▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Binary endorelation
Asymmetric binary relation
Formulation 0
A D4424: Binary endorelation $B = (X \times X, R)$ is asymmetric if and only if \begin{equation} \forall \, x, y \in X \left( (x, y) \in R \quad \implies \quad (y, x) \not\in R \right) \end{equation}
Also known as
Asymmetric binary endorelation