@prefix rdf: . @prefix dbr: . @prefix yago: . dbr:Division_by_zero rdf:type yago:Condition113920835 , yago:WikicatFractions , yago:WikicatProgrammingParadigms , yago:Organization108008335 , yago:WikicatCompaniesEstablishedIn1990 , yago:State100024720 , yago:LinguisticRelation113797142 , yago:Event100029378 , yago:Fraction114922107 , yago:PhysicalEntity100001930 , yago:Error107299569 , yago:PhysicalCondition114034177 , yago:Paradigm113804375 , yago:Company108058098 , yago:WikicatSoftwareCompaniesOfTheUnitedKingdom , yago:Anomaly114505821 , yago:PsychologicalFeature100023100 , yago:WikicatCompaniesDisestablishedIn1996 , yago:YagoLegalActor , yago:YagoLegalActorGeo , yago:YagoPermanentlyLocatedEntity , yago:Abstraction100002137 , yago:Matter100020827 . @prefix owl: . dbr:Division_by_zero rdf:type owl:Thing , yago:SocialGroup107950920 , yago:WikicatComputerErrors , yago:WikicatVideoGameDevelopmentCompanies , yago:Group100031264 , yago:Institution108053576 , yago:Part113809207 , yago:WikicatDefunctVideoGameCompanies , yago:Material114580897 , yago:Relation100031921 . @prefix dbo: . dbr:Division_by_zero rdf:type dbo:Organisation , yago:Inflection113803782 , yago:WikicatSoftwareAnomalies , yago:Attribute100024264 , yago:GrammaticalRelation113796779 , yago:WikicatVideoGameCompaniesOfTheUnitedKingdom , yago:Abnormality114501726 , yago:Chemical114806838 , yago:Happening107283608 , yago:Substance100019613 . @prefix rdfs: . dbr:Division_by_zero rdfs:label "Division durch null"@de , "0\uC73C\uB85C \uB098\uB204\uAE30"@ko , "Delen door nul"@nl , "D\u011Blen\u00ED nulou"@cs , "Division by zero"@en , "\u30BC\u30ED\u9664\u7B97"@ja , "Divisione per zero"@it , "Divisi\u00F3 entre zero"@ca , "Division med noll"@sv , "Division par z\u00E9ro"@fr , "\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 \u0627\u0644\u0635\u0641\u0631"@ar , "Dzielenie przez zero"@pl , "\u0414\u0435\u043B\u0435\u043D\u0438\u0435 \u043D\u0430 \u043D\u043E\u043B\u044C"@ru , "Divis\u00E3o por zero"@pt , "\u0414\u0456\u043B\u0435\u043D\u043D\u044F \u043D\u0430 \u043D\u0443\u043B\u044C"@uk , "\u9664\u4EE5\u96F6"@zh , "Divisi\u00F3n por cero"@es ; rdfs:comment "D\u011Blen\u00ED nulou je v matematice takov\u00E9 d\u011Blen\u00ED, p\u0159i n\u011Bm\u017E je d\u011Blitel nula. M\u016F\u017Ee b\u00FDt zaps\u00E1no jako , kde a je d\u011Blenec. V oborech re\u00E1ln\u00FDch ani komplexn\u00EDch \u010D\u00EDsel nem\u00E1 takov\u00E9 d\u011Blen\u00ED smysl \u2013 nula je jedin\u00E9 \u010D\u00EDslo, kter\u00FDm nelze d\u011Blit. V oboru komplexn\u00EDch \u010D\u00EDsel roz\u0161\u00ED\u0159en\u00FDch o (komplexn\u00ED) nekone\u010Dno je definov\u00E1no pro v\u0161echny nenulov\u00E9 d\u011Blence jako . P\u0159i d\u011Blen\u00ED v plovouc\u00ED \u0159\u00E1dov\u00E9 \u010D\u00E1rce m\u016F\u017Ee b\u00FDt v\u00FDsledkem speci\u00E1ln\u00ED hodnota not a number (nen\u00ED \u010D\u00EDslo) nebo nekone\u010Dno."@cs , "Dzielenie przez zero \u2013 dzielenie, w kt\u00F3rym dzielnik jest zerem; jako takie nie ma ono sensu liczbowego, przez co bywa \u017Ar\u00F3d\u0142em b\u0142\u0119d\u00F3w obliczeniowych, cz\u0119sto ukrytych. Prostym przyk\u0142adem b\u0142\u0119du wynik\u0142ego z dzielenia przez zero jest nast\u0119puj\u0105cy: niech i w\u00F3wczas skoro to r\u00F3wnie\u017C oraz a ze wzoru na r\u00F3\u017Cnic\u0119 kwadrat\u00F3w jest Dziel\u0105c stronami przez uzyskuje si\u0119 co jest r\u00F3wnowa\u017Cne a wi\u0119c sk\u0105d Otrzymana sprzeczno\u015B\u0107 wynika z zastosowania dzielenia przez"@pl , "In matematica, una divisione per zero \u00E8 una divisione della forma . Il risultato non esiste, poich\u00E9 l'espressione \u00E8 priva di significato in aritmetica e in algebra. \u00C8 piuttosto diffusa l'errata opinione per cui il valore di sarebbe (infinito). Questa affermazione fa riferimento, in modo non del tutto corretto, a un'interpretazione della divisione in termini della teoria dei limiti dell'analisi matematica. Esistono comunque particolari strutture matematiche all'interno delle quali la divisione per zero potrebbe essere definita in modo consistente (per esempio, la sfera di Riemann)."@it , "Division med noll inneb\u00E4r inom matematiken att man dividerar ett tal med noll, det vill s\u00E4ga att man har noll i n\u00E4mnaren. Det kan skrivas , d\u00E4r x \u00E4r t\u00E4ljaren och noll n\u00E4mnaren. Division med noll \u00E4r inte definierad f\u00F6r de reella talen eller komplexa talen inom matematiken."@sv , "\u30BC\u30ED\u9664\u7B97\uFF08\u30BC\u30ED\u3058\u3087\u3055\u3093\u3001\u82F1\u8A9E: division by zero\uFF09\u3068\u306F\u30010\u3067\u9664\u3059\u5272\u308A\u7B97\u306E\u3053\u3068\u3067\u3042\u308B\u3002\u3053\u306E\u3088\u3046\u306A\u9664\u7B97\u306F\u9664\u3055\u308C\u308B\u6570\u3092a\u3068\u3059\u308B\u306A\u3089\u3070\u3001\u5F62\u5F0F\u4E0A\u306F a/0\u3068\u66F8\u304F\u3053\u3068\u304C\u3067\u304D\u308B\u304C\u3001\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u3053\u306E\u3088\u3046\u306A\u5F0F\u3092\u77DB\u76FE\u306A\u304F\u5B9A\u7FA9\u3059\u308B\u3053\u3068\u306F\u3067\u304D\u306A\u3044\u3002\u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u306E\u6570\u5024\u8A08\u7B97\u306B\u304A\u3044\u3066\u30BC\u30ED\u9664\u7B97\u304C\u767A\u751F\u3057\u305F\u5834\u5408\u3001\u7121\u9650\u5927\u3084\u30BC\u30ED\u9664\u7B97\u3092\u610F\u5473\u3059\u308B\u30B7\u30F3\u30DC\u30EB\u3067\u7F6E\u304D\u63DB\u3048\u308B\u3001\u4F8B\u5916\u3068\u3057\u3066\u51E6\u7406\u3059\u308B\u306A\u3069\u306E\u5BFE\u5FDC\u304C\u53D6\u3089\u308C\u308B\u304B\u3001\u767A\u751F\u3057\u305F\u6642\u70B9\u3067\u51E6\u7406\u304C\u7834\u7DBB\u3059\u308B\uFF08\u30B7\u30B9\u30C6\u30E0\u30A8\u30E9\u30FC\u3068\u306A\u308B\uFF09\u3002 \u73FE\u4EE3\u6570\u5B66\u306E\u89B3\u70B9\u3067\u306F\u3001\u3044\u304B\u306A\u308B\u30A2\u30D7\u30ED\u30FC\u30C1\u304B\u3089\u5B9A\u7FA9\u3092\u8A66\u307F\u3088\u3046\u3068\u3082\u5FC5\u305A\u7834\u7DBB\u306B\u81F3\u308B\u3002\u7D50\u5C40\u3001\u300C\u5024\u3092\u5B9A\u7FA9\u3057\u5F97\u306A\u3044\u305F\u3081\u3001\u8A08\u7B97\u306F\u4E0D\u53EF\u80FD\u3067\u3042\u308B\u300D\u3068\u7406\u89E3\u3059\u308B\u4ED6\u306A\u3044\u6982\u5FF5\u3067\u3042\u308A\u3001\u305D\u308C\u4EE5\u4E0A\u306E\u8B70\u8AD6\u306B\u3088\u3063\u3066\u6570\u5B66\u7684\u306B\u6709\u7528\u306A\u7D50\u679C\u304C\u5F97\u3089\u308C\u308B\u3053\u3068\u306F\u671F\u5F85\u3067\u304D\u306A\u3044\u3002\u3057\u304B\u3057\u3001\u6982\u5FF5\u81EA\u4F53\u306F\u6975\u3081\u3066\u521D\u7B49\u7684\u306A\u77E5\u8B58\u3067\u6349\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u305F\u3081\u3001\u3057\u3070\u3057\u3070\u6570\u5B66\u7684\u539F\u5247\u3092\u524D\u63D0\u3068\u3057\u3066\u3044\u306A\u3044\u8B70\u8AD6\u3084\u72EC\u81EA\u306A\u89E3\u91C8\u304C\u5C55\u958B\u3055\u308C\u308B\u3053\u3068\u304C\u3042\u308B\u3002\u305D\u306E\u3088\u3046\u306A\u8B70\u8AD6\u3084\u89E3\u91C8\u306F\u3044\u305A\u308C\u3082\u8AD6\u7406\u7684\u7834\u7DBB\u3092\u542B\u3080\u304B\u4FE1\u983C\u6027\u306E\u3042\u308B\u6839\u62E0\u3092\u4F34\u308F\u306A\u3044\u70BA\u3001\u5B66\u8853\u7684\u306A\u8A55\u4FA1\u306E\u4F59\u5730\u3092\u307B\u3068\u3093\u3069\u6709\u3057\u306A\u3044\u3002 \u8A08\u7B97\u5C3A\u3067\u306F\u3001\u5BFE\u6570\u5C3A\u306B\u306F0\u306B\u76F8\u5F53\u3059\u308B\u4F4D\u7F6E\u304C\u5B58\u5728\u3057\u306A\u3044\uFF08\u7121\u9650\u306E\u5F7C\u65B9\u3067\u3042\u308B\uFF09\u305F\u3081\u8A08\u7B97\u4E0D\u53EF\u80FD\u3067\u3042\u308B\u3002"@ja , "In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as , where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by 0, gives a (assuming ); thus, division by zero is undefined. Since any number multiplied by zero is zero, the expression is also undefined; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst (\"ghosts of departed quantities\")."