The [[Identity Function]] [[Function]] for some [[Set]] $X$ is a [[Function]] that when applied is idempotent for any value $x\in X$, denoted as $\op{id}_{X}$. $\huge \op{id} : x \mapsto x \\ $ $\huge \op{id}_{X} : X\to X $ The [[Identity Function|Identity Function]] is [[Bijective]], with the [[Inverse Function]] of $\op{id}$ being $\op{id}$. $\huge \op{id}_{X}^{-1} = \op{id}_{X} $ An *Identity* can also refer to a object for a given [[Binary Operation]] $\circ: X \times X\to Y$. such that the identity $e$ of $\circ$ has the propery that for any element $x\in X$, $x \circ e = x$ and $e \circ x = x$.