Identity map

In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged. That is, when ${\displaystyle f}$ is the identity function, the equality${\displaystyle f(x)=x}$ is true for all values of ${\displaystyle x}$ to which ${\displaystyle f}$ can be applied.