@en , "En matem\u00E1ticas, la divisi\u00F3n entre cero es una divisi\u00F3n en la que el divisor es igual a cero, y que no tiene un resultado bien definido. En aritm\u00E9tica y \u00E1lgebra, es considerada una \u00ABindefinici\u00F3n\u00BB, y su mal uso puede dar lugar a aparentes paradojas matem\u00E1ticas. En an\u00E1lisis matem\u00E1tico, es frecuente encontrar l\u00EDmites en los que el denominador tiende a cero. Algunos de estos casos se denominan \u00ABindeterminaciones\u00BB, pero en ocasiones es posible calcular el valor de dicho l\u00EDmite."@es , "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 \u0635\u0641\u0631 \u0647\u064A \u0627\u0644\u0642\u0633\u0645\u0629 \u0627\u0644\u062A\u064A \u064A\u0643\u0648\u0646 \u0641\u064A\u0647\u0627 \u0627\u0644\u0645\u0642\u0633\u0648\u0645 \u0639\u0644\u064A\u0647 (\u0627\u0644\u0645\u0642\u0627\u0645) \u0645\u0633\u0627\u0648\u064A\u0627 \u0644\u0635\u0641\u0631.\u063A\u0627\u0644\u0628\u0627\u064B \u0645\u0627 \u062A\u0643\u062A\u0628 \u0628\u0627\u0644\u0635\u064A\u063A\u0629 (\u06330) \u062D\u064A\u062B \u0633 \u0647\u064A \u0627\u0644\u0645\u0642\u0633\u0648\u0645 (\u0627\u0644\u0628\u0633\u0637). \u0648\u0647\u0630\u0647 \u0627\u0644\u0642\u0633\u0645\u0629 \u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u062D\u0633\u0627\u0628\u064A\u0629 \u0627\u0644\u0639\u0627\u062F\u064A\u0629 \u0644\u0627\u0645\u0639\u0646\u0649 \u0644\u0647\u0627 \u0648\u0644\u0627\u064A\u0648\u062C\u062F \u0639\u062F\u062F \u0639\u0646\u062F \u0636\u0631\u0628\u0647 \u0628\u0635\u0641\u0631\u060C \u064A\u0639\u0637\u064A \u0627\u0644\u0642\u064A\u0645\u0629 \u0633 (\u0628\u0627\u0639\u062A\u0628\u0627\u0631 \u0623\u0646 \u0633 \u0644\u0627\u062A\u0633\u0627\u0648\u064A \u0627\u0644\u0635\u0641\u0631) \u0648\u0644\u0630\u0644\u0643 \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 \u0635\u0641\u0631 \u0647\u064A \u0639\u0645\u0644\u064A\u0629 \u063A\u064A\u0631 \u0645\u064F\u0639\u0631\u0641\u0629.\u0648\u0628\u0645\u0627 \u0623\u0646 \u0623\u064A \u0639\u062F\u062F \u064A\u064F\u0636\u0631\u0628 \u0641\u064A \u0635\u0641\u0631 \u064A\u0639\u0637\u064A \u0635\u0641\u0631\u0627\u060C \u0641\u0625\u0646 \u0627\u0644\u0635\u064A\u063A\u0629 \u0623\u064A\u0636\u0627\u064B \u0647\u064A \u0627\u0644\u0623\u062E\u0631\u0649 \u063A\u064A\u0631 \u0645\u064F\u0639\u0631\u0641\u0629\u060C \u0648\u0641\u064A \u062D\u0627\u0644\u0629 \u0648\u062C\u0648\u062F\u0647\u0627 \u0635\u064A\u063A\u0629 \u0646\u0647\u0627\u064A\u0629\u064D \u0628\u0627\u0644\u062A\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062A\u0643\u0627\u0645\u0644\u060C \u0641\u0647\u064A \u0635\u064A\u063A\u0629 \u063A\u064A\u0631 \u0645\u062D\u062F\u062F\u0629. \u0623\u0642\u062F\u0645 \u0627\u0644\u0645\u0631\u0627\u062C\u0639 \u0627\u0644\u062A\u0627\u0631\u064A\u062E\u064A\u0629 \u0627\u0644\u062A\u064A \u0630\u0643\u0631\u062A \u0627\u0633\u062A\u062D\u0627\u0644\u0629 \u062A\u0639\u064A\u064A\u0646 \u0642\u064A\u0645\u0629 \u0644\u0644\u0639\u0645\u0644\u064A\u0629 (\u06330) \u0631\u064A\u0627\u0636\u064A\u0627\u064B \u0645\u0648\u062C\u0648\u062F\u0629 \u0641\u064A \u0643\u062A\u0627\u0628 \u0627\u0644\u0645\u062D\u0644\u0644 \u0645\u0646 \u062A\u0623\u0644\u064A\u0641 \u062C\u0648\u0631\u062C \u0628\u064A\u0631\u0643\u0644\u064A \u0648\u0647\u0648 \u0646\u0642\u062F \u0644\u062D\u0633\u0627\u0628 \u0627\u0644\u062A\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062A\u0643\u0627\u0645\u0644 \u0627\u0644\u0645\u062A\u0646\u0627\u0647\u064A \u0641\u064A \u0627\u0644\u0635\u063A\u0631."@ar , "Na matem\u00E1tica, uma divis\u00E3o \u00E9 chamada divis\u00E3o por zero se o divisor \u00E9 zero. Tal divis\u00E3o pode ser formalmente expressada como = no qual a \u00E9 o dividendo. Um valor bem definido para essa express\u00E3o depende do contexto matem\u00E1tico. Para a aritm\u00E9tica com n\u00FAmeros reais, a express\u00E3o n\u00E3o possui significado.Se considerarmos no gr\u00E1fico de 1/x a quase-ass\u00EDntota com um infinitesimal \u00E0 direita do zero e um infinitesimal \u00E0 esquerda do zero, a reta passa por (0,0), pelo teorema do valor intermedi\u00E1rio. (Q.E.D)"@pt , "\u5728\u6578\u5B78\u4E2D\uFF0C\u88AB\u9664\u6578\u7684\u9664\u6578\uFF08\u5206\u6BCD\uFF09\u662F\u96F6\u6216\u5C07\u67D0\u6578\u9664\u4EE5\u96F6\uFF0C\u53EF\u8868\u9054\u70BA\uFF0C\u662F\u88AB\u9664\u6578\u3002\u5728\u7B97\u5F0F\u4E2D\u6C92\u6709\u610F\u7FA9\uFF0C\u56E0\u70BA\u6C92\u6709\u6578\u76EE\uFF0C\u4EE5\u96F6\u76F8\u4E58\uFF08\u5047\u8A2D\uFF09\uFF0C\u7531\u65BC\u4EFB\u4F55\u6578\u5B57\u4E58\u4EE5\u96F6\u5747\u7B49\u65BC\u96F6\uFF0C\u56E0\u6B64\u9664\u4EE5\u96F6\u662F\u4E00\u500B\u6C92\u6709\u5B9A\u7FA9\u7684\u503C\u3002\u6B64\u5F0F\u662F\u5426\u7AEF\u8996\u5176\u5728\u5982\u4F55\u7684\u6578\u5B78\u8A2D\u5B9A\u4E0B\u8A08\u7B97\u3002\u4E00\u822C\u5BE6\u6578\u7B97\u8853\u4E2D\uFF0C\u6B64\u5F0F\u70BA\u7121\u610F\u7FA9\u3002\u5728\u7A0B\u5E8F\u8A2D\u8A08\u4E2D\uFF0C\u7576\u9047\u4E0A\u6B63\u6574\u6578\u9664\u4EE5\u96F6\u7A0B\u5E8F\u6703\u4E2D\u6B62\uFF0C\u6B63\u5982\u6D6E\u9EDE\u6578\u6703\u51FA\u73FE\u7121\u9650\u5927\u6216NaN\u503C\u7684\u60C5\u6CC1\uFF0C\u800C\u5728Microsoft Excel\u53CAOpenoffice\u6216Libreoffice\u7684Calc\u4E2D\uFF0C\u9664\u4EE5\u96F6\u6703\u76F4\u63A5\u986F\u793A#DIV/0!\u3002"@zh , "\u0414\u0456\u043B\u0435\u043D\u043D\u044F \u043D\u0430 \u043D\u0443\u043B\u044C \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456 \u2014 \u0434\u0456\u043B\u0435\u043D\u043D\u044F, \u043F\u0440\u0438 \u044F\u043A\u043E\u043C\u0443 \u0434\u0456\u043B\u044C\u043D\u0438\u043A \u0434\u043E\u0440\u0456\u0432\u043D\u044E\u0454 \u043D\u0443\u043B\u044E. \u0422\u0430\u043A\u0438\u0439 \u043F\u043E\u0434\u0456\u043B \u043C\u043E\u0436\u0435 \u0431\u0443\u0442\u0438 \u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E \u0437\u0430\u043F\u0438\u0441\u0430\u043D\u043E \u0430 / 0, \u0434\u0435 \u0430 \u2014 \u0446\u0435 \u0434\u0456\u043B\u0435\u043D\u0435.