First, the concept of integer

Integer is a set of positive integers, zero and negative integers. All integers form an integer set, which is a number ring. In the integer system, zero and positive integers are collectively called natural numbers. -1, -2, -3, …, -n, …(n is a non-zero natural number) are negative integers. Positive integers, zero integers and negative integers form an integer system.

Integers exclude decimals and fractions. Unless otherwise specified, all the numbers involved are integers, and the letters used also represent integers. Integers can be regarded as fractions with the denominator 1

Second, the classification of integers

With 0 as the boundary, integers are divided into three categories:

1. positive integer, that is, an integer greater than 0, such as 1, 2, 3 ... until.

2. Zero is neither a positive integer nor a negative integer, but a number between positive and negative integers.

3.？ Negative integers, that is, integers less than 0, such as-1, -2, -3 ... until.

Note: Zero and positive integers are collectively called natural numbers.

Integers can also be divided into odd and even numbers.

Third, the parity of integers.

1.？ Odd+odd = even, even+even = even, odd+even = odd, even × even = even, odd × even = even, odd × odd = odd; That is, the sum, difference and product of any number of even numbers are still even, the sum and difference of odd numbers are odd, and the sum and difference of even numbers are even.

2. The square of odd number can be expressed as (8m+ 1)? The square of an even number can be expressed as? 8m or (8m+4) form.

3. If the product of a finite number of integers is odd, then every integer is odd; If the product of a finite number of integers is even, at least one of these integers is even; The sum and difference of two integers have the same parity; If the square root of an integer is an integer, then both have the same parity.

The benefits of learning math well

First, improve the logical thinking ability:

Mathematics is a subject with strict logic. Learning mathematics can help us cultivate our logical thinking ability and improve our ability to analyze and solve problems.

Second, enhance computing power:

Mathematics is a kind of calculation training. By studying mathematics, we can improve our computing ability and better meet the computing needs in daily life and work.

Third, cultivate abstract thinking and innovative thinking;

There are many abstract concepts and ways of thinking in mathematics. Learning mathematics can help us cultivate abstract thinking and innovative thinking, and make us more capable of discovery and creation.

Fourth, improve mathematics literacy and mathematics application ability;

Mathematics is a subject widely used in various fields. Learning mathematics can improve our mathematical literacy and mathematical application ability, so as to better cope with practical problems and challenges.

Five, improve the humanistic quality and cultural quality:

Mathematics, as a common form of knowledge in the development of human civilization, can improve our humanistic quality and cultural accomplishment and help us better understand and appreciate the essence of human civilization.