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
Binary endorelation
Reflexive binary relation
Definition D1837
Irreflexive binary relation
Formulation 0
A D4424: Binary endorelation $(X \times X, R)$ is irreflexive if and only if \begin{equation} \forall \, x \in X : (x, x) \not\in R \end{equation}