Identity map – TheoremDex

▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map

Identity map

Formulation 0

A D18: Map $f : X \to Y$ is an identity map on $X$ if and only if \begin{equation} \forall \, x \in X : f(x) = x \end{equation}

Formulation 1

A D18: Map $f : X \to Y$ is an identity map on $X$ if and only if $x$ is a D551: Fixed point of $f$ for every $x \in X$.

Also known as

Diagonal map

Child definitions