nLab
transitive relation

A (binary) relation $\sim$ on a set $A$ is transitive if in every chain of $3$ pairwise related elements, the first and last elements are also related:

which generalises from $3$ to any finite, positive number of elements.

In the language of the $2$-poset Rel of sets and relations, a relation $R:A\to A$ is transitive if it contains its composite with itself:

from which it follows that $R^n\subseteq R$ for any positive natural number $n$. To include the case where $n=0$, we must explicitly state that the relation is reflexive.

Transitive relations are often understood as orders.