N: non-negative integer set or natural number set {0, 1, 2, 3, ...}

N* or N+: positive integer set {1, 2,3, ...}

Z: integer set {…,-1, 0, 1, …}

P: a group of prime numbers

Q: Rational number set

Q+: Set of Positive Rational Numbers

Q-: set of negative rational numbers

R: real number set

R+: positive real number set

R-: negative real number set

C: complex set

: empty set (a set without any elements is called an empty set)

U: complete set (including all the elements discussed in the question)

Extended data:

First, the characteristics of the set:

(1) certainty

Given a set, any element, whether it belongs to the set or not, must be one of them, and there is no ambiguity.

(2) Anisotropy

Any two elements in a collection are considered different, that is, each element can only appear once. Sometimes it is necessary to describe the situation where the same element appears many times. You can use multiset, where elements are allowed to appear multiple times.

(3) Disorder

In a set, the state of each element is the same and the elements are out of order. You can define an order relation on the set. After defining the order relation, you can sort the elements according to the order relation. But as far as the characteristics of the set itself are concerned, there is no necessary order between elements. (See Order Theory)

(4) Symbol representation rules

Elements are usually represented by lowercase letters, such as a, b, c, d or x; Sets are usually represented by capital letters such as A, B, C, D or X. When element A belongs to set A, it is marked as a ∈ a If element A does not belong to A, it is marked as A? Answer: If two sets A and B contain exactly the same elements, they are equal, and it is recorded as A = B. ..

Second, the set algorithm:

(1) switching law: a ∩ b = b ∩ a; A∪B=B∪A

(2) the law of association: a ∪ (b ∪ c) = (a ∪ b) ∪ c; A∩(B∩C)=(A∩B)∩C

(3) law of distributive duality: a ∩ (b ∪ c) = (a ∪ b) ∩ (a ∪ c); A ∪( B∪C)=(A∪B)∪( A∪C)

(4) duality law: (a ∪ b) c = a c ∪ b c; (A∩B)^C=A^C∪B^C

(5) identity: A∨? = A； A∩U=A

(6) law of complement: a ∪ a' = u; A∩A'=？

(7) involution law: A''=A

(8) idempotent law: a ∪ a = a; A∩A=A

(9) Zero uniformity: a ∪ u = u; A∩？ =?

(10) absorption law: a ∨ (a ∩ b) = a; A∩(A∪B)=A

(1 1) inversion law (de Morgan's law): (a ∪ b)' = a' ∪ b'; (A∩B)'=A'∪B'. Text expression: 1. The complementary set of the intersection of set A and set B is equal to the union of the complementary sets of set A and set B; 2. The complement of the union of set A and set B is equal to the intersection of the complement of set A and the complement of set B. ..

(12) Exclusion principle (special case):

Card (A∪B)= Card (A)+ Card (B)- Card (A∪B)

Card (A∪B∪C)= Card (A)+ Card (B)+ Card (C)- Card (A∪B)- Card (C∪A)+ Card (A ∪.

References:

Baidu encyclopedia-collection

References:

Baidu encyclopedia-mathematics daquan