sequence

…,-2,- 1,0, 1,2,…

The numbers in are called integers. All the integers make up an integer set, which is a ring, marked Z (usually written as a hollow letter Z in modern times). The potential of ring z is Alef 0.

In an integer system, natural numbers are positive integers, 0 is zero,-1, -2, -3, …, -n, … are negative integers. Positive integers, zero integers and negative integers form an integer system.

Positive integers have been a tool for human counting since ancient times. It can be said that the process of abstracting from "one cow and two cows" or "five people and six people" into positive integers is quite natural. In fact, we sometimes call positive integers natural numbers.

Zero not only means "none", but also means a vacant symbol. In ancient China, a computer chip was used to calculate numbers. When performing operations, no space was placed in the computer chip. Although there is no vacancy sign, it still creates good conditions for digital counting and four operations. The word "zero" in Indian Arabic numerology comes from India, and its original meaning is also "empty" or "blank".

China first introduced negative numbers. "Positive Numbers and Negative Numbers" discussed in Nine Chapters of Arithmetic. Equation "is the addition and subtraction of integers." The need for subtraction also promotes the introduction of negative integers. The subtraction operation can be regarded as solving the equation A+X = B. If both A a+x=b are natural numbers, then the given equation may not have a natural number solution. In order to make it always have a solution, it is necessary to expand the natural number system into an integer system.

Positive integers, zero and negative integers are collectively referred to as integers. Integer is the most basic mathematical tool that human beings can master. /kloc-Kroneck, a great German mathematician in the 0 th and 9 th centuries, therefore said, "Only integers are created by God, and others are created by human beings themselves."

The given integer n can be negative (n∈Z-), nonnegative (n∈Z*), zero (n=0) or positive (n ∈ z+).

See: algebraic integer, complex number, countable, natural number set n, natural number, negative number, positive number, real number, z, z-, z+, z *, zero.

Example: positive integer 1 2 3

Negative integer-1-2-3