sot 集合 1.2集合 Sets 121集合的基本概念 Concepts of Sets 2/24/202111:37PM Deren Chen Zhejiang univ
S e t s 集合 2/24/2021 11:37 PM Deren Chen, Zhejiang Univ. 1 1.2 集合 Sets 1.2.1 集合的基本概念 Concepts of Sets
DEFINITION 1 80t8 集合 The objects in a set are also called the elements or members of the set, a set is said to contain its elements Null Set: There are no anything in the set O={x|x∈P(x)∧~(x∈P(x)) 2/24/202111:37PM Deren Chen Zhejiang univ 2
S e t s 集合 2/24/2021 11:37 PM Deren Chen, Zhejiang Univ. 2 DEFINITION 1. The objects in a set are also called the elements, or members, of the set. A set is said to contain its elements. Null Set: There are no anything in the set. Ø={x | xP(x) ∧ (x P(x) )}
EXAMPLE1 80t8 集合 The set v of all vowels in the english alphabet can written as --- V=a, e, i, 0, u. 2/24/202111:37PM Deren Chen Zhejiang univ 3
S e t s 集合 2/24/2021 11:37 PM Deren Chen, Zhejiang Univ. 3 EXAMPLE 1 The set V of all vowels in the English alphabet can written as ---- V = {a, e, i, o, u}
EXAMPLE 2 80t8 集合 The set o of odd positive integers less than 10 can be xpressed by O={1,3,5,7,9} O={x|x>=1∧x<=10∧ x is odd number} A={a,b,c,…,n}枚举法 A={x|x∈P(x)}谓词公式法 2/24/202111:37PM Deren Chen Zhejiang univ
S e t s 集合 2/24/2021 11:37 PM Deren Chen, Zhejiang Univ. 4 EXAMPLE 2 The set O of odd positive integers less than 10 can be expressed by O = {1, 3, 5, 7, 9}. O = {x | x >=1 ∧ x <=10 ∧x is odd number}. A = {a, b, c, …… n} 枚举法 A = {x | xP(x)} 谓词公式法
DEFINTION 2. 80t8 集合 Two sets are equal if and only if they have the same elements. Presented as A=B otherwise a= B A=B分Vx(x∈A+x∈B) 2/24/202111:37PM Deren Chen Zhejiang univ
S e t s 集合 2/24/2021 11:37 PM Deren Chen, Zhejiang Univ. 5 DEFINTION 2. Two sets are equal if and only if they have the same elements. Presented as A=B otherwise A B A = B x ( x A x B)