Transitivity: Difference between revisions
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* In [[grammar]], a verb is '''transitive''' if it takes an object. See [[transitive verb]]. |
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* 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]]. |
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* 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''. |
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See also [[transitive closure]], [[intransitivity]]. |
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Revision as of 04:39, 1 May 2005
- In grammar, a verb is transitive if it takes an object. See transitive verb.
- 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.
- In mathematics, a group action is transitive if it has just one 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 group action is also called metrically transitive.
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