\u0423 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u0456\u0439 \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u0446\u0456 (\u0437 \u0434\u0456\u0439\u0441\u043D\u0438\u043C\u0438 \u0447\u0438\u0441\u043B\u0430\u043C\u0438) \u0434\u0430\u043D\u0438\u0439 \u0432\u0438\u0440\u0430\u0437 \u043D\u0435 \u043C\u0430\u0454 \u0441\u0435\u043D\u0441\u0443, \u0442\u0430\u043A \u044F\u043A \u043D\u0435\u043C\u0430\u0454 \u0447\u0438\u0441\u043B\u0430, \u044F\u043A\u0435, \u043F\u043E\u043C\u043D\u043E\u0436\u0435\u043D\u0435 \u043D\u0430 0, \u0434\u0430\u0454 \u0430 (\u0430 \u2260 0), \u0456 \u0442\u043E\u043C\u0443 \u043F\u043E\u0434\u0456\u043B \u043D\u0430 \u043D\u0443\u043B\u044C \u043D\u0435 \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043E. \u0406\u0441\u0442\u043E\u0440\u0438\u0447\u043D\u043E \u043E\u0434\u043D\u0435 \u0437 \u043F\u0435\u0440\u0448\u0438\u0445 \u043F\u043E\u0441\u0438\u043B\u0430\u043D\u044C \u043D\u0430 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0443 \u043D\u0435\u043C\u043E\u0436\u043B\u0438\u0432\u0456\u0441\u0442\u044C \u043F\u0440\u0438\u0441\u0432\u043E\u0454\u043D\u043D\u044F \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0430 / 0 \u043C\u0456\u0441\u0442\u0438\u0442\u044C\u0441\u044F \u0432 \u043A\u0440\u0438\u0442\u0438\u0446\u0456 \u0414\u0436\u043E\u0440\u0434\u0436\u0430 \u0411\u0435\u0440\u043A\u043B\u0456 \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u043E \u043C\u0430\u043B\u0438\u0445.\u0423 \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u0443\u0432\u0430\u043D\u043D\u0456 \u0441\u043F\u0440\u043E\u0431\u0430 \u0440\u043E\u0437\u0434\u0456\u043B\u0438\u0442\u0438 \u0447\u0438\u0441\u043B\u043E \u0437 \u0440\u0443\u0445\u043E\u043C\u043E\u044E \u043A\u043E\u043C\u043E\u044E \u043D\u0430 \u043D\u0443\u043B\u044C \u043F\u0440\u0438\u0437\u0432\u0435\u0434\u0435 \u0434\u043E + INF /-INF (\u0421\u0442\u0430\u043D\u0434\u0430\u0440\u0442 IEEE 754), \u043F\u0440\u043E\u0442\u0435, \u0437\u0430\u043B\u0435\u0436\u043D\u043E \u0432\u0456\u0434 \u043C\u043E\u0432\u0438 \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u0443\u0432\u0430\u043D\u043D\u044F \u0456 \u0442\u0438\u043F\u0443 \u0434\u0430\u043D\u0438\u0445 (\u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, \u0446\u0456\u043B\u0435 \u0447\u0438\u0441\u043B\u043E) \u0447\u0438\u0441\u043B\u0430, \u044F\u043A\u0435 \u0434\u0456\u043B\u044F\u0442\u044C \u043D\u0430 \u043D\u0443\u043B\u044C, \u043C\u043E\u0436\u0435: \u0437\u0433\u0435\u043D\u0435\u0440\u0443\u0432\u0430\u0442\u0438 \u0432\u0438\u043A\u043B\u044E\u0447\u0435\u043D\u043D\u044F, \u043F\u043E\u0432\u0456\u0434\u043E\u043C\u043B\u0435\u043D\u043D\u044F \u043F\u0440\u043E \u043F\u043E\u043C\u0438\u043B\u043A\u0443, \u0437\u0443\u043F\u0438\u043D\u043A\u0443 \u0432\u0438\u043A\u043E\u043D\u0443\u0432\u0430\u043D\u043E\u0457 \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u0438, \u0437\u0433\u0435\u043D\u0435\u0440\u0443\u0432\u0430\u0442\u0438 \u043F\u043E\u0437\u0438\u0442\u0438\u0432\u043D\u0443 \u0430\u0431\u043E \u043D\u0435\u0433\u0430\u0442\u0438\u0432\u043D\u0443 \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0456\u0441\u0442\u044C, \u0430\u0431"@uk , "Una divisi\u00F3 s'anomena divisi\u00F3 entre zero quan el divisor \u00E9s el nombre zero. Aquestes divisions es denoten a / 0 en la notaci\u00F3 habitual, on a \u00E9s el dividend. La q\u00FCesti\u00F3 de si aquesta expressi\u00F3 matem\u00E0tica rep un valor ben definit dep\u00E8n del context concret. En l'aritm\u00E8tica te\u00F2rica dels nombres reals la divisi\u00F3 entre zero no t\u00E9 sentit, i el seu \u00FAs acostuma a portar a paradoxes mentre que a les aplicacions matem\u00E0tiques, per exemple a l'enginyeria, s'aproxima que un nombre qualsevol dividit entre zero t\u00E9 el valor \"infinit\", \u221E. El fet de poder-li donar un valor concret (l'infinit) permet resoldre un gran nombre de problemes que altrament es quedarien sense soluci\u00F3 per haver quedat estancats, sense sentit i com a no-resolubles, en algun pas intermedi. Aquest valor t\u00E9 sentit f\u00EDsic quan es dona a va"@ca , "La division par z\u00E9ro consiste \u00E0 chercher le r\u00E9sultat qu'on obtiendrait en prenant z\u00E9ro comme diviseur. Ainsi, une division par z\u00E9ro s'\u00E9crirait x/0, o\u00F9 x serait le dividende (ou num\u00E9rateur). Dans les d\u00E9finitions usuelles de la multiplication, cette op\u00E9ration n'a pas de sens : elle contredit notamment la d\u00E9finition de la multiplication en tant que seconde loi de composition d'un corps, car z\u00E9ro (l'\u00E9l\u00E9ment neutre de l'addition) est un \u00E9l\u00E9ment absorbant pour la multiplication."@fr , "Delen door nul is bij het gewone rekenen niet toegestaan als rekenkundige bewerking. Het gaat om een deling waarbij de deler het getal nul is. Bij het gewone rekenen kan geen zinnige betekenis gegeven worden aan het resultaat van een deling door nul. Een ezelsbruggetje om te onthouden dat de bewerking niet mag is \"delen door nul is flauwekul\". In de wiskunde is het in bepaalde gevallen met limieten of andere getalstelsels mogelijk een zinvolle betekenis aan deling door nul te geven."@nl , "0\uC73C\uB85C \uB098\uB204\uAE30\uB294 \uC5B4\uB5A4 \uC22B\uC790\uB97C 0\uC73C\uB85C \uB098\uB204\uB294 \uB098\uB217\uC148\uC744 \uC218\uD589\uD558\uB294 \uAC83\uC774\uC9C0\uB9CC \uC77C\uBC18\uC801\uC73C\uB85C \uB098\uB217\uC148 \uC5F0\uC0B0\uC740 0\uC73C\uB85C \uB098\uB204\uB294 \uACBD\uC6B0\uB97C \uC815\uC758\uD558\uC9C0 \uC54A\uAE30 \uB54C\uBB38\uC5D0 \uC218\uD559\uC801 \uC758\uBBF8\uB294 \uC5C6\uB2E4. \uC5B4\uB5A4 \uC218\uC5D0 0\uC744 \uACF1\uD558\uBA74 0\uC774 \uB41C\uB2E4. \uBC18\uB300\uB85C, 0\uC744 0\uC73C\uB85C \uB098\uB204\uBA74 0\uC744 \uACF1\uD55C \uACB0\uACFC\uAC00 \uD56D\uC0C1 0\uC778\uB370, 0\uC774 \uC5B4\uB5A4 \uC218\uC5D0 0\uC744 \uACF1\uD55C \uACB0\uACFC\uC640 \uAC19\uC544\uC57C \uD558\uAE30 \uB54C\uBB38\uC774\uB2E4. \uADF8\uB7EC\uD55C \uC2DD\uC774 \uC131\uB9BD\uD558\uB294 \uC218\uB294 \uC5B4\uB5A4 \uC218\uC5D0 0\uC758 \uACF1\uD55C \uACB0\uACFC\uAC00 \uD56D\uC0C1 0\uC774\uBBC0\uB85C \uBAA8\uB4E0 \uC218\uAC00 \uB418\uC5B4 \uADF8 \uAC12\uC744 \uD558\uB098\uB85C \uC815\uD560 \uC218 \uC5C6\uB2E4. \uC774\uAC83\uC740 \uBBF8\uD574\uACB0 \uBB38\uC81C\uB098 \uC5F0\uAD6C \uAE08\uAE30 \uC0AC\uD56D\uC774 \uC544\uB2C8\uBA70, \uB2E8\uC9C0 \uAC12\uC744 \uC815\uC758\uD560 \uD544\uC694\uAC00 \uC5C6\uC744 \uBFD0\uC774\uB2E4. \uBA87\uBA87 \uC774\uB860(\uC608 : \uC774\uC6D0\uC218)\uAC00 \uC81C\uD55C\uC801\uC778 \uD615\uD0DC\uB85C x\u00F70\uC640 \uAC19\uC740 \uD615\uD0DC\uB97C \uC815\uC758\uD558\uAE30\uB3C4 \uD558\uBA70, \uB610\uB294 \uB2E8\uC21C\uD788 \uC22B\uC790 \uAC12\uC774 \uC544\uB2C8\uB77C \uBD84\uC218 \uC790\uCCB4\uB97C \uAE30\uD638\uB85C \uC0AC\uC6A9\uD560 \uACBD\uC6B0\uB3C4 \uC788\uB2E4. \uCEF4\uD4E8\uD130 \uD504\uB85C\uADF8\uB798\uBC0D\uC5D0\uC11C\uB294 \uC5B4\uB5A4 \uC218\uB97C 0\uC73C\uB85C \uB098\uB204\uB294 \uACBD\uC6B0 \uC624\uB958\uB97C \uBC1C\uC0DD\uC2DC\uD0A4\uAC70\uB098, NaN, \uB610\uB294 \uBB34\uD55C\uB300\uB97C \uBC18\uD658\uD55C\uB2E4. \uCEF4\uD4E8\uD130 \uD504\uB85C\uADF8\uB798\uBC0D\uC740 A\u00F7B\uB97C A\uC5D0 B\uB85C \uBA87 \uBC88 \uBE84 \uC218 \uC788\uB290\uB0D0\uB85C \uC778\uC2DD\uD558\uAE30 \uB54C\uBB38\uC774\uB2E4. \uC774 \uACBD\uC6B0 \uADF8 \uBAAB\uC740 \uBB34\uD55C\uB300\uAC00 \uB418\uBA70, \uB098\uBA38\uC9C0\uB294 \uC5C6\uB2E4. \uD558\uC9C0\uB9CC \uB300\uBD80\uBD84\uC758 \uD504\uB85C\uADF8\uB7A8\uC740 \uACC4\uC18D 0\uC744 \uBE7C \uBB34\uD55C \uB8E8\uD504\uC5D0 \uAC78\uB9AC\uB294 \uAC83\uC744 \uBC29\uC9C0\uD558\uAE30 \uC704\uD574\uC11C \uCC98\uC74C\uBD80\uD130 \uC9C0\uC815\uB41C \uAC12\uC744 \uBC18\uD658\uD55C\uB2E4."