**identity map**on $X$ if and only if \begin{equation} \forall \, x \in X : f(x) = x \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ 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