The Concept of Integers in Mathematics 5, the Concept of Integers in Mathematics

Integer: Numbers like -2, -1, 0, 1, 2 are called integers. Integer is the most basic mathematical tool that humans can master.

The whole of an integer makes up an integer set, and the set of integers is a ring of numbers. In the integer system, the natural number is a collective term for 0 and positive integers, 0 is called zero, and it is called -1, -2, -3 、...、n、…n is an integer) is a negative integer. Positive integers, zeros, and negative integers make up the integer system.

A given integer n can be negative (n z-), non-negative (n z*), zero (n = 0), or positive (n z+).

Integer, divided into positive integers, negative integers, and zeros.

Integers are positive integers.

0 + negative integer, that is, except for fractions, decimals, e.g. , -4, -8, etc. are all integers.

The whole of an integer makes up an integer set.

An integer set is a ring of numbers. In the integer system, zeros and positive integers are collectively referred to as natural numbers.

1、-2、-3、…、n、…(n is a non-zero natural number) is a negative integer. then positive integers, zeros, and negative integers form an integer system. Integers do not include decimals and fractions.

Divisibility features1. If the last digit of a number is a single or even number, the number is divisible by 2.

2. If the sum of all digits of a number is divisible by 3, then the integer is divisible by 3.

3. If the last two digits of a number are divisible by 4, then the number is divisible by 4.

4. If the last digit of a number is 0 or 5, the number is divisible by 5.

An integer is a collection of positive integers, zeros, and negative integers. The whole of an integer makes up an integer set, and an integer set is a ring of numbers. In the integer system, zeros and positive integers are collectively referred to as natural numbers. Integers do not include decimals and fractions.

In addition, integers are also divided into two categories: odd and even. Among integers, the number that is divisible by 2 is called an even number. Numbers that are not divisible by 2 are called odd numbers.

Positive integer properties.

1. Fundamental theorem of arithmetic.

The only decomposition theorem for positive integers: also known as the fundamental theorem of arithmetic.

That is, every natural number greater than 1 can be written as the product of the powers of several prime numbers, and these prime factors are unique after they are arranged by size.

2. Discrete inequality.

If x,n n*, then x>n is equivalent to x n+1.

Integer: Numbers like -2, -1, 0, 1, 2 are called integers.

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

1.Positive integers, i.e. integers greater than 0. Such as: 1,2,3··· Until n.

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

3.Negative integers, i.e. integers less than 0. Such as: 1,2,3··· Until n. (n is a positive integer).

Integer numbers can also be divided into two categories: odd and even.

The whole of an integer makes up an integer set, and an integer set is a ring of numbers. In the integer system, zeros and positive integers are collectively referred to as natural numbers. Integers do not include decimals and fractions.

An integer isPositive integer, zero, a set of negative integers.

The whole of an integer makes up an integer set.

An integer set is a ring of numbers. In the integer system, zeros and positive integers are collectively referred to as natural numbers.

1、－2、－3、…, n, (n is a non-zero natural number) is a negative integer. then positive integers, zeros, and negative integers form an integer system. Integers do not include decimals and fractions.

Unless otherwise specified, the numbers involved are whole numbers, and the letters used also represent integers.

Odd and even

Among integers, the number that is divisible by 2 is called an even number. Numbers that are not divisible by 2 are called odd numbers. That is, when n is an integer, an even number can be expressed as 2n (n is an integer); Odd numbers can be expressed as 2n+1 (or 2n-1).

Even numbers include positive even numbers (also known as even numbers), negative even numbers, and 0s. All integers are either odd or even.

"Positive integers, zeros, and negative integers are collectively referred to as integers. Integers are divided into three parts, namely positive integers, zeros, and negative integers.

Integer: Numbers like 2, 1,0,1,2 are called integers, and integers are the most basic mathematical tools that humans can master. The whole of an integer makes up an integer set, and the set of integers is a ring of numbers.

Introduction

There are addition and multiplication operations in the set of natural numbers, and the result of adding or multiplying two natural numbers is still a natural number, and it can also be subtracted or divided, but the results of subtraction and division may not be natural numbers, so subtraction and division operations are not always true in the set of natural numbers.

In order to make the number system have a strict logical foundation, mathematicians in the 19th century established two equivalent theories of natural numbers: the ordinal number theory of natural numbers and the cardinal number theory, so that the concept, operation and related properties of natural numbers have been strictly discussed.

"Positive integers, zeros, and negative integers are collectively referred to as integers. The whole of an integer makes up an integer set, and the set of integers is a ring of numbers. Integers are divided into negative integers, 0s, and positive integers, among which non-negative integers are also called natural numbers.

Thus, negative integers, zeros, and positive integers form an integer system (also known as an integer set).

An integer is a set of positive integers, zeros, and negative collapses.

The whole of an integer makes up an integer set, and an integer set is a ring of numbers. In the integer system, zeros and positive integers are collectively referred to as natural numbers. Integers do not include decimals and fractions. Positive integers are a tool for human counting since ancient times. ”

Odd and evenAmong integers, the number that is divisible by 2 is called an even number. Numbers that are not divisible by 2 are called odd numbers. That is, when n is an integer, an even number can be expressed as 2n (n is an integer); Odd numbers can be expressed as 2n+1 (or 2n-1).

Even numbers include positive even numbers (also known as even numbers), negative even numbers, and 0s. All integers are either odd or even.

In the ten-tan conjugation system, we can determine whether the number is odd or even by looking at the single digit and pretending to be a circle number: the number with a single digit of 1, 3, 5, 7, and 9 is an odd number; Numbers with single digits of 0, 2, 4, 6, and 8 are even.

An integer is a number like -3, -2, -1, 0, 1, 2, 3, 10, etc.

The whole of an integer makes up an integer set, and an integer set is a ring of numbers. In the integer system, zeros and positive integers are collectively referred to as natural numbers. -1、-2、-3、?、n、?(n is a non-zero natural number) is a negative integer. then positive integers, zeros, and negative integers form an integer system.

In 1920, the concept of "left mold", "right mold" was introduced. The Ideal Theory of the Whole Ring, written in 1921, was a milestone in the development of commutative algebra. Among them, when Noether introduced the concept of integer rings (the set of integers itself is also a number ring), she was a German Qiaodongqiao, and the German integer is called zahlen, so she wrote the integer ring as z at that time.