Definition:Involution (Mapping)/Definition 3
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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 $f$ is both a bijection and a symmetric relation.
That is, if and only if $f$ is a bijection such that:
- $f = f^{-1}$
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 $11$: $(1)$