@ko , "\u0414\u0435\u043B\u0435\u043D\u0438\u0435 \u043D\u0430 \u043D\u043E\u043B\u044C \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u2014 \u0434\u0435\u043B\u0435\u043D\u0438\u0435, \u043F\u0440\u0438 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0434\u0435\u043B\u0438\u0442\u0435\u043B\u044C \u0440\u0430\u0432\u0435\u043D \u043D\u0443\u043B\u044E. \u0422\u0430\u043A\u043E\u0435 \u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E \u0437\u0430\u043F\u0438\u0441\u0430\u043D\u043E \u043A\u0430\u043A , \u0433\u0434\u0435 \u2014 \u0434\u0435\u043B\u0438\u043C\u043E\u0435."@ru ; rdfs:seeAlso . @prefix foaf: . dbr:Division_by_zero foaf:depiction , , . @prefix dcterms: . dbr:Division_by_zero dcterms:subject . @prefix dbc: . dbr:Division_by_zero dcterms:subject dbc:Infinity , , dbc:Mathematical_fallacies , dbc:Mathematical_analysis , dbc:Computer_arithmetic , , dbc:Computer_errors ; dbo:wikiPageID 185663 ; dbo:wikiPageRevisionID 1123857915 ; dbo:wikiPageWikiLink dbr:Extended_real_number_line , , dbr:Ring_of_integers , , dbr:Fallacy , dbr:Algebra , dbr:Zero_to_the_power_of_zero , dbr:One-point_compactification , , , , , dbr:Tangent_function , dbr:Computer_programming , dbr:IEEE_754 , dbr:Point_at_infinity , dbr:Zero_divisor , dbr:Mathematics , dbr:Calculator , dbr:Integral_domain , , dbc:Infinity , dbr:Zero_ring , dbr:Extended_real_line , , dbr:Ted_Chiang , dbr:SageMath , dbr:Exception_handling , dbr:Equivalence_relation , , dbr:Trigonometry , dbr:Division_ring , dbr:Ordered_pair , dbr:Mathematica , dbr:Inverse_trigonometric_functions , dbr:One-sided_limit , dbr:Transitive_relation , dbr:Skew_field , dbc:Mathematical_fallacies , , , dbr:Infinitesimal_calculus , dbr:George_Berkeley , dbr:Alfred_Tarski , , dbr:Riemann_sphere , dbr:Floating_point , dbr:Infinity , dbr:Arithmetic_underflow , dbr:Hewlett_Packard , , dbr:Cauchy_principal_value , , dbr:Singular_support , dbr:Fixed-point_arithmetic , dbr:Indeterminate_form , dbr:Infinitesimal , dbr:Mathematical_model , dbr:The_Analyst , dbc:Mathematical_analysis , , dbr:Floating-point_unit , , dbr:Rational_number , , dbr:Commutative_ring , , , dbc:Computer_arithmetic , , dbr:Programming_language , dbr:Well-defined , dbr:Elementary_algebra , dbr:Microsoft_Math , dbr:Texas_Instruments , dbr:Elementary_arithmetic , dbr:Formal_calculation , , , dbr:Anglo-Irish_people , dbr:Brahmagupta , dbr:Fractions , dbr:Error_message , dbr:Asymptote , dbr:If_statement , dbr:Wheel_theory , dbc:Computer_errors , dbr:Linear_algebra , dbr:NaN , dbr:IEEE_floating-point_standard , dbr:Equivalence_class , dbr:Projectively_extended_real_line , dbr:Surreal_number , dbr:Floating-point_arithmetic , , , , dbr:Arithmetic , dbr:Limit_of_a_function , dbr:Complex_number , , , dbr:Computer , dbr:Complex_plane , dbr:Undefined_behavior , dbr:Binary_relation , dbr:Hyperreal_number . @prefix ns9: . dbr:Division_by_zero dbo:wikiPageWikiLink ns9:_The_Biography_of_a_Dangerous_Idea , dbr:Patrick_Suppes , dbr:Trivial_ring , dbr:Cancellative_semigroup , dbr:Remainder , dbr:Integer , , dbr:Peano_axioms , dbr:Complex_analysis , dbr:Invalid_proof , dbr:Defined_and_undefined , dbr:Real_number , , dbr:Signed_zero , ; dbo:wikiPageExternalLink , ; owl:sameAs . @prefix dbpedia-no: . dbr:Division_by_zero owl:sameAs dbpedia-no:Divisjon_med_null . @prefix dbpedia-pl: . dbr:Division_by_zero owl:sameAs dbpedia-pl:Dzielenie_przez_zero , . @prefix wikidata: . dbr:Division_by_zero owl:sameAs wikidata:Q848539 . @prefix dbpedia-simple: . dbr:Division_by_zero owl:sameAs dbpedia-simple:Division_by_zero , , , , , . @prefix dbpedia-sk: . dbr:Division_by_zero owl:sameAs dbpedia-sk:Delenie_nulou , , . @prefix dbpedia-it: . dbr:Division_by_zero owl:sameAs dbpedia-it:Divisione_per_zero , , . @prefix yago-res: . dbr:Division_by_zero owl:sameAs yago-res:Division_by_zero , , . @prefix dbpedia-nl: . dbr:Division_by_zero owl:sameAs dbpedia-nl:Delen_door_nul , . @prefix dbpedia-fi: . dbr:Division_by_zero owl:sameAs dbpedia-fi:Nollalla_jakaminen , , , . @prefix dbpedia-de: . dbr:Division_by_zero owl:sameAs dbpedia-de:Division_durch_null . @prefix ns20: . dbr:Division_by_zero owl:sameAs ns20:Paghahati_sa_sero , , . @prefix dbpedia-gd: . dbr:Division_by_zero owl:sameAs dbpedia-gd:Roinn_le_neoni , , , . @prefix dbpedia-sv: . dbr:Division_by_zero owl:sameAs dbpedia-sv:Division_med_noll , , . @prefix dbp: . @prefix dbt: . dbr:Division_by_zero dbp:wikiPageUsesTemplate dbt:Math , dbt:Citation , dbt:Unreferenced_section , dbt:See_also , dbt:Mvar , dbt:Doi-inline , dbt:Short_description , dbt:More_footnotes , dbt:Reflist , dbt:Refend , dbt:Refbegin , dbt:Sfrac , dbt:Block_indent , dbt:Em_dash , dbt:Cite_web , dbt:Portal , dbt:ISBN , dbt:Other_uses , dbt:Details ; dbo:thumbnail . @prefix xsd: . dbr:Division_by_zero dbp:em "1.2"^^xsd:double ; dbp:text "Let .\nMultiply by to get\n \nSubtract from each side to get\n\nDivide both sides by \n\nwhich simplifies to\n\nBut, since ,\n\nand therefore"@en ; dbo:abstract "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 \u0635\u0641\u0631 \u0647\u064A \u0627\u0644\u0642\u0633\u0645\u0629 \u0627\u0644\u062A\u064A \u064A\u0643\u0648\u0646 \u0641\u064A\u0647\u0627 \u0627\u0644\u0645\u0642\u0633\u0648\u0645 \u0639\u0644\u064A\u0647 (\u0627\u0644\u0645\u0642\u0627\u0645) \u0645\u0633\u0627\u0648\u064A\u0627 \u0644\u0635\u0641\u0631.