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Transitivity

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In mathematics, the word transitive admits at least two distinct meanings:

  • A group G acts transitively on a set S if for any x, y ∈ S, there is some g ∈ G such that gx = y. See group action. A somewhat related meaning is explained at ergodic theory.
  • A binary relation is transitive if whenever A is related to B and B is related to C, then A is related to C, for all A, B, and C in the domain of the relation. See transitive relation.

See also transitive closure, Intransitivity

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