# Definition:Non-transitive Relation

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## Contents

## Definition

Let $\RR \subseteq S \times S$ be a relation in $S$.

$\RR$ 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.

## Sources

- 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): $\S 4.5$: Properties of Relations - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**non-transitive**(of a relation)