Integer sets have the following properties:
1. closure: For any two integers A and B, their sum a+b, difference a-b and product a×b are still integers.
2. Integer operation: Integer set defines operations such as addition, subtraction and multiplication, which meet the corresponding operation rules.
3. Sortability: The integers in the integer set can be sorted by size to form an integer number axis.
4. Anti-elementality: For every integer A, there is a corresponding integer -b, so that a+(-b)=0.
5. Divisibility: For integers A and B, if A is divisible by B (that is, the quotient of A ÷b is an integer), then A is a multiple of B, or B is a divisor of A. ..
Extended data:
Common number sets and number set symbols in mathematics;
1, positive integer set
The positive integer set is the set of all positive integers, and the symbol set of the positive integer set is an uppercase English letter "N+" or "N*". Positive integers include all positive integers: 1, 2, 3, 4, 5, etc.
2. natural number set
Natural number set is the set of all natural numbers, and collection of symbols is the capital letter "n". Natural numbers include positive integers and 0.
3. Integer set
The integer set is the set of all integers, and the symbol set is the capital letter "z". Integers include negative integers, 0 and positive integers.
4. Rational number set
The set of rational numbers is the set of all rational numbers, and the set of symbols is the capital English letter "Q". Rational numbers include integers, finite decimals, infinite cyclic decimals and fractions that can be converted into finite decimals and infinite cyclic decimals.
5. Real number set
Real numbers can be divided into rational numbers and irrational numbers. Irrational numbers include infinite numbers and infinite acyclic decimals. Common irrational numbers in middle school mathematics, such as pi t and the base e of natural logarithm. The symbol set of the real number set is the capital letter "r".