集合论的子集和幂集(Subset and power set of set theory)

二,集合论的子集

在集合论中,子集是一个较常用的概念,当给出一个集合 {0,1,2,…,n-1} 时,常需要生成所有的子集。

生成子集有三种方法:增量构造法、位向量法、二进制法

其中,二进制法除了可以生成子集,还是一种集合的表示方法。、

三,集合论的幂集、

  • 幂集是指一个集合的所有子集的集合
  • 有n个元素形成的集合的幂集共有2的n次方个元素,而且每一个元素都是一个集合.

例如:集合A={a,b,c} 空集是每个集合的子集,所以A的幂集为{,{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c}},

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2、 Subset of set theory

In set theory, subset is a commonly used concept. When a set {0,1,2,…, n-1} is given, it is often necessary to generate all subsets.

There are three methods to generate subsets: incremental construction method, bit vector method and binary method

In addition to generating subsets, binary method is also a representation of sets

3、 Power set of set theory

  • A power set is a set of all subsets of a set
  • The power set of a set formed by n elements has n elements to the power of 2, and each element is a set

For example: set a = {a, B, C} the empty set is a subset of each set, so the power set of a is {, {a}, {B}, {C}, {a, B}, {a, C}, {B, C}, {a, B, C},