\u063A\u0627\u0644\u0628\u0627\u064B \u0645\u0627 \u062A\u0643\u062A\u0628 \u0628\u0627\u0644\u0635\u064A\u063A\u0629 (\u06330) \u062D\u064A\u062B \u0633 \u0647\u064A \u0627\u0644\u0645\u0642\u0633\u0648\u0645 (\u0627\u0644\u0628\u0633\u0637). \u0648\u0647\u0630\u0647 \u0627\u0644\u0642\u0633\u0645\u0629 \u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u062D\u0633\u0627\u0628\u064A\u0629 \u0627\u0644\u0639\u0627\u062F\u064A\u0629 \u0644\u0627\u0645\u0639\u0646\u0649 \u0644\u0647\u0627 \u0648\u0644\u0627\u064A\u0648\u062C\u062F \u0639\u062F\u062F \u0639\u0646\u062F \u0636\u0631\u0628\u0647 \u0628\u0635\u0641\u0631\u060C \u064A\u0639\u0637\u064A \u0627\u0644\u0642\u064A\u0645\u0629 \u0633 (\u0628\u0627\u0639\u062A\u0628\u0627\u0631 \u0623\u0646 \u0633 \u0644\u0627\u062A\u0633\u0627\u0648\u064A \u0627\u0644\u0635\u0641\u0631) \u0648\u0644\u0630\u0644\u0643 \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 \u0635\u0641\u0631 \u0647\u064A \u0639\u0645\u0644\u064A\u0629 \u063A\u064A\u0631 \u0645\u064F\u0639\u0631\u0641\u0629.\u0648\u0628\u0645\u0627 \u0623\u0646 \u0623\u064A \u0639\u062F\u062F \u064A\u064F\u0636\u0631\u0628 \u0641\u064A \u0635\u0641\u0631 \u064A\u0639\u0637\u064A \u0635\u0641\u0631\u0627\u060C \u0641\u0625\u0646 \u0627\u0644\u0635\u064A\u063A\u0629 \u0623\u064A\u0636\u0627\u064B \u0647\u064A \u0627\u0644\u0623\u062E\u0631\u0649 \u063A\u064A\u0631 \u0645\u064F\u0639\u0631\u0641\u0629\u060C \u0648\u0641\u064A \u062D\u0627\u0644\u0629 \u0648\u062C\u0648\u062F\u0647\u0627 \u0635\u064A\u063A\u0629 \u0646\u0647\u0627\u064A\u0629\u064D \u0628\u0627\u0644\u062A\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062A\u0643\u0627\u0645\u0644\u060C \u0641\u0647\u064A \u0635\u064A\u063A\u0629 \u063A\u064A\u0631 \u0645\u062D\u062F\u062F\u0629. \u0623\u0642\u062F\u0645 \u0627\u0644\u0645\u0631\u0627\u062C\u0639 \u0627\u0644\u062A\u0627\u0631\u064A\u062E\u064A\u0629 \u0627\u0644\u062A\u064A \u0630\u0643\u0631\u062A \u0627\u0633\u062A\u062D\u0627\u0644\u0629 \u062A\u0639\u064A\u064A\u0646 \u0642\u064A\u0645\u0629 \u0644\u0644\u0639\u0645\u0644\u064A\u0629 (\u06330) \u0631\u064A\u0627\u0636\u064A\u0627\u064B \u0645\u0648\u062C\u0648\u062F\u0629 \u0641\u064A \u0643\u062A\u0627\u0628 \u0627\u0644\u0645\u062D\u0644\u0644 \u0645\u0646 \u062A\u0623\u0644\u064A\u0641 \u062C\u0648\u0631\u062C \u0628\u064A\u0631\u0643\u0644\u064A \u0648\u0647\u0648 \u0646\u0642\u062F \u0644\u062D\u0633\u0627\u0628 \u0627\u0644\u062A\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062A\u0643\u0627\u0645\u0644 \u0627\u0644\u0645\u062A\u0646\u0627\u0647\u064A \u0641\u064A \u0627\u0644\u0635\u063A\u0631."@ar , "In matematica, una divisione per zero \u00E8 una divisione della forma . Il risultato non esiste, poich\u00E9 l'espressione \u00E8 priva di significato in aritmetica e in algebra. \u00C8 piuttosto diffusa l'errata opinione per cui il valore di sarebbe (infinito). Questa affermazione fa riferimento, in modo non del tutto corretto, a un'interpretazione della divisione in termini della teoria dei limiti dell'analisi matematica. Un primissimo riferimento registrato dell'impossibilit\u00E0 di assegnare un risultato alla divisione per zero si ha nella critica al calcolo infinitesimale contenuta in The Analyst di George Berkeley. Esistono comunque particolari strutture matematiche all'interno delle quali la divisione per zero potrebbe essere definita in modo consistente (per esempio, la sfera di Riemann). In informatica, e in particolare nell'implementazione elettronica dell'aritmetica nelle ALU dei processori, una divisione per zero causa un'eccezione (o trap) hardware e di conseguenza (in genere) la terminazione del programma che ha tentato l'operazione. Nei linguaggi interpretati come , un tentativo di eseguire una divisione per zero viene generalmente intercettato dall'interprete, che segnala l'anomalia (per esempio attraverso una eccezione) senza tentare di eseguire l'operazione. In JavaScript, al contrario, il risultato \u00E8 Infinity."@it , "Na matem\u00E1tica, uma divis\u00E3o \u00E9 chamada divis\u00E3o por zero se o divisor \u00E9 zero. Tal divis\u00E3o pode ser formalmente expressada como = no qual a \u00E9 o dividendo. Um valor bem definido para essa express\u00E3o depende do contexto matem\u00E1tico. Para a aritm\u00E9tica com n\u00FAmeros reais, a express\u00E3o n\u00E3o possui significado.Se considerarmos no gr\u00E1fico de 1/x a quase-ass\u00EDntota com um infinitesimal \u00E0 direita do zero e um infinitesimal \u00E0 esquerda do zero, a reta passa por (0,0), pelo teorema do valor intermedi\u00E1rio. (Q.E.D) Em programa\u00E7\u00E3o, uma tentativa de dividir um n\u00FAmero de ponto flutuante por zero deve resultar em infinito de acordo com o padr\u00E3o IEEE 754 para pontos flutuantes. No entanto, dependendo do ambiente de programa\u00E7\u00E3o e do tipo de n\u00FAmero sendo dividido por zero (como o inteiro, por exemplo), \u00E9 poss\u00EDvel que: seja gerada uma exce\u00E7\u00E3o, seja produzida uma mensagem de erro, fa\u00E7a o programa terminar, resulte em infinito positivo ou negativo ou resulte em um valor especial n\u00E3o num\u00E9rico (NaN)."@pt , "D\u011Blen\u00ED nulou je v matematice takov\u00E9 d\u011Blen\u00ED, p\u0159i n\u011Bm\u017E je d\u011Blitel nula. M\u016F\u017Ee b\u00FDt zaps\u00E1no jako , kde a je d\u011Blenec. V oborech re\u00E1ln\u00FDch ani komplexn\u00EDch \u010D\u00EDsel nem\u00E1 takov\u00E9 d\u011Blen\u00ED smysl \u2013 nula je jedin\u00E9 \u010D\u00EDslo, kter\u00FDm nelze d\u011Blit. V oboru komplexn\u00EDch \u010D\u00EDsel roz\u0161\u00ED\u0159en\u00FDch o (komplexn\u00ED) nekone\u010Dno je definov\u00E1no pro v\u0161echny nenulov\u00E9 d\u011Blence jako . P\u0159i d\u011Blen\u00ED v plovouc\u00ED \u0159\u00E1dov\u00E9 \u010D\u00E1rce m\u016F\u017Ee b\u00FDt v\u00FDsledkem speci\u00E1ln\u00ED hodnota not a number (nen\u00ED \u010D\u00EDslo) nebo nekone\u010Dno."@cs , "\u0414\u0435\u043B\u0435\u043D\u0438\u0435 \u043D\u0430 \u043D\u043E\u043B\u044C \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u2014 \u0434\u0435\u043B\u0435\u043D\u0438\u0435, \u043F\u0440\u0438 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0434\u0435\u043B\u0438\u0442\u0435\u043B\u044C \u0440\u0430\u0432\u0435\u043D \u043D\u0443\u043B\u044E. \u0422\u0430\u043A\u043E\u0435 \u0434\u0435\u043B\u0435\u043D\u0438\u0435 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E \u0437\u0430\u043F\u0438\u0441\u0430\u043D\u043E \u043A\u0430\u043A , \u0433\u0434\u0435 \u2014 \u0434\u0435\u043B\u0438\u043C\u043E\u0435."@ru , "Dzielenie przez zero \u2013 dzielenie, w kt\u00F3rym dzielnik jest zerem; jako takie nie ma ono sensu liczbowego, przez co bywa \u017Ar\u00F3d\u0142em b\u0142\u0119d\u00F3w obliczeniowych, cz\u0119sto ukrytych. Prostym przyk\u0142adem b\u0142\u0119du wynik\u0142ego z dzielenia przez zero jest nast\u0119puj\u0105cy: niech i w\u00F3wczas skoro to r\u00F3wnie\u017C oraz a ze wzoru na r\u00F3\u017Cnic\u0119 kwadrat\u00F3w jest Dziel\u0105c stronami przez uzyskuje si\u0119 co jest r\u00F3wnowa\u017Cne a wi\u0119c sk\u0105d Otrzymana sprzeczno\u015B\u0107 wynika z zastosowania dzielenia przez"@pl , "\u0414\u0456\u043B\u0435\u043D\u043D\u044F \u043D\u0430 \u043D\u0443\u043B\u044C \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456 \u2014 \u0434\u0456\u043B\u0435\u043D\u043D\u044F, \u043F\u0440\u0438 \u044F\u043A\u043E\u043C\u0443 \u0434\u0456\u043B\u044C\u043D\u0438\u043A \u0434\u043E\u0440\u0456\u0432\u043D\u044E\u0454 \u043D\u0443\u043B\u044E. \u0422\u0430\u043A\u0438\u0439 \u043F\u043E\u0434\u0456\u043B \u043C\u043E\u0436\u0435 \u0431\u0443\u0442\u0438 \u0444\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u043E \u0437\u0430\u043F\u0438\u0441\u0430\u043D\u043E \u0430 / 0, \u0434\u0435 \u0430 \u2014 \u0446\u0435 \u0434\u0456\u043B\u0435\u043D\u0435.