翻訳と辞書 Words near each other ・ 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 ・ Axiom schema of replacement ・ Axiom schema of specification 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 infinity ： ウィキペディア英語版 Axiom of infinity In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908.〔Zermelo: ''Untersuchungen über die Grundlagen der Mengenlehre'', 1907, in: Mathematische Annalen 65 (1908), 261-281; Axiom des Unendlichen p. 266f.〕 == Formal statement == In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: :$\backslash exists\; \backslash mathbf\; \backslash ,\; (\; \backslash empty\; \backslash in\; \backslash mathbf\; \backslash ,\; \backslash and\; \backslash ,\; \backslash forall\; x\; \backslash in\; \backslash mathbf\; \backslash ,\; (\; \backslash ,\; (\; x\; \backslash cup\; \backslash \; )\; \backslash in\; \backslash mathbf\; )\; )\; .$ In words, there is a set I (the set which is postulated to be infinite), such that the empty set is in I and such that whenever any ''x'' is a member of I, the set formed by taking the union of ''x'' with its singleton is also a member of I. Such a set is sometimes called an inductive set. 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 infinity」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.