Arithmetic is the oldest, most basic and primitive part of mathematics. It studies the properties and operations of numbers. The oldest mathematics, arithmetic, is formed by the nature of numbers and the accumulation of experience in four operations between numbers. All mathematics in ancient times was called arithmetic, and modern algebra and number theory originally developed from arithmetic. Later, the concepts of arithmetic and mathematics appeared, which replaced the meaning of arithmetic and included all mathematics, and arithmetic became a branch of it.
About the generation of arithmetic, we still have to talk about numbers. Numbers are used to express and discuss quantitative problems. There are different types of quantities and also different types of numbers. As early as the initial stage of ancient development, due to the needs of human daily life and production practice, the simplest concept of natural numbers came into being in the initial stage of cultural development. One of the characteristics of natural numbers is that they are composed of inseparable individuals. For example, two things, a tree and a sheep, if two trees are in tandem; If there are three sheep, it is one, one after another. But you can't say that there are half trees and half sheep. Half a tree or half a sheep can only be counted as wood or mutton at best, but not as trees and sheep.
There are different relationships between numbers. In order to calculate these numbers, there are methods of addition, subtraction, multiplication and division. These four methods are four operations. The oldest mathematics, arithmetic, is formed by the nature of numbers and the accumulation of experience in four operations between numbers. During the development of the algorithm, many new problems have been raised due to the needs of practice and theory. In the process of solving these new problems, ancient arithmetic has been further developed from two aspects.
On the one hand, in learning the four operations of natural numbers, it is found that only division is more complicated, some can be divided, some can be divided, some cannot be decomposed, some are greater than the common divisor of 1, and some cannot. In order to seek the laws of these numbers, it has developed into an independent branch of mathematics, called integer theory or elementary number theory, which specializes in the properties of numbers and is independent from ancient arithmetic, and has made new development in the future.
Arithmetic, on the other hand, discusses various types of application problems in ancient arithmetic and various solutions to these problems. In the long-term research, it will naturally inspire people to seek general methods to solve these application problems. That is to say, can we find a universal and more universal method to solve the same type of application problems, so we invented abstract mathematical symbols, which developed into another ancient branch of mathematics, namely elementary algebra.
With the development of mathematics, arithmetic is no longer a branch of mathematics. What we usually call arithmetic is only a teaching subject in primary schools. The purpose is to enable students to understand and master the most basic knowledge about quantitative relations and spatial forms, correctly and quickly perform the four operations of integers, decimals and fractions, initially understand some of the simplest ideas in modern mathematics, and have preliminary logical thinking ability and spatial concepts.