Definition:Involution (Mapping)/Definition 1
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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.
Sources
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 5$. Induced mappings; composition; injections; surjections; bijections: Exercise $11$: $(2)$