\begin{definition}[Definition:Involution (Mapping)/Definition 1]
Let $A$ be a set.
Let $f: A \to A$ be a mapping on $A$.
$f$ is an '''involution''' {{iff}}:
:$\forall x \in A: \map f {\map f x} = x$
That is:
:$f \circ f = I_A$
where $I_A$ denotes the identity mapping on $A$.
\end{definition}