Transitivity

• In grammar, a verb is transitive if it takes an object. See transitive verb.

• In logic and mathematics, a binary relation R is transitive if xRy and yRz together imply xRz. For example, the less-than relation is transitive. See transitive relation, intransitivity.

• In mathematics, a group action is transitive if it has just one orbit. It is called doubly transitive if it is transitive on ordered pairs of distinct elements, and so on for triply transitive, etc. An ergodic group action is also called metrically transitive.