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In mathematics, -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: : '''' This principle, sometimes called the axiom of induction (in set theory), is equivalent to the axiom of regularity given the other ZF axioms. -induction is a special case of well-founded induction. The name is most often pronounced "epsilon-induction", because the set membership symbol historically developed from the Greek letter . ==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
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