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 a function includes three elements: the domain A, the domain B and the corresponding rule F, among which the core is the corresponding rule F, which is the essential feature of the function relationship.
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.
Functions are related to inequalities and equations (elementary functions). Let the function value be equal to zero. From a geometric point of view, the value of the corresponding independent variable is the abscissa of the intersection of the image and the X axis.
From the algebraic point of view, the corresponding independent variable is the solution of the equation. In addition, replacing "=" in the expression of a function (except a function without expression) with "",and then replacing "y" with other algebraic expressions, the function becomes an inequality, and the norm of the independent variable can be obtained.
The set x of input values is called the domain of f; The set y of possible output values is called the range of f. The range of a function refers to the set of actual output values obtained by mapping f to all elements in the definition field. Note that it is incorrect to call the corresponding domain, and the function's domain is a subset of the corresponding domain.
In computer science, the data types of parameters and return values determine the definition domain and corresponding domain of subroutines respectively. Therefore, the domain and the corresponding domain are mandatory constraints determined at the beginning of the function. On the other hand, the scope is related to the actual implementation.