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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+{{wiktionary|transitivity|transitive}}
-In [[mathematics]], '''transitivity''' is a mathematical property of [[binary relation]]s such that if A and B are related, and B and C are related, then it follows that A and C are also related.
+'''Transitivity''' or '''transitive''' may refer to:
+{{TOC right}}
-In notation, this is:
+==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==
-:<math>a R b  \wedge  b R c \Rightarrow a R c</math>
+* [[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==
-For example, "is greater than" and "is equal to" are transitive relations: if a=b and b=c, then a=c.
+* [[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==
-On the other hand, "is the mother of" is not a transitive relation, because if Alice is the mother of Brenda, and Brenda is the mother of Claire, then Alice is not the mother of Claire.
+* [[Intransitive (disambiguation)]]
+{{disambiguation|math}}
-See also [[Transitive closure]].