Involutive Function

Definition

Involutive Function

Let $X$ be a set. An involution on $X$ is a function $f:X\to X$ such that applying it twice returns every element to itself:

$$\forall x\in X:f(f(x))=x.$$

Equivalently, using function composition,

$$f\circ f={\mathrm{id}}_X,$$

where ${\mathrm{id}}_X$ is the identity function on $X$.