# 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 if and only if:

$\forall x \in A: \map f {\map f x} = x$

That is:

$f \circ f = I_A$

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

## Also 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

• Results about involutions can be found here.