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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 Inhabited set ： ウィキペディア英語版 Inhabited set In constructive mathematics, a set ''A'' is inhabited if there exists an element $a\backslash in\; A$. In classical mathematics, this is the same as the set being nonempty; however, this equivalence is not valid in intuitionistic logic. == Comparison with nonempty sets == In classical mathematics, a set is inhabited if and only if it is not the empty set. These definitions diverge in constructive mathematics, however. A set ''A'' is ''nonempty'' if it is not empty, that is, if :$\backslash lnot\; (z\; (z\; \backslash not\; \backslash in\; A)).$ It is ''inhabited'' if :$\backslash exists\; z\; (z\; \backslash in\; A).$ In intuitionistic logic, the negation of a universal quantifier is weaker than an existential quantifier, not equivalent to it as in classical logic. 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「Inhabited set」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.