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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 .
The transitive extension of R 1 would be denoted by R 2, and continuing in this way, in general, the transitive extension of R i would be R i + 1. The transitive closure of R, denoted by R* or R ∞ is the set union of R, R 1, R 2, ... . [8] The transitive closure of a relation is a transitive relation. [8]
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
Many languages, such as Hungarian, mark transitivity through morphology; transitive verbs and intransitive verbs behave in distinctive ways. In languages with polypersonal agreement, an intransitive verb will agree with its subject only, while a transitive verb will agree with both subject and direct object.
The transitive closure of this relation is a different relation, namely "there is a sequence of direct flights that begins at city x and ends at city y". Every relation can be extended in a similar way to a transitive relation. An example of a non-transitive relation with a less meaningful transitive closure is "x is the day of the week after y".
If X has cardinality n, the action of the alternating group is (n − 2)-transitive but not (n − 1)-transitive. The action of the general linear group of a vector space V on the set V ∖ {0} of non-zero vectors is transitive, but not 2-transitive (similarly for the action of the special linear group if the dimension of v is at least 2).
A transitive dependency is an indirect dependency relationship between software components. This kind of dependency is held by virtue of a transitive relation from a component that the software depends on directly.
English has a number of ergative verbs: verbs which can be used either intransitively or transitively, where in the intransitive use it is the subject that is receiving the action, and in the transitive use the direct object is receiving the action while the subject is causing it.