Definition:Non-Transitive Relation

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

 * Definition:Transitivity (Relation Theory)


 * Definition:Transitive Relation
 * Definition:Antitransitive Relation