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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.

In set theory, a set is transitive if it contains all elements of its elements. See transitive set.

Transitive Corporation is a computer software firm based in Manchester, England and Los Gatos, California.

This disambiguation page lists articles associated with the title Transitivity.
If an internal link led you here, you may wish to change the link to point directly to the intended article.

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-In [[mathematics]], the word '''''transitive''''' admits at least two distinct meanings:
+* In [[grammar]], a verb is '''transitive''' if it takes an object.  See [[transitive verb]].
-* A [[group (mathematics)|group]] ''G'' acts '''transitively''' on a [[set]] ''S'' if for any ''x'', ''y'' &isin; ''S'', there is some ''g'' &isin; ''G'' such that ''gx'' = ''y''.  See [[group action]].  A somewhat related meaning is explained at [[ergodic theory]].
+* 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]].
-* A [[binary relation]] is '''transitive''' if whenever A is related to B and B is related to C, then A is related to C, for all A, B, and C in the domain of the relation.  See [[transitive relation]].
+* 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''.
+* In [[set theory]], a set is '''transitive''' if it contains all [[Element (mathematics)|element]]s of its elements.  See [[transitive set]].
-==See also==
-* [[transitive closure]]
-* [[intransitivity]]
+* [[Transitive Corporation]] is a [[computer software]] firm based in [[Manchester, England]] and [[Los Gatos]], [[California]].
-{{disambig}} [[Category:Mathematical disambiguation]]
-[[de:Transitivit%C3%A4t_%28Mathematik%29]]
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+[[de:Transitivität]]
+[[es:Transitividad (gramática)]]