“union”的概念、定义、习题解题方法及翻译-数学辞典

单词

union

释义

union

The union of sets A and B is the set consisting of all objects that belong to A or B (or both), and it is denoted by A ∪ B (read as ‘A union B'). Thus the term ‘union' is used for both the resulting set and the operation, a binary operation on the set of all subsets of a given set. The following properties hold:

(i) For all A, A ∪ A = A and A ∪ Ø = A.

(ii) For all A and B, A ∪ B = B ∪ A; that is, ∪ is commutative.

(iii) For all A, B, and C, (A ∪ B) ∪ C = A ∪ (B ∪ C); that is, ∪ is associative.

Given a family of sets Ai with index set I, the union

consists of those elements x such that x is an element of Ai for at least one i in I.

Compare disjoint union. For the union of two events, see event.

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