Transitivity or transitive may refer to:
Grammar
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Transitivity (grammar)
In linguistics, transitivity is a property of verbs that relates to whether a verb can take objects and how many such objects a verb can take. It is closely related to valency, which considers other verb arguments in addition to direct objects. ...
, a property of verbs that relates to whether a verb can take direct objects
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Transitive verb
A transitive verb is a verb that accepts one or more objects, for example, 'cleaned' in ''Donald cleaned the window''. This contrasts with intransitive verbs, which do not have objects, for example, 'panicked' in ''Donald panicked''.
Transitiv ...
, a verb which takes an object
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Transitive case In linguistic typology, transitive alignment is a type of morphosyntactic alignment used in a small number of languages in which a single grammatical case is used to mark both arguments of a transitive verb, but not with the single argument of an in ...
, a grammatical case to mark arguments of a transitive verb
Logic and mathematics
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Transitive group action
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism ...
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Transitive relation
In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive.
Definition
A homo ...
, a binary relation in which if ''A'' is related to ''B'' and ''B'' is related to ''C'', then ''A'' is related to ''C''
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Syllogism
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
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, a related notion in propositional logic
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Intransitivity
In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. This may include any relation that is not transitive, or the stronger property of antitransitivity, which descri ...
, properties of binary relations in mathematics
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Arc-transitive graph
In the mathematical field of graph theory, a graph is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices and of , there is an automorphism
:f : V(G) \rightarrow V(G)
such that
:f(u_1) = u_2 and f(v_1) = v_2.
In oth ...
, a graph whose automorphism group acts transitively upon ordered pairs of adjacent vertices
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Edge-transitive graph
In the mathematical field of graph theory, an edge-transitive graph is a graph such that, given any two edges and of , there is an automorphism of that maps to .
In other words, a graph is edge-transitive if its automorphism group acts t ...
, a graph whose automorphism group acts transitively upon its edges
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Vertex-transitive graph
In the mathematical field of graph theory, a vertex-transitive graph is a graph in which, given any two vertices and of , there is some automorphism
:f : G \to G\
such that
:f(v_1) = v_2.\
In other words, a graph is vertex-transitive i ...
, a graph whose automorphism group acts transitively upon its vertices
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Transitive set
In set theory, a branch of mathematics, a set A is called transitive if either of the following equivalent conditions hold:
* whenever x \in A, and y \in x, then y \in A.
* whenever x \in A, and x is not an urelement, then x is a subset of A.
Sim ...
a set ''A'' such that whenever ''x'' ∈ ''A'', and ''y'' ∈ ''x'', then ''y'' ∈ ''A''
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Topological transitivity
In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, industrial mixing, ''etc''.
The concept appear ...
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
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Transitive Corporation, a computer software firm that developed QuickTransit cross-platform virtualization
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Transitive dependency A transitive dependency is a functional dependency which holds by virtue of transitivity among various software components.
Computer programs
In a computer program a direct dependency is functionality exported by a library, or API, or any softwar ...
, a functional dependency of database management which holds by virtue of transitive relation
See also
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Intransitive (disambiguation)
{{disambiguation, math