ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Inverse binary relation
▼ Inverse map
Definition D702
Involution
Formulation 2
Let $f : X \to X$ be a D18: Map such that
(i) $f$ is an D976: Invertible map
(ii) $f^{-1}$ is an D216: Inverse map of $f$
Then $f$ is an involution if and only if \begin{equation} f = f^{-1} \end{equation}
Results
▶ R2950: Complex conjugation operation is an involution