\u0423 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u0456\u0439 \u0430\u0440\u0438\u0444\u043C\u0435\u0442\u0438\u0446\u0456 (\u0437 \u0434\u0456\u0439\u0441\u043D\u0438\u043C\u0438 \u0447\u0438\u0441\u043B\u0430\u043C\u0438) \u0434\u0430\u043D\u0438\u0439 \u0432\u0438\u0440\u0430\u0437 \u043D\u0435 \u043C\u0430\u0454 \u0441\u0435\u043D\u0441\u0443, \u0442\u0430\u043A \u044F\u043A \u043D\u0435\u043C\u0430\u0454 \u0447\u0438\u0441\u043B\u0430, \u044F\u043A\u0435, \u043F\u043E\u043C\u043D\u043E\u0436\u0435\u043D\u0435 \u043D\u0430 0, \u0434\u0430\u0454 \u0430 (\u0430 \u2260 0), \u0456 \u0442\u043E\u043C\u0443 \u043F\u043E\u0434\u0456\u043B \u043D\u0430 \u043D\u0443\u043B\u044C \u043D\u0435 \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043E. \u0406\u0441\u0442\u043E\u0440\u0438\u0447\u043D\u043E \u043E\u0434\u043D\u0435 \u0437 \u043F\u0435\u0440\u0448\u0438\u0445 \u043F\u043E\u0441\u0438\u043B\u0430\u043D\u044C \u043D\u0430 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0443 \u043D\u0435\u043C\u043E\u0436\u043B\u0438\u0432\u0456\u0441\u0442\u044C \u043F\u0440\u0438\u0441\u0432\u043E\u0454\u043D\u043D\u044F \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0430 / 0 \u043C\u0456\u0441\u0442\u0438\u0442\u044C\u0441\u044F \u0432 \u043A\u0440\u0438\u0442\u0438\u0446\u0456 \u0414\u0436\u043E\u0440\u0434\u0436\u0430 \u0411\u0435\u0440\u043A\u043B\u0456 \u043E\u0431\u0447\u0438\u0441\u043B\u0435\u043D\u043D\u044F \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u043E \u043C\u0430\u043B\u0438\u0445.\u0423 \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u0443\u0432\u0430\u043D\u043D\u0456 \u0441\u043F\u0440\u043E\u0431\u0430 \u0440\u043E\u0437\u0434\u0456\u043B\u0438\u0442\u0438 \u0447\u0438\u0441\u043B\u043E \u0437 \u0440\u0443\u0445\u043E\u043C\u043E\u044E \u043A\u043E\u043C\u043E\u044E \u043D\u0430 \u043D\u0443\u043B\u044C \u043F\u0440\u0438\u0437\u0432\u0435\u0434\u0435 \u0434\u043E + INF /-INF (\u0421\u0442\u0430\u043D\u0434\u0430\u0440\u0442 IEEE 754), \u043F\u0440\u043E\u0442\u0435, \u0437\u0430\u043B\u0435\u0436\u043D\u043E \u0432\u0456\u0434 \u043C\u043E\u0432\u0438 \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u0443\u0432\u0430\u043D\u043D\u044F \u0456 \u0442\u0438\u043F\u0443 \u0434\u0430\u043D\u0438\u0445 (\u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, \u0446\u0456\u043B\u0435 \u0447\u0438\u0441\u043B\u043E) \u0447\u0438\u0441\u043B\u0430, \u044F\u043A\u0435 \u0434\u0456\u043B\u044F\u0442\u044C \u043D\u0430 \u043D\u0443\u043B\u044C, \u043C\u043E\u0436\u0435: \u0437\u0433\u0435\u043D\u0435\u0440\u0443\u0432\u0430\u0442\u0438 \u0432\u0438\u043A\u043B\u044E\u0447\u0435\u043D\u043D\u044F, \u043F\u043E\u0432\u0456\u0434\u043E\u043C\u043B\u0435\u043D\u043D\u044F \u043F\u0440\u043E \u043F\u043E\u043C\u0438\u043B\u043A\u0443, \u0437\u0443\u043F\u0438\u043D\u043A\u0443 \u0432\u0438\u043A\u043E\u043D\u0443\u0432\u0430\u043D\u043E\u0457 \u043F\u0440\u043E\u0433\u0440\u0430\u043C\u0438, \u0437\u0433\u0435\u043D\u0435\u0440\u0443\u0432\u0430\u0442\u0438 \u043F\u043E\u0437\u0438\u0442\u0438\u0432\u043D\u0443 \u0430\u0431\u043E \u043D\u0435\u0433\u0430\u0442\u0438\u0432\u043D\u0443 \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0456\u0441\u0442\u044C, \u0430\u0431\u043E \u043F\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u0434\u043E \u0441\u043F\u0435\u0446\u0456\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u043D\u0435\u0447\u0438\u0441\u043B\u043E\u0432\u043E\u0433\u043E \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F\u043C (NaN)."@uk , "La division par z\u00E9ro consiste \u00E0 chercher le r\u00E9sultat qu'on obtiendrait en prenant z\u00E9ro comme diviseur. Ainsi, une division par z\u00E9ro s'\u00E9crirait x/0, o\u00F9 x serait le dividende (ou num\u00E9rateur). Dans les d\u00E9finitions usuelles de la multiplication, cette op\u00E9ration n'a pas de sens : elle contredit notamment la d\u00E9finition de la multiplication en tant que seconde loi de composition d'un corps, car z\u00E9ro (l'\u00E9l\u00E9ment neutre de l'addition) est un \u00E9l\u00E9ment absorbant pour la multiplication."@fr , "Una divisi\u00F3 s'anomena divisi\u00F3 entre zero quan el divisor \u00E9s el nombre zero. Aquestes divisions es denoten a / 0 en la notaci\u00F3 habitual, on a \u00E9s el dividend. La q\u00FCesti\u00F3 de si aquesta expressi\u00F3 matem\u00E0tica rep un valor ben definit dep\u00E8n del context concret. En l'aritm\u00E8tica te\u00F2rica dels nombres reals la divisi\u00F3 entre zero no t\u00E9 sentit, i el seu \u00FAs acostuma a portar a paradoxes mentre que a les aplicacions matem\u00E0tiques, per exemple a l'enginyeria, s'aproxima que un nombre qualsevol dividit entre zero t\u00E9 el valor \"infinit\", \u221E. El fet de poder-li donar un valor concret (l'infinit) permet resoldre un gran nombre de problemes que altrament es quedarien sense soluci\u00F3 per haver quedat estancats, sense sentit i com a no-resolubles, en algun pas intermedi. Aquest valor t\u00E9 sentit f\u00EDsic quan es dona a variables corresponents a magnituds f\u00EDsiques a l'enginyeria. En inform\u00E0tica, la divisi\u00F3 entera entre zero pot causar la interrupci\u00F3 d'un programa i generalment el seu resultat \u00E9s el codi NaN (No Num\u00E8ric, de l'angl\u00E8s: Not a Number)."