Definition:Transitive Relation/Definition 2

Definition
Let $\mathcal R \subseteq S \times S$ be a relation in $S$. $\mathcal R$ is transitive :


 * $\mathcal R \circ \mathcal R \subseteq \mathcal R$

where $\circ$ denotes composite relation.

Also see

 * Equivalence of Definitions of Transitive Relation