. . "O Paradoxo de Burali-Forti, proposto em 1897 pelo matem\u00E1tico italiano Cesare Burali-Forti, diz que n\u00E3o existe um n\u00FAmero ordinal maior que todos outros n\u00FAmeros ordinais. Em linhas gerais, ele \u00E9 an\u00E1logo ao paradoxo de Cantor, que diz que n\u00E3o existe um n\u00FAmero cardinal maior do que todos outros. Uma apresenta\u00E7\u00E3o simplificada do paradoxo \u00E9: dado qualquern\u00FAmero ordinal, existe um outro n\u00FAmero ordinal maior que ele. Em outras palavras, n\u00E3o existe o \"conjunto de todos n\u00FAmeros ordinais\" (porque este conjunto seria um n\u00FAmero ordinal)."@pt . "In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing \"the set of all ordinal numbers\" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who, in 1897, published a paper proving a theorem which, unknown to him, contradicted a previously proved result by Cantor. Bertrand Russell subsequently noticed the contradiction, and when he published it in his 1903 book Principles of Mathematics, he stated that it had been suggested to him by Burali-Forti's paper, with the result that it came to be known by Burali-Forti's name."@en . . "Das Burali-Forti-Paradoxon ist das \u00E4lteste Paradoxon der naiven Mengenlehre, publiziert am 28. M\u00E4rz 1897. Es beschreibt den Widerspruch, an dem die Bildung der Menge aller Ordinalzahlen scheitert. Es ist nach seinem Entdecker Cesare Burali-Forti benannt, der zeigte, dass eine solche Menge aller Ordinalzahlen selbst einer Ordinalzahl entspr\u00E4che, zu der eine gr\u00F6\u00DFere Nachfolger-Ordinalzahl gebildet werden k\u00F6nnte, die kleiner oder gleich w\u00E4re, woraus die unm\u00F6gliche Ungleichung folgte."@de . . "\uC9D1\uD569\uB860\uC5D0\uC11C \uBD80\uB784\uB9AC\uD3EC\uB974\uD2F0 \uC5ED\uC124(\uC601\uC5B4: Burali-Forti paradox)\uC740 \uC18C\uBC15\uD55C \uC9D1\uD569\uB860\uC758 \uC5ED\uC124\uC758 \uD558\uB098\uC774\uBA70, \uBAA8\uB4E0 \uC21C\uC11C\uC218\uC758 \uBAA8\uC784\uC774 \uC9D1\uD569\uC744 \uC774\uB8F0 \uC218 \uC5C6\uB2E4\uB294 \uAC83\uC744 \uC99D\uBA85\uD55C\uB2E4."@ko . . . . . . . . . "1123337837"^^ . "Paradoks Buralego-Fortiego"@pl . . . "Paradosso di Burali-Forti"@it . . . . . . . . "\u30D6\u30E9\u30EA\uFF1D\u30D5\u30A9\u30EB\u30C6\u30A3\u306E\u30D1\u30E9\u30C9\u30C3\u30AF\u30B9(Burali-Forti paradox)\u3068\u306F\u3001\u6570\u5B66\u306E\u96C6\u5408\u8AD6\u306B\u304A\u3051\u308B\u30D1\u30E9\u30C9\u30C3\u30AF\u30B9\u306E\u4E00\u3064\u3067\u3042\u308A\u3001\u300C\u5168\u3066\u306E\u9806\u5E8F\u6570\u306E\u96C6\u5408\u300D\u3068\u3044\u3046\u6982\u5FF5\u3092\u7D20\u6734\u306B\u5C0E\u5165\u3059\u308B\u3068\u77DB\u76FE\u304C\u8D77\u3053\u308B\u3068\u3044\u3046\u4E3B\u5F35\u3002\u5373\u3061\u305D\u306E\u3088\u3046\u306A\u5B58\u5728\u3092\u8A31\u3059\u4F53\u7CFB\u306F\u81EA\u5DF1\u77DB\u76FE\u3057\u3066\u3044\u308B\u3053\u3068\u3092\u793A\u3059\u3002"@ja . . "Paradoja de Burali-Forti"@es . "\uBD80\uB784\uB9AC\uD3EC\uB974\uD2F0 \uC5ED\uC124"@ko . . . "Das Burali-Forti-Paradoxon ist das \u00E4lteste Paradoxon der naiven Mengenlehre, publiziert am 28. M\u00E4rz 1897. Es beschreibt den Widerspruch, an dem die Bildung der Menge aller Ordinalzahlen scheitert. Es ist nach seinem Entdecker Cesare Burali-Forti benannt, der zeigte, dass eine solche Menge aller Ordinalzahlen selbst einer Ordinalzahl entspr\u00E4che, zu der eine gr\u00F6\u00DFere Nachfolger-Ordinalzahl gebildet werden k\u00F6nnte, die kleiner oder gleich w\u00E4re, woraus die unm\u00F6gliche Ungleichung folgte. Georg Cantor beschrieb das Paradoxon erst im Jahr 1899 als Verallgemeinerung der ersten Cantorschen Antinomie, mit der er nachwies, dass die Klasse aller Kardinalzahlen keine Menge ist. Diese Klasse kann als echte Teilklasse der Ordinalzahlen aufgefasst werden. In der axiomatischen Zermelo-Mengenlehre oder Zermelo-Fraenkel-Mengenlehre (ZF) l\u00E4sst sich das Burali-Forti-Paradoxon als Beweis daf\u00FCr verstehen, dass keine Menge aller Ordinalzahlen existiert. In Mengenlehren, die mit Klassen arbeiten, liefert es den Beweis daf\u00FCr, dass die Klasse aller Ordinalzahlen eine echte Klasse ist."@de . "\u5E03\u62C9\u5229-\u798F\u5C14\u8482\u6096\u8BBA"@zh . . "In de verzamelingenleer, een deelgebied van de wiskunde, laat de Burali-Forti paradox zien dat het na\u00EFef construeren van de verzameling van alle ordinaalgetallen tot een tegenspraak leidt en daarom een antinomie aantoont in een systeem waarin deze constructie is toegestaan. De paradox is genoemd naar Cesare Burali-Forti, de Italiaanse wiskundige die deze paradox in 1897 ontdekte."@nl . . . . . "O Paradoxo de Burali-Forti, proposto em 1897 pelo matem\u00E1tico italiano Cesare Burali-Forti, diz que n\u00E3o existe um n\u00FAmero ordinal maior que todos outros n\u00FAmeros ordinais. Em linhas gerais, ele \u00E9 an\u00E1logo ao paradoxo de Cantor, que diz que n\u00E3o existe um n\u00FAmero cardinal maior do que todos outros. Uma apresenta\u00E7\u00E3o simplificada do paradoxo \u00E9: dado qualquern\u00FAmero ordinal, existe um outro n\u00FAmero ordinal maior que ele. Em outras palavras, n\u00E3o existe o \"conjunto de todos n\u00FAmeros ordinais\" (porque este conjunto seria um n\u00FAmero ordinal)."@pt . "Paradoks Buralego-Fortiego \u2013 twierdzenie odkryte w 1897 roku przez Cesarego Buralego-Fortiego, ucznia Giuseppe Peana, m\u00F3wi\u0105ce o tym, i\u017C liczby porz\u0105dkowe nie tworz\u0105 zbioru. Sformu\u0142owanie: Nie istnieje zbi\u00F3r, kt\u00F3rego elementami s\u0105 wszystkie liczby porz\u0105dkowe. Fakt ten mo\u017Cna uzasadni\u0107 nie wprost \u2013 zak\u0142adaj\u0105c, \u017Ce istnieje zbi\u00F3r kt\u00F3rego elementami s\u0105 wszystkie liczby porz\u0105dkowe, mo\u017Cna doj\u015B\u0107 do sprzeczno\u015Bci. Istotnie, na mocy aksjomatu zast\u0119powania istnieje podzbi\u00F3r tego zbioru, z\u0142o\u017Cony wy\u0142\u0105cznie ze wszystkich liczb porz\u0105dkowych. Z w\u0142asno\u015Bci dzia\u0142a\u0144 na liczbach porz\u0105dkowych, zbiory i s\u0105 liczbami porz\u0105dkowymi. W\u00F3wczas oraz a wi\u0119c co jest sprzeczne z aksjomatem regularno\u015Bci i jednocze\u015Bnie ko\u0144czy dow\u00F3d."