/kloc-Leibniz, a German mathematician in the 7th century, first put forward the concept of function. At first, Leibniz used the word "function" to express strength. Later, he used functions to represent the abscissa and ordinate of a point on a curve in a rectangular coordinate system. 17 18, a student of Leibniz, johann bernoulli1667-1748, based on the concept of Leibniz function, he clearly defined the concept of function: "the quantity composed of a variable and an arbitrary constant." This means that all formulas formed by a variable X and a constant are called functions of X, and he emphasizes that functions should be expressed by formulas. 1755, Euler (L. 1707- 1783) defines a function as: "If some variables depend on other variables in some way, that is, when the latter variable changes, the former variable also changes, so we call the former variable a function of the latter variable." And the function symbol that has been used up to now, namely years+082 1, is given. 1789- 1857) gives a function definition similar to the current middle school textbook: "Some variables have certain relationships. When the value of one variable is given and can be used to determine the values of other variables, this initial variable is called an independent variable and other variables are called functions. " On Cauchy's definition, the word independent variable appeared for the first time. France, 1768- 1830) found that some functions can be expressed by curves, one formula or multiple formulas, thus ending the debate on whether the concept of functions can be expressed by a single formula and pushing the understanding of functions to a new height. Dirichlet, 6438+0837, 1805- 1859) thinks that it is not important how to establish the relationship between X and Y. He extends the concept of function and points out: "For every certain value of X in a certain interval, Y has one or more certain values, so Y is called a function of X." At this point, it can be said that the concept of function and the essential definition of function have been formed, that is, the classical function definition that people often say. After the set theory founded by Cantor (,German, 1845- 19 18) was accepted by everyone, the concept of defining functions by set correspondence is now used in high school textbooks. The word "function" used in China's mathematics books is a translated word. It was translated into "function" by Li, an algebra expert in Qing Dynasty, when he translated Algebra (1895). In ancient China, the word "Xin" and "Han" were very common. This is providence. "In ancient China, heaven, earth, people and things were used to represent four different unknowns or variables. The meaning of this definition is: "Any formula containing the variable X is called a function of X", so "function" means that the formula contains variables.