Transitivity: Difference between revisions

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Transitivity or transitive may refer to:

Grammar

Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object
Transitive verb, a verb which takes an object
Transitive case, a grammatical case to mark arguments of a transitive verb

Logic and mathematics

Transitive group action
Transitive relation, a binary relation in which if A is related to B and B is related to C, then A is related to C
Syllogism, a related notion in propositional logic
Intransitivity, properties of binary relations in mathematics
Arc-transitive graph, a graph whose automorphism group acts transitively upon ordered pairs of adjacent vertices
Edge-transitive graph, a graph whose automorphism group acts transitively upon its edges
Vertex-transitive graph, a graph whose automorphism group acts transitively upon its vertices
Transitive set a set A such that whenever x ∈ A, and y ∈ x, then y ∈ A
Topological transitivity property of a continuous map for which every open subset U' of the phase space intersects every other open subset V, when going along trajectory

Other

Transitive Corporation, a computer software firm that developed QuickTransit cross-platform virtualization
Transitive dependency, a functional dependency of database management which holds by virtue of transitive relation

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-{{Wiktionarypar|transitivity}}
+{{wiktionary|transitivity|transitive}}
-'''Transitivity''' may refer to:
+'''Transitivity''' or '''transitive''' may refer to:
+{{TOC right}}
-==In grammar==
+==Grammar==
-* [[Intransitive verb]]
-* [[Transitive verb]], when a verb takes an object
+* [[Transitivity (grammar)]], a property regarding whether a lexical item denotes a transitive object
+* [[Transitive verb]], a verb which takes an object
-* [[Transitivity (grammar)]]
+* [[Transitive case]], a grammatical case to mark arguments of a transitive verb
-==In logic and mathematics==
+==Logic and mathematics==
-* [[Arc-transitive graph]]
-* [[Edge-transitive graph]]
-* [[Ergodic theory]], a group action that is metrically transitive
 * [[Transitive group action]]
-* [[Transitive relation]], a binary relation
+* [[Transitive relation]], a binary relation in which if ''A'' is related to ''B'' and ''B'' is related to ''C'', then ''A'' is related to ''C''
+* [[Syllogism]], a related notion in propositional logic
-* [[Vertex-transitive graph]]
+* [[Intransitivity]], properties of binary relations in mathematics
-* A [[group (mathematics)|group]] ''G'' acts '''transitively''' on a [[Set (mathematics)|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]].
+* [[Arc-transitive graph]], a graph whose automorphism group acts transitively upon ordered pairs of adjacent vertices
-* 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]].
+* [[Edge-transitive graph]], a graph whose automorphism group acts transitively upon its edges
-* A '''[[transitive set]]''' is a [[Set (mathematics)|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.
+* [[Vertex-transitive graph]], a graph whose automorphism group acts transitively upon its vertices
-* 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>.
+* [[Transitive set]] a set ''A'' such that whenever ''x'' ∈ ''A'', and ''y'' ∈ ''x'', then ''y'' ∈ ''A''
+* [[Topological transitivity]] property of a continuous map for which every open subset ''U''' of the phase space intersects every other open subset ''V'', when going along trajectory
 ==Other==
-* Transitive Corporation, a computer software firm that developed [[QuickTransit]]
+* [[Transitive Corporation]], a computer software firm that developed QuickTransit cross-platform virtualization
+* [[Transitive dependency]], a functional dependency of database management which holds by virtue of transitive relation
 ==See also==
+* [[Intransitive (disambiguation)]]
+{{disambiguation|math}}
-* [[intransitivity]]
-{{disambiguation}}
-{{mathdab}}
-[[uk:Транзитивність]]
-[[de:Transitivität]]
-[[de:Transitivität (Mathematik)]]
-[[es:Transitividad]]
-[[fr:Transitivité]]
-[[fi:Transitiivisuus]]