information:extraction
Definition

Formally, if X is a set, the identity function f on X is defined to be a function with X as its domain and codomain, satisfying

In other words, the function value f (x) in the codomain X is always the same as the input element x in the domain X. The identity function on X is clearly an injective function as well as a surjective function (its codomain is also its range), so it is bijective.

The identity function f on X is often denoted by id.

In set theory, where a function is defined as a particular kind of binary relation, the identity function is given by the identity relation, or diagonal of X.