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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 Epsilon-induction ： ウィキペディア英語版 Epsilon-induction In mathematics, $\backslash in$-induction (epsilon-induction) is a variant of transfinite induction that can be used in set theory to prove that all sets satisfy a given property ''P''(). If the truth of the property for ''x'' follows from its truth for all elements of ''x'', for every set ''x'', then the property is true of all sets. In symbols: : ''$\backslash forall\; x\; \backslash Big(\backslash forall\; y\; (y\; \backslash in\; x\; \backslash rightarrow\; P())\; \backslash rightarrow\; P()\backslash Big)\; \backslash rightarrow\; \backslash forall\; x\; \backslash ,\; P()$'' This principle, sometimes called the axiom of induction (in set theory), is equivalent to the axiom of regularity given the other ZF axioms. $\backslash in$-induction is a special case of well-founded induction. The name is most often pronounced "epsilon-induction", because the set membership symbol $\backslash in$ historically developed from the Greek letter $\backslash epsilon$. ==See also== * Mathematical induction * Transfinite induction * Well-founded induction 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「Epsilon-induction」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.