is the element in the codomain. The pre-image of an element is any element in the domain such that . Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set.

A function is bijective if and only if it is invertible; that is, a function is bijective if and only if there is a function the inverse of , such that each of the two ways for composing