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{{Wiktionarypar|transitivity}}
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'''Transitivity''' may refer to:


==In grammar==
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* [[Intransitive verb]]
* [[Transitive verb]], when a verb takes an object
* [[Transitivity (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'', ''y'' ∈ ''S'', there is some ''g'' ∈ ''G'' 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 ''x'' ∈ ''A'', and ''y'' ∈ ''x'', then ''y'' ∈ ''A''. The smallest transitive set containing a set A is called the [[transitive closure]] of A.
* A discrete dynamical system ''f'' is [[Topological transitivity#Topological mixing|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 <math>f^n(U)\cap V\neq\emptyset</math>.
 
==Other==
* Transitive Corporation, a computer software firm that developed [[QuickTransit]]
 
==See also==
 
* [[intransitivity]]
 
{{disambiguation}}
{{mathdab}}
 
[[uk:Транзитивність]]

Latest revision as of 23:33, 20 December 2014

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