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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 Set-theoretic definition of natural numbers ： ウィキペディア英語版 Set-theoretic definition of natural numbers Several ways have been proposed to define the natural numbers using set theory. == Contemporary standard == In standard, Zermelo–Fraenkel (ZF) set theory the natural numbers are defined recursively by 0 = (the empty set) and ''n'' + 1 = ''n'' ∪ . Then ''n'' = for each natural number ''n''. The first few numbers defined this way are 0 = , 1 = = , 2 = = }}, 3 = = ,}}}}. The set ''N'' of natural numbers is defined as the smallest set containing 0 and closed under the successor function ''S'' defined by ''S(n)'' = ''n'' ∪ . (For the existence of such a set we need an axiom of infinity.) The structure ⟨''N'',0,''S''⟩ is a model of Peano arithmetic. The set ''N'' and its elements, when constructed this way, are examples of von Neumann ordinals. 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「Set-theoretic definition of natural numbers」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.