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Function, a mathematical term. Its definition 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.
The modern definition of a function is to give a number set A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of function consists of three elements: domain A, domain B and corresponding rule F..
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.
In the process of a change, the amount of change is called a variable (in mathematics, the variable is X, and Y changes with the change of X value), and some numerical values do not change with the variable, so they are called constants. Independent variable (function): a variable related to other quantities, and any value in this quantity can find a corresponding fixed value in other quantities.
The word "function" used in China's math book is translated. It was Li, an algebra expert in China's Qing Dynasty, who translated "function" into "function" when he translated Algebra (1859).
In ancient China, the word "Xin" and the word "Han" were universal and both had the meaning of "Han". Li's definition is: "every formula contains heaven, which is a function of heaven." In ancient China, four different unknowns or variables were represented by four words: heaven, earth, people and things. The meaning of this definition is: "Whenever a formula contains the variable X, the formula is called a function of X."
So "function" means that the formula contains variables. The exact definition of an equation refers to an equation containing unknowns. However, in the early mathematical monograph "Nine Chapters Arithmetic" in China, the word "equation" means simultaneous linear equations with many unknowns, which are called linear equations.
Dependent variable (function): it changes with the change of independent variable. When the independent variable takes a unique value, the dependent variable (function) has and only has a unique value corresponding to it. Function value: in a function where y is x, x determines a value, and y determines a value accordingly. When x takes a, y is determined as b, and b is called the function value of a. ..