Definition:Involution (Mapping)/Definition 1

Definition
Let $A$ be a set.

Let $f: A \to A$ be a mapping on $A$.

$f$ is an involution :
 * $\forall x \in A: \map f {\map f x} = x$

That is:
 * $f \circ f = I_A$

where $I_A$ denotes the identity mapping on $A$.

Also see

 * Equivalence of Definitions of Involutive Mapping