Similarities:

(1) function and mapping are the corresponding relations 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;

Difference:

The (1) function must be a mapping, and the mapping is not necessarily a function. Mapping is an extension of a function.

(2) It is enough that the elements on one side of the map correspond to the other side. It is not necessary to ask the other party to object to the response, but the function requires both parties to eat enough.

(3) Function is a special mapping, which is the corresponding relationship between non-empty number sets; Mapping contains not only one correspondence of functions, but also other correspondences. There is a special case of mapping: surjection, that is, there are no redundant elements in the image set; A function is a surjection between sets of numbers.

(4) Function is a special kind of mapping, which requires that the elements in two sets must be numbers, and the elements in two sets in the mapping are arbitrary mathematical objects. Functions are included in the map.