What exactly is mapping in mathematics? What is the relationship among definition domain, value domain and culture domain, and how to understand their definitions?

Mapping is a corresponding relationship between the independent variable X and the dependent variable Y, that is, Y = X 2. Mapping is a square, and the domain is the set of values that the independent variable X can take, and the range is the set of values that the dependent variable Y can get.

(1) function and mapping are the corresponding relationships of elements in two non-empty sets.

(2) The correspondence between function and mapping is directional.

(3) The elements in A are arbitrary and the elements in B are unique; That is, any element B in A has a unique element corresponding to it. (Except for multivalued functions, they are generally not included in the category of functions).

function

The essence of the two definitions is the same, but the starting point of describing the 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..