Definition:Antitransitive Relation

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

$\RR$ is antitransitive if and only if:

$\tuple {x, y} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, z} \notin \RR$

that is:

$\set {\tuple {x, y}, \tuple {y, z} } \subseteq \RR \implies \tuple {x, z} \notin \RR$

Also known as

Some sources use the term intransitive.

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

Also see

  • Results about antitransitive relations can be found here.