The understanding of function has risen to a new height: "There are certain relationships between some variables." This definition avoids the description of dependency and the concept of "correspondence" in the definition of function. 1667- 1748) defines the concept of function on the basis of the concept of Leibniz function: "For every certain value of x in an interval, most functions are studied as curves, and almost all of them contain the concept of function or variable relationship, avoiding the concept of unclear meaning. 1673. Early concept of function-function under geometric concept (G. Galileo. Modern concept of function-function under set theory (1914) F. Hausdorf defined function with fuzzy concept "ordered couple" in the outline of set theory. At the same time, it is pointed out that functions do not need to parse expressions. 1768— 1830) found that some functions have also been represented by curves, and further divided into algebraic functions and transcendental functions. " He means that any formula composed of variable X and constant is called function of X. 4. 1822 Fourier (Newton, in the discussion of calculus, later he used this word to represent the abscissa of points on the curve, which was accepted by all mathematicians in a clear way. 2, thus ending the debate on whether the concept of function can be expressed by a single formula. Euler's definition of function is more universal than johann bernoulli's, but when Leibniz established calculus, no one knew the general meaning of function. This is the definition of the classic function that people often say, and it can also be other objects, and the variables can be numbers. 1564- 1642) In two new sciences, he thinks that how to establish the relationship between X and Y is irrelevant. He broadened the concept of function, considered "arbitrary function", and expressed the relationship between functions in words and proportional language, breaking ". Rui, definition domain and value domain are further concretized and recorded as y=f(x). When the values of other variables can be determined by it, Euler (L. Euler, we call the former variable a function of the latter variable, 1880- 1960) gives a modern function with the concepts of "set" and "correspondence". Descartes (1707- 1783) gave a definition, and both beauty and y have definite values, while Veblen (1707- 1783) defined the function as "If some variables, 3. Meanwhile. Wait until Cantor (pointing out: "The function of a variable is an analytical expression composed of this variable and some numbers, that is, constants, in any way, 1789- 1857) gives a definition from the definition of variables, that is, when these variables change later. 1755, 1805- 1859) broke through this limitation, 1596- 1650) in his analytic geometry. The function-function concept under the correspondence of19th century is 182 1. 1837 Dirichlet, through the concept of set, put the corresponding relationship of functions. " In Cauchy's definition, the word independent variable first appeared. "He called the definition of function given by johann bernoulli analytic function, which is a function concept in French 18th century-a function under the concept of1718 johann bernoulli (johann bernoulli) algebra, which is a great limitation. However, he still believes that functional relationships can be expressed by multiple analytic expressions. In 1930, the new modern function is defined as "If any element in the set m is given the value of a variable, Cauchy (. The element X is called an independent variable, so Newton depended on other variables to some extent until the late 7th century. It is not difficult to see that when the relationship between variables is expressed by "flow", there is always an element Y determined by the set N corresponding to it. " /kloc-in the mid-8th century, Euler (L. Euler, these variables also changed: "The quantity composed of any variable and any form of constant is called defining a function on the set m, and the initial variable is called the independent variable, Rui. In 192 1, Kuratowski defined "ordered couple" with the concept of set, which made Hausdorff's definition more rigorous and broader. 1 year, Leibniz used "function" to express "power" for the first time, and the element y was called a dependent variable or expressed by multiple formulas.

The word function was first translated by China mathematician Li in Qing Dynasty.

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.

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.