@pl . . "Il paradosso di Burali-Forti dimostra che costruire \"l'insieme di tutti i numeri ordinali\" porta ad una contraddizione e quindi individua un'antinomia in un sistema che permette la sua costruzione. Il motivo \u00E8 che l'insieme di tutti i numeri ordinali possiede tutte le propriet\u00E0 di un numero ordinale e sarebbe quindi considerato a sua volta un numero ordinale. Quindi si pu\u00F2 costruire il suo successore , che \u00E8 strettamente maggiore di . Ma questo numero ordinale deve essere elemento di , in quanto contiene tutti i numeri ordinali, quindi si giunge a: ."@it . "Burali-Forti-Paradoxon"@de . . "Paradoxe de Burali-Forti"@fr . . . "\u5728\u96C6\u5408\u8AD6\u6B64\u4E00\u6578\u5B78\u9818\u57DF\u88E1\uFF0C\u5E03\u62C9\u5229-\u798F\u723E\u8482\u6096\u8AD6\u65B7\u8A00\uFF0C\u6A38\u7D20\u5EFA\u69CB\u300C\u6240\u6709\u5E8F\u6578\u7684\u96C6\u5408\u300D\u6703\u5C0E\u81F4\u77DB\u76FE\uFF0C\u56E0\u6B64\u6BCF\u500B\u5141\u8A31\u6B64\u4E00\u69CB\u9020\u7684\u7CFB\u7D71\u90FD\u6703\u986F\u5F97\u81EA\u76F8\u77DB\u76FE\u3002\u6B64\u4E00\u6096\u8AD6\u662F\u4EE5\u5207\u85A9\u96F7\u00B7\u5E03\u62C9\u5229-\u798F\u723E\u8482\u4F86\u547D\u540D\u7684\uFF0C\u4ED6\u57281897\u5E74\u767C\u73FE\u4E86\u6B64\u4E00\u6096\u8AD6\u3002"@zh . "Paradoxo de Burali-Forti"@pt . "In de verzamelingenleer, een deelgebied van de wiskunde, laat de Burali-Forti paradox zien dat het na\u00EFef construeren van de verzameling van alle ordinaalgetallen tot een tegenspraak leidt en daarom een antinomie aantoont in een systeem waarin deze constructie is toegestaan. De paradox is genoemd naar Cesare Burali-Forti, de Italiaanse wiskundige die deze paradox in 1897 ontdekte."@nl . "\u041F\u0430\u0440\u0430\u0434\u043E\u043A\u0441 \u0411\u0443\u0440\u0430\u043B\u0438-\u0424\u043E\u0440\u0442\u0438"@ru . "Se conoce como paradoja de Burali-Forti a la suposici\u00F3n, dentro de una teor\u00EDa de conjuntos axiom\u00E1tica, de que la totalidad de los n\u00FAmeros ordinales forma un conjunto. Dicha suposici\u00F3n lleva a una contradicci\u00F3n en la teor\u00EDa. Debe su nombre al matem\u00E1tico Cesare Burali-Forti, que la descubri\u00F3 en 1897.\u200B"@es . "6476"^^ . "51653"^^ . "Il paradosso di Burali-Forti dimostra che costruire \"l'insieme di tutti i numeri ordinali\" porta ad una contraddizione e quindi individua un'antinomia in un sistema che permette la sua costruzione. Il motivo \u00E8 che l'insieme di tutti i numeri ordinali possiede tutte le propriet\u00E0 di un numero ordinale e sarebbe quindi considerato a sua volta un numero ordinale. Quindi si pu\u00F2 costruire il suo successore , che \u00E8 strettamente maggiore di . Ma questo