Transitivity: Difference between revisions
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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: |
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* A [[group (mathematics)|group]] ''G'' acts '''transitively''' on a [[set]] ''S'' if for any ''x'', ''y'' |
* 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]]. |
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* 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]] |
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[[de: |
[[de:Transitivität (Mathematik)]] |
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[[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, 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.