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
Definition D288
Transitive binary relation
Formulation 0
A D4424: Binary endorelation $B = (X \times Y, R)$ is transitive if and only if \begin{equation} \forall \, x, y, z \in X \left( (x, y), (y, z) \in R \quad \implies \quad (x, z) \in R \right) \end{equation}
Formulation 1
A D4424: Binary endorelation $B = (X \times Y, R)$ is transitive if and only if \begin{equation} \forall \, x, y, z \in X \left( x R y, y R z \quad \implies \quad x R z \right) \end{equation}
Also known as
Transitive binary endorelation