@ca , "\u30BC\u30ED\u9664\u7B97\uFF08\u30BC\u30ED\u3058\u3087\u3055\u3093\u3001\u82F1\u8A9E: division by zero\uFF09\u3068\u306F\u30010\u3067\u9664\u3059\u5272\u308A\u7B97\u306E\u3053\u3068\u3067\u3042\u308B\u3002\u3053\u306E\u3088\u3046\u306A\u9664\u7B97\u306F\u9664\u3055\u308C\u308B\u6570\u3092a\u3068\u3059\u308B\u306A\u3089\u3070\u3001\u5F62\u5F0F\u4E0A\u306F a/0\u3068\u66F8\u304F\u3053\u3068\u304C\u3067\u304D\u308B\u304C\u3001\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u3053\u306E\u3088\u3046\u306A\u5F0F\u3092\u77DB\u76FE\u306A\u304F\u5B9A\u7FA9\u3059\u308B\u3053\u3068\u306F\u3067\u304D\u306A\u3044\u3002\u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u306E\u6570\u5024\u8A08\u7B97\u306B\u304A\u3044\u3066\u30BC\u30ED\u9664\u7B97\u304C\u767A\u751F\u3057\u305F\u5834\u5408\u3001\u7121\u9650\u5927\u3084\u30BC\u30ED\u9664\u7B97\u3092\u610F\u5473\u3059\u308B\u30B7\u30F3\u30DC\u30EB\u3067\u7F6E\u304D\u63DB\u3048\u308B\u3001\u4F8B\u5916\u3068\u3057\u3066\u51E6\u7406\u3059\u308B\u306A\u3069\u306E\u5BFE\u5FDC\u304C\u53D6\u3089\u308C\u308B\u304B\u3001\u767A\u751F\u3057\u305F\u6642\u70B9\u3067\u51E6\u7406\u304C\u7834\u7DBB\u3059\u308B\uFF08\u30B7\u30B9\u30C6\u30E0\u30A8\u30E9\u30FC\u3068\u306A\u308B\uFF09\u3002 \u73FE\u4EE3\u6570\u5B66\u306E\u89B3\u70B9\u3067\u306F\u3001\u3044\u304B\u306A\u308B\u30A2\u30D7\u30ED\u30FC\u30C1\u304B\u3089\u5B9A\u7FA9\u3092\u8A66\u307F\u3088\u3046\u3068\u3082\u5FC5\u305A\u7834\u7DBB\u306B\u81F3\u308B\u3002\u7D50\u5C40\u3001\u300C\u5024\u3092\u5B9A\u7FA9\u3057\u5F97\u306A\u3044\u305F\u3081\u3001\u8A08\u7B97\u306F\u4E0D\u53EF\u80FD\u3067\u3042\u308B\u300D\u3068\u7406\u89E3\u3059\u308B\u4ED6\u306A\u3044\u6982\u5FF5\u3067\u3042\u308A\u3001\u305D\u308C\u4EE5\u4E0A\u306E\u8B70\u8AD6\u306B\u3088\u3063\u3066\u6570\u5B66\u7684\u306B\u6709\u7528\u306A\u7D50\u679C\u304C\u5F97\u3089\u308C\u308B\u3053\u3068\u306F\u671F\u5F85\u3067\u304D\u306A\u3044\u3002\u3057\u304B\u3057\u3001\u6982\u5FF5\u81EA\u4F53\u306F\u6975\u3081\u3066\u521D\u7B49\u7684\u306A\u77E5\u8B58\u3067\u6349\u3048\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u305F\u3081\u3001\u3057\u3070\u3057\u3070\u6570\u5B66\u7684\u539F\u5247\u3092\u524D\u63D0\u3068\u3057\u3066\u3044\u306A\u3044\u8B70\u8AD6\u3084\u72EC\u81EA\u306A\u89E3\u91C8\u304C\u5C55\u958B\u3055\u308C\u308B\u3053\u3068\u304C\u3042\u308B\u3002\u305D\u306E\u3088\u3046\u306A\u8B70\u8AD6\u3084\u89E3\u91C8\u306F\u3044\u305A\u308C\u3082\u8AD6\u7406\u7684\u7834\u7DBB\u3092\u542B\u3080\u304B\u4FE1\u983C\u6027\u306E\u3042\u308B\u6839\u62E0\u3092\u4F34\u308F\u306A\u3044\u70BA\u3001\u5B66\u8853\u7684\u306A\u8A55\u4FA1\u306E\u4F59\u5730\u3092\u307B\u3068\u3093\u3069\u6709\u3057\u306A\u3044\u3002 \u30BC\u30ED\u9664\u7B97\u306E\u5B9A\u7FA9\u53EF\u80FD\u6027\u306B\u95A2\u3059\u308B\u8AA4\u3063\u305F\u7406\u89E3\u306E\u5178\u578B\u3068\u3057\u3066\u306F\u3001\u4F8B\u3048\u3070\u306E\u3088\u3046\u306A\u6975\u9650\u304C\u901A\u5E38\u300C+\u221E\u300D\u3068\u3044\u3046\u8A18\u53F7\u3067\u8868\u73FE\u3055\u308C\u308B\u3053\u3068\u304B\u3089\u3001\u300C\u30BC\u30ED\u9664\u7B97\u306E\u5024\u3092\u221E\u3067\u5B9A\u7FA9\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u300D\u306A\u3069\u3068\u8AA4\u89E3\u3057\u3001\u3053\u308C\u3092\u8D77\u70B9\u3068\u3057\u3066\u3001\u3042\u308B\u7A2E\u306E\u96C6\u5408\u306B\u304A\u3044\u3066\u306F\u30BC\u30ED\u9664\u7B97\u306E\u5B9A\u7FA9\u53EF\u80FD\u6027\u304C\u6392\u9664\u3055\u308C\u306A\u3044\u3001\u3068\u3044\u3046\u65E8\u306E\u89E3\u91C8\u3092\u5C55\u958B\u3059\u308B\u30B1\u30FC\u30B9\u3067\u3042\u308B\u3002\u3059\u306A\u308F\u3061\u3001\u300C = +\u221E\u300D\u306E\u3088\u3046\u306A\u3001\u6975\u9650\u306B\u3064\u3044\u3066\u306E\u5358\u306A\u308B\u300C\u8A18\u53F7\u7684\u306A\u8868\u73FE\u5F0F\u300D\u3092\u300C\u7B49\u5F0F\u300D\uFF081/0 = +\u221E\uFF09\u3068\u3057\u3066\u6210\u7ACB\u3055\u305B\u308B\u305F\u3081\u306B\u5B9A\u7FA9\u3092\u62E1\u5F35\u3057\u3088\u3046\u3068\u8A66\u307F\u308B\u3082\u306E\u3067\u3042\u308B\u304C\u3001\u3044\u305A\u308C\u3082\u57FA\u790E\u7684\u306A\u89B3\u70B9\u306B\u304A\u3044\u3066\u7834\u7DBB\u3092\u62DB\u3044\u3066\u3057\u307E\u3044\u3001\u7D50\u5C40\u3001\u30BC\u30ED\u9664\u7B97\u306E\u5B9A\u7FA9\u53EF\u80FD\u6027\u3092\u751F\u307F\u51FA\u3059\u3053\u3068\u306B\u306F\u7E4B\u304C\u3089\u306A\u3044\u3002\u4F8B\u3048\u3070\u3001\u5B9F\u6570\u4F53\uFF08\u307E\u305F\u306F\u8907\u7D20\u6570\u4F53\uFF09\u306B\u7121\u9650\u9060\u70B9\u3092\u4ED8\u52A0\u3057\u305F\u96C6\u5408\u306B\u304A\u3051\u308B\u30BC\u30ED\u9664\u7B97\u306E\u5B9A\u7FA9\u53EF\u80FD\u6027\u3092\u8B70\u8AD6\u3059\u308B\u89E3\u91C8\u306B\u3064\u3044\u3066\u306F\u3001\u7121\u9650\u9060\u70B9\u306E\u4ED8\u52A0\u306B\u3088\u3063\u3066\u305D\u308C\u3089\u306E\u96C6\u5408\u306E\u4EE3\u6570\u69CB\u9020\u304C\u7834\u58CA\u3055\u308C\u308B\uFF08\u3059\u306A\u308F\u3061\u3001\u65E2\u5B58\u306E\u4EE3\u6570\u69CB\u9020\u304C\u7DAD\u6301\u3067\u304D\u306A\u3044\uFF09\u3053\u3068\u304C\u76F4\u3061\u306B\u78BA\u8A8D\u3067\u304D\u308B\u305F\u3081\u3001\u9664\u7B97\u306F\u304A\u308D\u304B\u52A0\u6CD5\u3084\u4E57\u6CD5\u3068\u3044\u3046\u6700\u4F4E\u9650\u306E\u6F14\u7B97\u3059\u3089\u826F\u304F\u5B9A\u7FA9\u3055\u308C\u306A\u3044\u96C6\u5408\u3067\u3042\u308B\u3068\u3044\u3046\u4E8B\u5B9F\u306B\u81F3\u308B\u3002\u7D50\u5C40\u3001\u300C1/0 = +\u221E\u300D\u306E\u3088\u3046\u306A\u5F0F\u306F\u3001\u6975\u9650\u8A08\u7B97\u306E\u5B9A\u7FA9\u3092\u8868\u73FE\u3059\u308B\u30B7\u30F3\u30DC\u30EB\u3068\u3057\u3066\u7406\u89E3\u3067\u304D\u308B\u3060\u3051\u3067\u3001\u3042\u308B\u7A2E\u306E\u9664\u7B97\u306E\u5024\u306B\u3064\u3044\u3066\u306E\u5B9A\u7FA9\u53EF\u80FD\u6027\u3092\u793A\u5506\u3059\u308B\u3082\u306E\u3067\u306F\u306A\u3044\u3002 \u30B3\u30F3\u30D4\u30E5\u30FC\u30BF\u306A\u3069\u8A08\u7B97\u6A5F\u306B\u304A\u3044\u3066\u3001\u30BC\u30ED\u9664\u7B97\u306F\u3001\u6D6E\u52D5\u5C0F\u6570\u70B9\u6570\u306E\u6271\u3044\u306B\u95A2\u3059\u308B\u6A19\u6E96\u3067\u3042\u308BIEEE 754\u3067\u306F\u3001\u6570\u3068\u306F\u7570\u306A\u308B\u7121\u9650\u5927\u3092\u8868\u73FE\u3059\u308B\u3082\u306E\u304C\u7D50\u679C\u3068\u306A\u308B\u3002 \u3057\u304B\u3057\u3001\u6D6E\u52D5\u5C0F\u6570\u70B9\u4EE5\u5916\u306E\u6570\u5024\u578B\uFF08\u6574\u6570\u578B\u306A\u3069\uFF09\u306B\u304A\u3044\u3066\u306F\u591A\u304F\u306E\u5834\u5408\u7121\u9650\u5927\u306B\u76F8\u5F53\u3059\u308B\u5024\u306F\u5B9A\u7FA9\u3055\u308C\u3066\u304A\u3089\u305A\u3001\u307E\u305F\u3044\u304F\u3064\u304B\u306E\u9664\u7B97\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u306E\u5358\u7D14\u306A\u5B9F\u88C5\uFF08\u53D6\u5C3D\u3057\u6CD5\u306A\u3069\uFF09\u306B\u304A\u3044\u3066\u306F\u7121\u9650\u30EB\u30FC\u30D7\u306B\u9665\u308A\u304B\u306D\u306A\u3044\u306A\u3069\u6F14\u7B97\u51E6\u7406\u306E\u4E2D\u3067\u3082\u7279\u7570\u306A\u3075\u308B\u307E\u3044\u3068\u306A\u308B\u305F\u3081\u3001\u6F14\u7B97\u524D\u306B\u30BC\u30ED\u9664\u7B97\u4F8B\u5916\u3092\u767A\u751F\u3055\u305B\u308B\u3053\u3068\u3067\u8A08\u7B97\u305D\u306E\u3082\u306E\u3092\u884C\u308F\u305B\u306A\u3044\u304B\u3001\u4FBF\u5B9C\u4E0A\u578B\u304C\u8868\u73FE\u3067\u304D\u308B\u6700\u5927\u306E\u6570\u5024\u3001\u3042\u308B\u3044\u306F\u30BC\u30ED\u3092\u8FD4\u3059\u306A\u3069\u306E\u7279\u6B8A\u306A\u51E6\u7406\u3068\u3055\u308C\u308B\u5834\u5408\u304C\u591A\u3044\uFF08\u5F8C\u8FF0\uFF09\u3002 \u8A08\u7B97\u5C3A\u3067\u306F\u3001\u5BFE\u6570\u5C3A\u306B\u306F0\u306B\u76F8\u5F53\u3059\u308B\u4F4D\u7F6E\u304C\u5B58\u5728\u3057\u306A\u3044\uFF08\u7121\u9650\u306E\u5F7C\u65B9\u3067\u3042\u308B\uFF09\u305F\u3081\u8A08\u7B97\u4E0D\u53EF\u80FD\u3067\u3042\u308B\u3002"@ja , "In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as , where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by 0, gives a (assuming ); thus, division by zero is undefined. Since any number multiplied by zero is zero, the expression is also undefined; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst (\"ghosts of departed quantities\"). There are mathematical structures in which is defined for some a such as in the Riemann sphere (a model of the extended complex plane) and the Projectively extended real line; however, such structures do not satisfy every ordinary rule of arithmetic (the field axioms). In computing, a program error may result from an attempt to divide by zero. Depending on the programming environment and the type of number (e.g., floating point, integer) being divided by zero, it may generate positive or negative infinity by the IEEE 754 floating-point standard, generate an exception, generate an error message, cause the program to terminate, result in a special not-a-number value, or crash."