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In set theory and related branches of mathematics, a collection ''F'' of subsets of a given set ''S'' is called a family of subsets of ''S'', or a family of sets over ''S''. More generally, a collection of any sets whatsoever is called a family of sets. The term "collection" is used here because, in some contexts, a family of sets may be allowed to contain repeated copies of any given member, and in other contexts it may form a proper class rather than a set. == Examples == * The power set P(''S'') is a family of sets over ''S''. * The ''k''-subsets ''S''(''k'') of a set ''S'' form a family of sets. * Let ''S'' = , an example of a family of sets over ''S'' (in the multiset sense) is given by ''F'' = where A1 = , A2 = , A3 = and A4 = . * The class Ord of all ordinal numbers is a ''large'' family of sets; that is, it is not itself a set but instead a proper class. 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「family of sets」の詳細全文を読む スポンサード リンク
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