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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Burali-Forti paradox ： ウィキペディア英語版 Burali-Forti paradox In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that naïvely 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. ==Stated in terms of von Neumann ordinals== Let $\backslash Omega$ be the set of all ordinals. Since $\backslash Omega$ carries all properties of an ordinal number, it is an ordinal number itself. We can therefore construct its successor $\backslash Omega\; +\; 1$, which is strictly greater than $\backslash Omega$. However, this ordinal number must be an element of $\backslash Omega$, since $\backslash Omega$ contains all ordinal numbers. Finally, we arrive at : and . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Burali-Forti paradox」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.