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单词 power set
释义

power set

The set of all subsets of a set S is the power set of S, denoted by ℘(S). Suppose that S has n elements a1, a2,…, an, and let A be a subset of S. For each element ai of S, there are two possibilities: either ai ε A or not. Considering all n elements leads to 2n possibilities in all. Hence, S has 2n subsets; that is, ℘(S) has 2n elements. If S =  {a,b,c}, the 8 ( = 23) elements of ℘(S) are

Cantor's Diagonal Theorem states that the power set of a set always has greater cardinality than the cardinality of the set.

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更新时间:2025/4/29 3:56:56