Intransitivity

In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. That is, we can find three values ${\displaystyle a}$, ${\displaystyle b}$, and ${\displaystyle c}$ where the transitive condition does not hold.

Antitransitivity is a stronger property which describes a relation where, for any three values, the transitivity condition never holds.

Be warned, some authors use the term intransitive to refer to antitransitivity.^[1][2]