Mathematical function

https://en.wikipedia.org/wiki/Function_(mathematics)

Function := a relation between sets that associates to every element of a first set exactly one element of the second set.

The words map, mapping, transformation, correspondence and operator are often used synonymously with the term function.

A bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set; there are no unpaired elements.

In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y.

The term one-to-one correspondence must not be confused with one-to-one (injective) function