Definition:Antitransitive Relation

Definition
Let $\RR \subseteq S \times S$ be a relation in $S$. $\RR$ is antitransitive :
 * $\tuple {x, y} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, z} \notin \RR$

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

 * Definition:Transitivity (Relation Theory)


 * Definition:Transitive Relation
 * Definition:Non-Transitive Relation