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In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets. == Definition == A partition of a set ''X'' is a set of nonempty subsets of ''X'' such that every element ''x'' in ''X'' is in exactly one of these subsets (i.e., ''X'' is a disjoint union of the subsets). Equivalently, a family of sets ''P'' is a partition of ''X'' if and only if all of the following conditions hold: #''P'' does not contain the empty set. # The union of the sets in ''P'' is equal to ''X''. (The sets in ''P'' are said to cover ''X''.) # The intersection of any two distinct sets in ''P'' is empty. (We say the elements of ''P'' are pairwise disjoint.) In mathematical notation, these conditions can be represented as # # # if and then , where is the empty set. The sets in ''P'' are called the blocks, parts or cells of the partition.〔Brualdi, ''pp''. 44–45〕 The rank of ''P'' is |''X''| − |''P''|, if ''X'' is finite. 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「partition of a set」の詳細全文を読む スポンサード リンク
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