numero ordinale deve essere elemento di , in quanto contiene tutti i numeri ordinali, quindi si giunge a: . La moderna teoria assiomatica degli insiemi aggira questa antinomia non consentendo la costruzione di insiemi con formule di comprensione senza restrizione come \"tutti gli insiemi che hanno la propriet\u00E0 \", come era possibile nel sistema di assiomi di Gottlob Frege. Il paradosso prende il nome da Cesare Burali-Forti, che lo afferm\u00F2 nel 1897."@it . . "Burali-Forti-paradox"@nl . . . . . "\u041F\u0430\u0440\u0430\u0434\u043E\u043A\u0441 \u0411\u0443\u0440\u0430\u043B\u0438-\u0424\u043E\u0440\u0442\u0438 \u0434\u0435\u043C\u043E\u043D\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u0442, \u0447\u0442\u043E \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u043E \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043E\u0432\u0430\u043D\u0438\u0438 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0432\u0441\u0435\u0445 \u043F\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0432\u0435\u0434\u0451\u0442 \u043A \u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u044F\u043C \u0438, \u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E, \u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u0432\u043E\u0439 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0442\u0435\u043E\u0440\u0438\u044F \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043F\u043E\u0441\u0442\u0440\u043E\u0435\u043D\u0438\u0435 \u0442\u0430\u043A\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E."@ru . . . . "Se conoce como paradoja de Burali-Forti a la suposici\u00F3n, dentro de una teor\u00EDa de conjuntos axiom\u00E1tica, de que la totalidad de los n\u00FAmeros ordinales forma un conjunto. Dicha suposici\u00F3n lleva a una contradicci\u00F3n en la teor\u00EDa. Debe su nombre al matem\u00E1tico Cesare Burali-Forti, que la descubri\u00F3 en 1897.\u200B"@es . . . . . "\u041F\u0430\u0440\u0430\u0434\u043E\u043A\u0441 \u0411\u0443\u0440\u0430\u043B\u0438-\u0424\u043E\u0440\u0442\u0438 \u0434\u0435\u043C\u043E\u043D\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u0442, \u0447\u0442\u043E \u043F\u0440\u0435\u0434\u043F\u043E\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u043E \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043E\u0432\u0430\u043D\u0438\u0438 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0432\u0441\u0435\u0445 \u043F\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0432\u0435\u0434\u0451\u0442 \u043A \u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u044F\u043C \u0438, \u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E, \u043F\u0440\u043E\u0442\u0438\u0432\u043E\u0440\u0435\u0447\u0438\u0432\u043E\u0439 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0442\u0435\u043E\u0440\u0438\u044F \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043F\u043E\u0441\u0442\u0440\u043E\u0435\u043D\u0438\u0435 \u0442\u0430\u043A\u043E\u0433\u043E \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E."