@en , "En matem\u00E1ticas, la divisi\u00F3n entre cero es una divisi\u00F3n en la que el divisor es igual a cero, y que no tiene un resultado bien definido. En aritm\u00E9tica y \u00E1lgebra, es considerada una \u00ABindefinici\u00F3n\u00BB, y su mal uso puede dar lugar a aparentes paradojas matem\u00E1ticas. En an\u00E1lisis matem\u00E1tico, es frecuente encontrar l\u00EDmites en los que el denominador tiende a cero. Algunos de estos casos se denominan \u00ABindeterminaciones\u00BB, pero en ocasiones es posible calcular el valor de dicho l\u00EDmite. No se debe confundir este concepto con el de los divisores de cero que existen en algunos anillos matem\u00E1ticos (espec\u00EDficamente los que no son dominios de integridad). Estos aparecen cuando el cero es el dividendo, no el divisor (dividen al cero, no son divisibles por \u00E9l). Todo n\u00FAmero a divide al cero trivialmente, puesto que , pero los divisores de cero lo hacen de manera no trivial. Este problema surgi\u00F3 en los a\u00F1os 650, cuando en India se comenz\u00F3 a popularizar el uso del cero y los n\u00FAmeros negativos. El primero en aproximarse al planteamiento de este problema fue el matem\u00E1tico indio Bhaskara I, quien escribi\u00F3 que , en el siglo VII.\u200B"@es , "Delen door nul is bij het gewone rekenen niet toegestaan als rekenkundige bewerking. Het gaat om een deling waarbij de deler het getal nul is. Bij het gewone rekenen kan geen zinnige betekenis gegeven worden aan het resultaat van een deling door nul. Een ezelsbruggetje om te onthouden dat de bewerking niet mag is \"delen door nul is flauwekul\". In de wiskunde is het in bepaalde gevallen met limieten of andere getalstelsels mogelijk een zinvolle betekenis aan deling door nul te geven."@nl , "0\uC73C\uB85C \uB098\uB204\uAE30\uB294 \uC5B4\uB5A4 \uC22B\uC790\uB97C 0\uC73C\uB85C \uB098\uB204\uB294 \uB098\uB217\uC148\uC744 \uC218\uD589\uD558\uB294 \uAC83\uC774\uC9C0\uB9CC \uC77C\uBC18\uC801\uC73C\uB85C \uB098\uB217\uC148 \uC5F0\uC0B0\uC740 0\uC73C\uB85C \uB098\uB204\uB294 \uACBD\uC6B0\uB97C \uC815\uC758\uD558\uC9C0 \uC54A\uAE30 \uB54C\uBB38\uC5D0 \uC218\uD559\uC801 \uC758\uBBF8\uB294 \uC5C6\uB2E4. \uC5B4\uB5A4 \uC218\uC5D0 0\uC744 \uACF1\uD558\uBA74 0\uC774 \uB41C\uB2E4. \uBC18\uB300\uB85C, 0\uC744 0\uC73C\uB85C \uB098\uB204\uBA74 0\uC744 \uACF1\uD55C \uACB0\uACFC\uAC00 \uD56D\uC0C1 0\uC778\uB370, 0\uC774 \uC5B4\uB5A4 \uC218\uC5D0 0\uC744 \uACF1\uD55C \uACB0\uACFC\uC640 \uAC19\uC544\uC57C \uD558\uAE30 \uB54C\uBB38\uC774\uB2E4. \uADF8\uB7EC\uD55C \uC2DD\uC774 \uC131\uB9BD\uD558\uB294 \uC218\uB294 \uC5B4\uB5A4 \uC218\uC5D0 0\uC758 \uACF1\uD55C \uACB0\uACFC\uAC00 \uD56D\uC0C1 0\uC774\uBBC0\uB85C \uBAA8\uB4E0 \uC218\uAC00 \uB418\uC5B4 \uADF8 \uAC12\uC744 \uD558\uB098\uB85C \uC815\uD560 \uC218 \uC5C6\uB2E4. \uC774\uAC83\uC740 \uBBF8\uD574\uACB0 \uBB38\uC81C\uB098 \uC5F0\uAD6C \uAE08\uAE30 \uC0AC\uD56D\uC774 \uC544\uB2C8\uBA70, \uB2E8\uC9C0 \uAC12\uC744 \uC815\uC758\uD560 \uD544\uC694\uAC00 \uC5C6\uC744 \uBFD0\uC774\uB2E4. \uBA87\uBA87 \uC774\uB860(\uC608 : \uC774\uC6D0\uC218)\uAC00 \uC81C\uD55C\uC801\uC778 \uD615\uD0DC\uB85C x\u00F70\uC640 \uAC19\uC740 \uD615\uD0DC\uB97C \uC815\uC758\uD558\uAE30\uB3C4 \uD558\uBA70, \uB610\uB294 \uB2E8\uC21C\uD788 \uC22B\uC790 \uAC12\uC774 \uC544\uB2C8\uB77C \uBD84\uC218 \uC790\uCCB4\uB97C \uAE30\uD638\uB85C \uC0AC\uC6A9\uD560 \uACBD\uC6B0\uB3C4 \uC788\uB2E4. \uCEF4\uD4E8\uD130 \uD504\uB85C\uADF8\uB798\uBC0D\uC5D0\uC11C\uB294 \uC5B4\uB5A4 \uC218\uB97C 0\uC73C\uB85C \uB098\uB204\uB294 \uACBD\uC6B0 \uC624\uB958\uB97C \uBC1C\uC0DD\uC2DC\uD0A4\uAC70\uB098, NaN, \uB610\uB294 \uBB34\uD55C\uB300\uB97C \uBC18\uD658\uD55C\uB2E4. \uCEF4\uD4E8\uD130 \uD504\uB85C\uADF8\uB798\uBC0D\uC740 A\u00F7B\uB97C A\uC5D0 B\uB85C \uBA87 \uBC88 \uBE84 \uC218 \uC788\uB290\uB0D0\uB85C \uC778\uC2DD\uD558\uAE30 \uB54C\uBB38\uC774\uB2E4. \uC774 \uACBD\uC6B0 \uADF8 \uBAAB\uC740 \uBB34\uD55C\uB300\uAC00 \uB418\uBA70, \uB098\uBA38\uC9C0\uB294 \uC5C6\uB2E4. \uD558\uC9C0\uB9CC \uB300\uBD80\uBD84\uC758 \uD504\uB85C\uADF8\uB7A8\uC740 \uACC4\uC18D 0\uC744 \uBE7C \uBB34\uD55C \uB8E8\uD504\uC5D0 \uAC78\uB9AC\uB294 \uAC83\uC744 \uBC29\uC9C0\uD558\uAE30 \uC704\uD574\uC11C \uCC98\uC74C\uBD80\uD130 \uC9C0\uC815\uB41C \uAC12\uC744 \uBC18\uD658\uD55C\uB2E4."@ko , "\u5728\u6578\u5B78\u4E2D\uFF0C\u88AB\u9664\u6578\u7684\u9664\u6578\uFF08\u5206\u6BCD\uFF09\u662F\u96F6\u6216\u5C07\u67D0\u6578\u9664\u4EE5\u96F6\uFF0C\u53EF\u8868\u9054\u70BA\uFF0C\u662F\u88AB\u9664\u6578\u3002\u5728\u7B97\u5F0F\u4E2D\u6C92\u6709\u610F\u7FA9\uFF0C\u56E0\u70BA\u6C92\u6709\u6578\u76EE\uFF0C\u4EE5\u96F6\u76F8\u4E58\uFF08\u5047\u8A2D\uFF09\uFF0C\u7531\u65BC\u4EFB\u4F55\u6578\u5B57\u4E58\u4EE5\u96F6\u5747\u7B49\u65BC\u96F6\uFF0C\u56E0\u6B64\u9664\u4EE5\u96F6\u662F\u4E00\u500B\u6C92\u6709\u5B9A\u7FA9\u7684\u503C\u3002\u6B64\u5F0F\u662F\u5426\u7AEF\u8996\u5176\u5728\u5982\u4F55\u7684\u6578\u5B78\u8A2D\u5B9A\u4E0B\u8A08\u7B97\u3002\u4E00\u822C\u5BE6\u6578\u7B97\u8853\u4E2D\uFF0C\u6B64\u5F0F\u70BA\u7121\u610F\u7FA9\u3002\u5728\u7A0B\u5E8F\u8A2D\u8A08\u4E2D\uFF0C\u7576\u9047\u4E0A\u6B63\u6574\u6578\u9664\u4EE5\u96F6\u7A0B\u5E8F\u6703\u4E2D\u6B62\uFF0C\u6B63\u5982\u6D6E\u9EDE\u6578\u6703\u51FA\u73FE\u7121\u9650\u5927\u6216NaN\u503C\u7684\u60C5\u6CC1\uFF0C\u800C\u5728Microsoft Excel\u53CAOpenoffice\u6216Libreoffice\u7684Calc\u4E2D\uFF0C\u9664\u4EE5\u96F6\u6703\u76F4\u63A5\u986F\u793A#DIV/0!\u3002"@zh , "Division med noll inneb\u00E4r inom matematiken att man dividerar ett tal med noll, det vill s\u00E4ga att man har noll i n\u00E4mnaren. Det kan skrivas , d\u00E4r x \u00E4r t\u00E4ljaren och noll n\u00E4mnaren. Division med noll \u00E4r inte definierad f\u00F6r de reella talen eller komplexa talen inom matematiken."@sv . @prefix gold: . dbr:Division_by_zero gold:hypernym dbr:Division . @prefix prov: . dbr:Division_by_zero prov:wasDerivedFrom ; dbo:wikiPageLength "32378"^^xsd:nonNegativeInteger . @prefix wikipedia-en: . dbr:Division_by_zero foaf:isPrimaryTopicOf wikipedia-en:Division_by_zero .