Definition:Non-Transitive Relation

Definition
Let $\mathcal R \subseteq S \times S$ be a relation in $S$. $\mathcal R$ is non-transitive iff it is neither transitive nor antitransitive.

Also known as
Some sources use the term intransitive.

However, as intransitive is also found in other sources to mean antitransitive, it is better to use the clumsier, but less ambiguous, non-transitive.

Also see

 * Transitivity of Relations


 * Transitive Relation
 * Antitransitive Relation