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Transitivity

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Transitivity may refer to:

In grammar

In logic and mathematics

  • Transitive relation. 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.
  • Arc-transitive graph
  • Edge-transitive graph
  • Ergodic theory, a group action that is metrically transitive
  • Vertex-transitive graph
  • A group G acts transitively on a set S if for any x, yS, there is some gG such that gx = y. See group action. A somewhat related meaning is explained at ergodic theory.
  • A transitive set is a set A such that whenever xA, and yx, then yA. The smallest transitive set containing a set A is called the transitive closure of A.
  • A discrete dynamical system f is topologically transitive if every open subset U' of the phase space intersects every other open subset V, when going along trajectory, i.e. there exists an integer n, for which .

Other

  • Transitive Corporation, a computer software firm that developed QuickTransit

See also