# Definition:Non-transitive Relation

## Definition

Let $\mathcal R \subseteq S \times S$ be a relation in $S$.

$\mathcal R$ is non-transitive if and only if 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

• Results about relation transitivity can be found here.