică discretă">Matematică discretă (categorie)</a> </th></tr> <tr> <td style="font-size:95%"> <div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><b><a href="/wiki/List%C4%83_de_matematicieni" title="Listă de matematicieni">Matematicieni</a></b> specializați în <b><a href="/wiki/Categorie:Teoria_numerelor" title="Categorie:Teoria numerelor">Teoria numerelor (categorie)</a></b></div> <p><span style="white-space: nowrap;"> •</span><span style="white-space: nowrap;"> •</span> <a href="/wiki/Num%C4%83r_natural" title="Număr natural"><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></a> <span style="white-space: nowrap;"> •</span><span style="white-space: nowrap;"> •</span> <a href="/wiki/Num%C4%83r_%C3%AEntreg" title="Număr întreg"><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></a> <span style="white-space: nowrap;"> •</span><span style="white-space: nowrap;"> •</span> <a href="/wiki/Num%C4%83r_ra%C8%9Bional" title="Număr rațional"><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></a> <span style="white-space: nowrap;"> •</span><span style="white-space: nowrap;"> •</span> <a class="mw-selflink selflink"><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 {I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8205f06e0d279689ed04a1ac04a3d9c249c637df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.905ex; height:2.176ex;" alt="{\displaystyle \mathbb {I} }"></span></a> <span style="white-space: nowrap;"> •</span><span style="white-space: nowrap;"> •</span> <a href="/wiki/Num%C4%83r_transcendent" title="Număr transcendent"><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 {T} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">T</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {T} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c039979935c00b3b216cbb065999207872677f6" 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 {T} }"></span></a> <span style="white-space: nowrap;"> •</span><span style="white-space: nowrap;"> •</span> <a href="/wiki/Num%C4%83r_real" title="Număr real"><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></a> <span style="white-space: nowrap;"> •</span><span style="white-space: nowrap;"> •</span> <a href="/wiki/Num%C4%83r_complex" title="Număr complex"><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 {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7" 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 {C} }"></span></a> <span style="white-space: nowrap;"> •</span><span style="white-space: nowrap;"> •</span> </p> </td></tr></tbody></table> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text">Matematică - Algebră - Manual pentru clasa a VII-a, Editura Didactică și Pedagogică, 1994, pagina 27</span> </li> </ol></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Adus de la <a dir="ltr" href="https://ro.wikipedia.org/w/index.php?title=Număr_irațional&oldid=16442406">https://ro.wikipedia.org/w/index.php?title=Număr_irațional&oldid=16442406</a></div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categorii" title="Special:Categorii">Categorii</a>: <ul><li><a href="/wiki/Categorie:Numere_ira%C8%9Bionale" title="Categorie:Numere iraționale">Numere iraționale</a></li><li><a href="/wiki/Categorie:Algebr%C4%83" title="Categorie:Algebră">Algebră</a></li><li><a href="/wiki/Categorie:Teoria_numerelor" title="Categorie:Teoria numerelor">Teoria numerelor</a></li><li><a href="/wiki/Categorie:Numere" title="Categorie:Numere">Numere</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categorii ascunse: <ul><li><a href="/wiki/Categorie:Articole_cu_suport_bibliografic_necorespunz%C4%83tor" title="Categorie:Articole cu suport bibliografic necorespunzător">Articole cu suport bibliografic necorespunzător</a></li><li><a href="/wiki/Categorie:Webarchive_template_wayback_links" title="Categorie:Webarchive template wayback links">Webarchive template wayback links</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"> Ultima editare a paginii a fost efectuată la 15 august 2024, ora 13:50.</li> <li id="footer-info-copyright">Acest text este disponibil sub licența <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ro">Creative Commons cu atribuire și distribuire în condiții identice</a>; 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