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 deeper understanding, it is undoubtedly beneficial to deepen their understanding of classroom knowledge and stimulate their interest in learning.
The concept of function was first put forward by the German mathematician Leibniz in17th century. Function? This word stands for a kind of power, such as
They 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 18.2008, Bernoulli, a student of Leibniz and a Swiss mathematician, defined the function as:? A quantity composed of a variable and an arbitrary constant. It means that any formula composed of variable X and constant is called a function of X, and Bernoulli emphasized that functions should be expressed by formulas.
Later, mathematicians felt that the concept of function should not be limited to formulas. As long as some variables change, other variables 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 the function as:? If some variables depend on other variables in some way, that is, when the latter variable changes, the former variable also changes, 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. He believes that a function is a curve drawn at will.
At that time, some mathematicians were not used to expressing functions without formulas, and some mathematicians were even skeptical. They call it a function that can be expressed by formulas? True function? Call a function that cannot be expressed in a formula? False function? 182 1 year, French mathematician Cauchy gave a function definition similar to the current middle school textbook:? There are certain relationships between some variables. When the value of one variable is given and can be used to determine the values of other variables, the initial variable is called an independent variable and the other variables are called functions. In Cauchy's definition, the word independent variable first appeared.
1834, Russian mathematician Lobachevsky further put forward the definition of function:? The function of x is a number, which has a definite value for each x and changes with it. The function value can be given by an analytical formula or a condition, which provides a method to find all the corresponding values. This dependence of the function can exist, but it is still unknown. This definition points out the necessity of correspondence (condition), through which the corresponding value of each x can be obtained.
1837, the German mathematician Dirichlet thought that how to establish the corresponding relationship between X and Y was irrelevant, so his definition was:? If for every value of x, y always has a completely definite value corresponding to it, then y is a function of x, and this definition captures the essential attribute of the concept. The variable y is called a function of x, and there is only one rule, so that every value in the range of this function has 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 universal 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 middle school textbooks.
Used in China's math book? Function? The word "algebra" is translated. It was put forward by Li, an mathematician in Qing Dynasty, when he translated Algebra (1895). Function? Translation? Function? Yes Ancient China? Letter? Word sum? Including? Words are universal, and all of them are available? Contain? Li's definition is:? Where the formula contains heaven, it is the function of heaven. In ancient China, four words were used to represent four different unknowns or variables: heaven, earth, people and things. What does this definition mean? When a formula contains the variable x, the formula is called a function of X. So what? Function? This means that the formula contains variables.
In the foreseeable future, the debate, research, development and extension of functions will not end, and it is these that affect the development of mathematics and its adjacent disciplines.