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}