The concept of a function is that there are two variables x and y during a certain change. If x takes a certain value and y changes with the change of x, then we call y a function of x ... Function is an important concept in mathematics. It is a rule that maps one or more input values to output values. In modern mathematics, function is a basic mathematical object, which is widely used in various fields, such as physics, engineering, economy and so on.

Function definition:

Function, a mathematical term. Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.

The modern definition of a function is to give a set of numbers A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another set of numbers B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of function consists of three elements: domain A, domain B and corresponding rule F..

. Among them, the core is the corresponding rule F, which is the essential feature of the functional relationship. Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, the function means that one quantity changes with another quantity, or that one quantity contains another quantity.

Source of function:

In ancient China, the word "Xin" and the word "Han" were universal and both had the meaning of "Han". Li's definition is: "every formula contains heaven, which is a function of heaven." In ancient China, four words were used to represent four different unknowns or variables: heaven, earth, people and things. The meaning of this definition is: "Whenever a formula contains the variable X, the formula is called a function of X."

So "function" means that the formula contains variables. The exact definition of an equation refers to an equation containing unknowns. However, in the early mathematical monograph "Nine Chapters Arithmetic" in China, the word "equation" means simultaneous linear equations with many unknowns, which are called linear equations.