definition

display method

set of natural numbers

set of positive integers

set of integers

set of rational numbers

set of real numbers

List the elements in the set one by one

Generally, if any element A can be represented by its characteristic property p(x) as ﹛x丨p(x)﹜

if a<b

If any element in set A is an element in set B, then set A is called a subset of set B.

If a set A is a subset of a set B, and at least one element in B does not belong to A, then the set A is called a proper subset of the set B.

Given two sets A and B, the set consisting of all elements belonging to both A and B is called the intersection of A and B.

Given two sets A and B, the set consisting of all elements of these two sets is called the union of A and B.

If the sets to be studied are all subsets of a given set, then the given set is called the complete set, usually represented by U.

If a set A is a subset of the complete set U, then the set consisting of all elements in U that do not belong to A is called the complement of A in U

Statements and sentences that can be judged as true or false, such as "opposite angles are equal", are propositions.

The general "any" and "all" in a statement express the entirety of the stated affairs, and are called universal quantifiers.

"Existence" and "have" represent the individual or part of the stated matter in the statement, which are called existential quantifiers

By negating the proposition p, we get a new proposition, denoted as ┐p

The negation of existential quantifier proposition is universal quantifier proposition

The negation of the universal quantifier proposition is the existential quantifier proposition

When p ⇒ q, it is said that p is a sufficient condition for q and q is a necessary condition for p.

If p⇒q, q⇒p, then p is said to be an essential condition of q