翻訳と辞書 Words near each other ・ AXL Guitars ・ Axl Hazarika ・ Axl Osborne ・ AXL receptor tyrosine kinase ・ Axl Rose ・ Axl Rotten ・ Axl Smith ・ Axle ・ Axle counter ・ Axle hitch ・ Axiom of countable choice ・ Axiom of dependent choice ・ Axiom of determinacy ・ Axiom of empty set ・ Axiom of Equity ・ Axiom of extensionality ・ Axiom of global choice ・ Axiom of infinity ・ Axiom of limitation of size ・ Axiom of Maria ・ Axiom of pairing ・ Axiom of power set ・ Axiom of projective determinacy ・ Axiom of real determinacy ・ Axiom of reducibility ・ Axiom of regularity ・ Axiom of union ・ Axiom S5 ・ Axiom schema ・ Axiom schema of predicative separation Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Axiom of extensionality ： ウィキペディア英語版 Axiom of extensionality In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory. == Formal statement == In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: :$\backslash forall\; A\; \backslash ,\; \backslash forall\; B\; \backslash ,\; (\; \backslash forall\; X\; \backslash ,\; (X\; \backslash in\; A\; \backslash iff\; X\; \backslash in\; B)\; \backslash Rightarrow\; A\; =\; B)$ or in words: :Given any set ''A'' and any set ''B'', if for every set ''X'', ''X'' is a member of ''A'' if and only if ''X'' is a member of ''B'', then ''A'' is equal to ''B''. :(It is not really essential that ''X'' here be a ''set'' — but in ZF, everything is. See Ur-elements below for when this is violated.) The converse, $\backslash forall\; A\; \backslash ,\; \backslash forall\; B\; \backslash ,\; (A\; =\; B\; \backslash Rightarrow\; \backslash forall\; X\; \backslash ,\; (X\; \backslash in\; A\; \backslash iff\; X\; \backslash in\; B)\; )$, of this axiom follows from the substitution property of equality. 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「Axiom of extensionality」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.