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In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. ==Formal definition== A recursive definition of well-founded hereditarily finite sets goes as follows: : ''Base case'': The empty set is a hereditarily finite set. : ''Recursion rule'': If ''a''1,...,''a''''k'' are hereditarily finite, then so is . The set of all well-founded hereditarily finite sets is denoted ''V''ω. If we denote ''P''(''S'') for the power set of ''S'', ''V''ω can also be constructed by first taking the empty set written ''V''0, then ''V''1 = ''P''(''V''0), ''V''2 = ''P''(''V''1),..., ''V''''k'' = ''P''(''V''''k''−1),... Then : 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「hereditarily finite set」の詳細全文を読む スポンサード リンク
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