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"taking a direct object" (of verbs), 1570s (implied in transitively), from Late Latin transitivus (Priscian) "transitive," literally "that may pass over (to another person)," from transire "go or cross over" (see transient).
Of or relating to a mathematical or logical relation between three elements such that if the relation holds between the first and second elements and between the second and third elements, it necessarily holds between the first and third elements. The relation of being greater than in mathematics is transitive, since if a > b and b > c, then a > c.
A relation R is transitive if x R y & y R z => x R z. Equivalence relations, pre-, partial and total orders are all transitive.