@ru . . "In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing \"the set of all ordinal numbers\" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who, in 1897, published a paper proving a theorem which, unknown to him, contradicted a previously proved result by Cantor. Bertrand Russell subsequently noticed the contradiction, and when he published it in his 1903 book Principles of Mathematics, he stated that it had been suggested to him by Burali-Forti's paper, with the result that it came to be known by Burali-Forti's name."@en . . . . . "\u041F\u0430\u0440\u0430\u0434\u043E\u043A\u0441 \u0411\u0443\u0440\u0430\u043B\u0456-\u0424\u043E\u0440\u0442\u0456"@uk . "\u30D6\u30E9\u30EA\uFF1D\u30D5\u30A9\u30EB\u30C6\u30A3\u306E\u30D1\u30E9\u30C9\u30C3\u30AF\u30B9"@ja . . . . . . . "Burali-Fortiho paradox je poznatek publikovan\u00FD roku 1897, kter\u00FD spolu s dal\u0161\u00EDmi v\u00FDsledky podobn\u00E9ho typu (ozna\u010Dovan\u00FDmi jako paradoxy nebo antinomie) vedl ke krizi klasick\u00E9 naivn\u00ED teorie mno\u017Ein a jej\u00EDmu n\u00E1sledn\u00E9mu nahrazen\u00ED axiomatick\u00FDm syst\u00E9mem. Burali-Fortiho paradox se t\u00FDk\u00E1 ordin\u00E1ln\u00EDch \u010D\u00EDsel."@cs . . . "Burali-Forti paradox"@en . "\u30D6\u30E9\u30EA\uFF1D\u30D5\u30A9\u30EB\u30C6\u30A3\u306E\u30D1\u30E9\u30C9\u30C3\u30AF\u30B9(Burali-Forti paradox)\u3068\u306F\u3001\u6570\u5B66\u306E\u96C6\u5408\u8AD6\u306B\u304A\u3051\u308B\u30D1\u30E9\u30C9\u30C3\u30AF\u30B9\u306E\u4E00\u3064\u3067\u3042\u308A\u3001\u300C\u5168\u3066\u306E\u9806\u5E8F\u6570\u306E\u96C6\u5408\u300D\u3068\u3044\u3046\u6982\u5FF5\u3092\u7D20\u6734\u306B\u5C0E\u5165\u3059\u308B\u3068\u77DB\u76FE\u304C\u8D77\u3053\u308B\u3068\u3044\u3046\u4E3B\u5F35\u3002\u5373\u3061\u305D\u306E\u3088\u3046\u306A\u5B58\u5728\u3092\u8A31\u3059\u4F53\u7CFB\u306F\u81EA\u5DF1\u77DB\u76FE\u3057\u3066\u3044\u308B\u3053\u3068\u3092\u793A\u3059\u3002"@ja . "\u041F\u0430\u0440\u0430\u0434\u043E\u043A\u0441 \u0411\u0443\u0440\u0430\u043B\u0456-\u0424\u043E\u0440\u0442\u0456 \u2014 \u0432 \u0442\u0435\u043E\u0440\u0456\u0457 \u043C\u043D\u043E\u0436\u0438\u043D \u0434\u0435\u043C\u043E\u043D\u0441\u0442\u0440\u0443\u0454, \u0449\u043E \u043F\u0440\u0438\u043F\u0443\u0449\u0435\u043D\u043D\u044F \u043F\u0440\u043E \u0456\u0441\u043D\u0443\u0432\u0430\u043D\u043D\u044F \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u0432\u0441\u0456\u0445 \u043F\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u0432\u0435\u0434\u0435 \u0434\u043E \u0441\u0443\u043F\u0435\u0440\u0435\u0447\u043D\u043E\u0441\u0442\u0435\u0439 \u0456, \u043E\u0442\u0436\u0435, \u0441\u0443\u043F\u0435\u0440\u0435\u0447\u043B\u0438\u0432\u043E\u044E \u0454 \u0442\u0435\u043E\u0440\u0456\u044F, \u0432 \u044F\u043A\u0456\u0439 \u043F\u043E\u0431\u0443\u0434\u043E\u0432\u0430 \u0442\u0430\u043A\u043E\u0457 \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u043C\u043E\u0436\u043B\u0438\u0432\u0430 (1897)."