The history of mathematics shows that the emergence and development of important mathematical concepts play an inestimable role in the development of mathematics, and some important mathematical concepts play a fundamental role in the emergence of mathematical branches. The function we just learned is a very important concept.

Since Descartes introduced variables, concepts such as variables and functions have increasingly penetrated into various fields of science and technology. Observing the universe, operating celestial bodies, exploring heat conduction and revealing electromagnetic secrets are all closely related to the concept of function. It is in these practices that people deepen the concept of function.

Looking back on the development history of the concept of function, although it is impossible for junior middle school students who are new to function to have a deep understanding, it is undoubtedly beneficial to deepen their understanding of classroom knowledge and stimulate their interest in learning.

/kloc-Leibniz, a German mathematician in the 7th century, first put forward the concept of function. The word turtle stands for strength, such as x, x2 and x3, which are all called functions. Later, he used functions to represent the abscissa and ordinate of a point on a curve in a rectangular coordinate system.

17 18, Bernoulli, a student of Leibniz and a Swiss mathematician, defined a function as "a quantity composed of a variable and an arbitrary constant", which means that any formula composed of a variable x and a constant is called a function of X. Bernoulli emphasized that a function should be expressed by a formula.

Later, mathematicians felt that the concept of function should not be limited to formulas. As long as some variables change, others can also change accordingly. Whether the relationship between these two variables should be expressed by formulas is not the criterion for judging functions.

1755, the Swiss mathematician Euler defined a function as "if some variables:" which depends 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. "In Euler's definition, it is not emphasized that functions should be expressed by formulas. Because functions don't have to be expressed by formulas, Euler once called the curve drawn in the coordinate system a function.

At that time, some mathematicians were not used to expressing functions with formulas, and some mathematicians were even skeptical. They call functions that can be expressed by formulas "true functions" and functions that cannot be expressed by formulas "false functions".

In 182 1, French mathematician Cauchy gave a function definition similar to the current middle school textbook: "There is a certain relationship between some variables. When the value of one variable is given and other variables can be determined by it, the initial variable is called independent variable, and other variables are called functions. In Cauchy's definition, the word independent variable first appeared.

1834, the Russian mathematician Lobachevsky further put forward the definition of function: "The function of x is such a number that it has a certain value for each x" and changes with x, and the function value can be given by an analytical formula or a condition, which provides a method to find all the corresponding values. Functional dependencies can exist, but they are still unknown. This definition States that

1837 Dirichlet, a German mathematician, thinks that how to establish the corresponding relationship between X and Y is irrelevant, so his definition is: "If for every value of X, Y always has a completely determined value corresponding to it, then Y is a function of X". This definition captures the essential attribute of the concept, and the variable Y is called the function of X, so there is only one law to make this function take every value within the range of values. It is enough to have a certain Y value corresponding to it, no matter whether this rule is a formula, an image, a table or other forms. This definition is more general than the previous definition, which provides convenience for theoretical research and practical application. So this definition has been used for a long time.

Since the German mathematician Cantor's set theory was accepted by everyone, the concept of function is now defined by set correspondence in high school textbooks. The word "function" used in China's mathematics books is a translated word. The book Algebra (1895) was translated by Li, an algebra expert in Qing Dynasty. Translate it into a function number? The word "Xin" and "Han" were commonly used in ancient China, both of which had the meaning of "Han". The definition given by Li is that "every formula contains days, which is a function of days." 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: "When a formula contains a variable X, the formula is called a function of X."

We can predict that the argument, research, development and extension of functions will not end, and it is these that affect the development of mathematics and its adjacent disciplines.