Function (translated as "equation" according to Japanese and English pronunciation in the late Qing Dynasty) was named after mathematician Li's 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.

The definition of function 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.

Chinese name

function

Foreign name

function

Another name

Containment number

express

y=f(x)

presenter

Leibniz

One answer after another.

tradition

Generally speaking, in the process of a change, it is assumed that there are two variables X and Y. If there is a unique Y corresponding to any X, it is said that Y is a function of X, where X is an independent variable and Y is a dependent variable. The range of x is called the domain of the function, and the range of y is called the domain of the function.

Modern Times

Let a and b be a set of non-empty numbers. If any number x in set A has a unique number corresponding to it according to a certain correspondence F, it is called a function from set A to set B, and it is called or.

Where x is called independent variable, dependent variable, set is called the domain of function, y corresponding to x is called the function value, and the set of function values is called the range of function.

Definition domain, value domain and corresponding rules are called the three elements of a function. Generally written. If the domain is omitted, it is usually a set of meaningful directional functions.