i.e. a mapping establishes a correspondence between the elements of and the elements of such that every element of appears in a single pair in .

- Let be the set of students in a classroom; the correspondence which assigns to each student his left neighbour is not a mapping from to , because at the left end of a row, there is a student who has no left neighbour (i.e. there exists at least an element of which can have no image in this correspondence).
- Let be the set of inhabitants of a given town and be the set of all blood types (O+, O-, A+, etc.). When we assign to each element of his/her blood type, we define a mapping .
- Let be the set of all the natural numbers. Let us assign to each natural number its double , we define a mapping .
- The correspondence determines a mapping from to .

The mappings and have the same domain and the same range, but their graphs are different (i.e. the correspondences they define are different). For example, we have and , hence .