Definition:Involution (Mapping)/Definition 2

Definition

Let $A$ be a set.

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

$f$ is an involution if and only if:

$\forall x, y \in A: \map f x = y \implies \map f y = x$

Also known as

An involution is also known as an involutive mapping or an involutive function.

An involutive mapping can also be found described as self-inverse.

Also see

• Equivalence of Definitions of Involutive Mapping

• Results about involutions can be found here.