**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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

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