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


* A [[group (mathematics)|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 [[group (mathematics)|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]].
* 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]].
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[[Category:Mathematical disambiguation]]
[[Category:Mathematical disambiguation]]


[[de:Transitivität_(Mathematik)]]
[[de:Transitivität (Mathematik)]]
[[uk:Транзитивність]]
[[uk:Транзитивність]]

Revision as of 16:14, 11 May 2006

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

  • 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 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