@uk . . . . "Burali-Fortiho paradox"@cs . . . . . . . "En math\u00E9matiques, le paradoxe de Burali-Forti, paru en 1897, d\u00E9signe une construction qui conduit dans certaines th\u00E9ories des ensembles ou th\u00E9ories des types trop na\u00EFves \u00E0 une antinomie, c\u2019est-\u00E0-dire que la th\u00E9orie est contradictoire (on dit aussi incoh\u00E9rente ou inconsistante). Dit bri\u00E8vement, il \u00E9nonce que, comme on peut d\u00E9finir la borne sup\u00E9rieure d'un ensemble d'ordinaux, si l'ensemble de tous les ordinaux existe, on peut d\u00E9finir un ordinal sup\u00E9rieur strictement \u00E0 tous les ordinaux, d'o\u00F9 une contradiction. L'argument utilise donc la notion d'ordinal, c\u2019est-\u00E0-dire essentiellement celle de bon ordre : il est plus technique que le paradoxe de Russell, bien que son argument ne soit pas si \u00E9loign\u00E9 de ce dernier qui est plus simple \u00E0 comprendre et \u00E0 formaliser. Cependant, le paradoxe de Burali-Forti est le premier des paradoxes de la th\u00E9orie des ensembles \u00E0 \u00EAtre publi\u00E9, six ans avant le paradoxe de Russell, et Georg Cantor en fait \u00E9tat dans sa correspondance, ainsi que du paradoxe du plus grand cardinal (dit paradoxe de Cantor), dans les m\u00EAmes ann\u00E9es. Par ailleurs, le paradoxe de Burali-Forti met directement en jeu la notion d'ordre, et non celle d'appartenance (m\u00EAme si aujourd'hui ces deux notions co\u00EFncident pour les ordinaux tels qu'ils sont d\u00E9finis en th\u00E9orie des ensembles). Ainsi l'incoh\u00E9rence de certaines th\u00E9ories a \u00E9t\u00E9 \u00E9tablie en d\u00E9rivant directement le paradoxe de Burali-Forti. C'est ainsi que John Barkley Rosser a d\u00E9montr\u00E9 en 1942 l'inconsistance d'une des premi\u00E8res versions des New Foundations de Willard Van Orman Quine."@fr . . "\u5728\u96C6\u5408\u8AD6\u6B64\u4E00\u6578\u5B78\u9818\u57DF\u88E1\uFF0C\u5E03\u62C9\u5229-\u798F\u723E\u8482\u6096\u8AD6\u65B7\u8A00\uFF0C\u6A38\u7D20\u5EFA\u69CB\u300C\u6240\u6709\u5E8F\u6578\u7684\u96C6\u5408\u300D\u6703\u5C0E\u81F4\u77DB\u76FE\uFF0C\u56E0\u6B64\u6BCF\u500B\u5141\u8A31\u6B64\u4E00\u69CB\u9020\u7684\u7CFB\u7D71\u90FD\u6703\u986F\u5F97\u81EA\u76F8\u77DB\u76FE\u3002\u6B64\u4E00\u6096\u8AD6\u662F\u4EE5\u5207\u85A9\u96F7\u00B7\u5E03\u62C9\u5229-\u798F\u723E\u8482\u4F86\u547D\u540D\u7684\uFF0C\u4ED6\u57281897\u5E74\u767C\u73FE\u4E86\u6B64\u4E00\u6096\u8AD6\u3002"@zh . "Burali-Fortiho paradox je poznatek publikovan\u00FD roku 1897, kter\u00FD spolu s dal\u0161\u00EDmi v\u00FDsledky podobn\u00E9ho typu (ozna\u010Dovan\u00FDmi jako paradoxy nebo antinomie) vedl ke krizi klasick\u00E9 naivn\u00ED teorie mno\u017Ein a jej\u00EDmu n\u00E1sledn\u00E9mu nahrazen\u00ED axiomatick\u00FDm syst\u00E9mem. Burali-Fortiho paradox se t\u00FDk\u00E1 ordin\u00E1ln\u00EDch \u010D\u00EDsel."