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''' or '''transitive''' may refer to:
-The word '''transitivity''' is used in severals contexts:
-* In [[grammar]], a verb is '''transitive''' if it takes an object.  See [[Transitivity (grammatical category)]] and [[transitive verb]].
+{{TOC right}}
-* In [[logic]] and [[mathematics]], a [[binary relation]] ''R'' is '''transitive''' if ''xRy'' and ''yRz'' together imply ''xRz''.  For example, the ''less-than'' relation is transitive.  See [[transitive relation]], [[intransitivity]].
+==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==
-* In [[mathematics]], a [[group action]] is '''transitive''' if it has just one [[orbit (group theory)|orbit]]. It is called '''doubly transitive''' if it is transitive on ordered pairs of distinct elements, and so on for '''triply transitive''', etc.  An [[ergodic theory|ergodic]] group action is also called ''metrically transitive''.
+* [[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==
-* In [[set theory]], a set is '''transitive''' if it contains all [[Element (mathematics)|element]]s of its elements.  See [[transitive set]].
+* [[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}}
-'''Transitive''' may refer to:
-* [[Transitive Corporation]], a [[computer software]] firm based in [[Manchester]], [[England]] and [[Los Gatos]], [[California]].
-{{disambig-cleanup}}
-[[de:Transitivität]]
-[[es:Transitividad]]
-[[fr:Transitivité]]