Transitivity or transitive may refer to:
Grammar
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Transitivity (grammar)
Transitivity is a linguistics property that relates to whether a verb, participle, or gerund denotes a Object (grammar), transitive object. It is closely related to valency (linguistics), valency, which considers other argument (linguistics), ...
, a property regarding whether a lexical item denotes a transitive object
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Transitive verb
A transitive verb is a verb that entails one or more transitive objects, for example, 'enjoys' in ''Amadeus enjoys music''. This contrasts with intransitive verbs, which do not entail transitive objects, for example, 'arose' in ''Beatrice arose ...
, 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 of a group G on a set S is a group homomorphism from G to some group (under function composition) of functions from S to itself. It is said that G acts on S.
Many sets of transformations form a group under func ...
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Transitive relation
In mathematics, a binary relation on a set (mathematics), set is transitive if, for all elements , , in , whenever relates to and to , then also relates to .
Every partial order and every equivalence relation is transitive. For example ...
, 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 (, ''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.
In its earliest form (defin ...
, 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. That is, we can find three values a, b, and c where the transitive condition does not hold.
Antitransitivity ...
, 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 ordered pairs of adjacent vertices (u_1,v_1) and (u_2,v_2) of , there is an automorphism
:f : V(G) \rightarrow V(G)
such that
:f(u_1) = u_2 a ...
, 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 mathematics, mathematical field of graph theory, an Graph automorphism, automorphism is a permutation of the Vertex (graph theory), vertices such that edges are mapped to edges and non-edges are mapped to non-edges. A graph is a vertex-tr ...
, 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 holds:
* 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.
S ...
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: e.g. mixing paint, mixing drinks, industrial mixing.
The concept appears in ...
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 functional dependency of database management which holds by virtue of transitive relation
See also
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Intransitive (disambiguation)
{{disambiguation, math