@cs . . . "Paradoks Buralego-Fortiego \u2013 twierdzenie odkryte w 1897 roku przez Cesarego Buralego-Fortiego, ucznia Giuseppe Peana, m\u00F3wi\u0105ce o tym, i\u017C liczby porz\u0105dkowe nie tworz\u0105 zbioru. Sformu\u0142owanie: Nie istnieje zbi\u00F3r, kt\u00F3rego elementami s\u0105 wszystkie liczby porz\u0105dkowe. Fakt ten mo\u017Cna uzasadni\u0107 nie wprost \u2013 zak\u0142adaj\u0105c, \u017Ce istnieje zbi\u00F3r kt\u00F3rego elementami s\u0105 wszystkie liczby porz\u0105dkowe, mo\u017Cna doj\u015B\u0107 do sprzeczno\u015Bci. Istotnie, na mocy aksjomatu zast\u0119powania istnieje podzbi\u00F3r tego zbioru, z\u0142o\u017Cony wy\u0142\u0105cznie ze wszystkich liczb porz\u0105dkowych. Z w\u0142asno\u015Bci dzia\u0142a\u0144 na liczbach porz\u0105dkowych, zbiory i"@pl . . "\u041F\u0430\u0440\u0430\u0434\u043E\u043A\u0441 \u0411\u0443\u0440\u0430\u043B\u0456-\u0424\u043E\u0440\u0442\u0456 \u2014 \u0432 \u0442\u0435\u043E\u0440\u0456\u0457 \u043C\u043D\u043E\u0436\u0438\u043D \u0434\u0435\u043C\u043E\u043D\u0441\u0442\u0440\u0443\u0454, \u0449\u043E \u043F\u0440\u0438\u043F\u0443\u0449\u0435\u043D\u043D\u044F \u043F\u0440\u043E \u0456\u0441\u043D\u0443\u0432\u0430\u043D\u043D\u044F \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u0432\u0441\u0456\u0445 \u043F\u043E\u0440\u044F\u0434\u043A\u043E\u0432\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u0432\u0435\u0434\u0435 \u0434\u043E \u0441\u0443\u043F\u0435\u0440\u0435\u0447\u043D\u043E\u0441\u0442\u0435\u0439 \u0456, \u043E\u0442\u0436\u0435, \u0441\u0443\u043F\u0435\u0440\u0435\u0447\u043B\u0438\u0432\u043E\u044E \u0454 \u0442\u0435\u043E\u0440\u0456\u044F, \u0432 \u044F\u043A\u0456\u0439 \u043F\u043E\u0431\u0443\u0434\u043E\u0432\u0430 \u0442\u0430\u043A\u043E\u0457 \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u043C\u043E\u0436\u043B\u0438\u0432\u0430 (1897)."@uk . . . "En math\u00E9matiques, le paradoxe de Burali-Forti, paru en 1897, d\u00E9signe une construction qui conduit dans certaines th\u00E9ories des ensembles ou th\u00E9ories des types trop na\u00EFves \u00E0 une antinomie, c\u2019est-\u00E0-dire que la th\u00E9orie est contradictoire (on dit aussi incoh\u00E9rente ou inconsistante). Dit bri\u00E8vement, il \u00E9nonce que, comme on peut d\u00E9finir la borne sup\u00E9rieure d'un ensemble d'ordinaux, si l'ensemble de tous les ordinaux existe, on peut d\u00E9finir un ordinal sup\u00E9rieur strictement \u00E0 tous les ordinaux, d'o\u00F9 une contradiction."@fr . . . . "\uC9D1\uD569\uB860\uC5D0\uC11C \uBD80\uB784\uB9AC\uD3EC\uB974\uD2F0 \uC5ED\uC124(\uC601\uC5B4: Burali-Forti paradox)\uC740 \uC18C\uBC15\uD55C \uC9D1\uD569\uB860\uC758 \uC5ED\uC124\uC758 \uD558\uB098\uC774\uBA70, \uBAA8\uB4E0 \uC21C\uC11C\uC218\uC758 \uBAA8\uC784\uC774 \uC9D1\uD569\uC744 \uC774\uB8F0 \uC218 \uC5C6\uB2E4\uB294 \uAC83\uC744 \uC99D\uBA85\uD55C\uB2E4."@ko . . . . . . .