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In mathematics, the word transitive admits at least two distinct meanings:

A group G acts transitively on a set S if for any x, y ∈ S, there is some g ∈ G such that gx = y. See group action. A somewhat related meaning is explained at ergodic theory.

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.

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-* In [[grammar]], a verb is '''transitive''' if it takes an object.  See [[transitive verb]].
+In [[mathematics]], the word '''''transitive''''' admits at least two distinct meanings:
-* 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 [[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 [[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''.
+* 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]].
+==See also==
-* In [[set theory]], a set is '''transitive''' if it contains all [[Element (mathematics)|element]]s of its elements.  See [[transitive set]].
+* [[transitive closure]]
+* [[intransitivity]]
+{{disambig}} [[Category:Mathematical disambiguation]]
-* [[Transitive Corporation]] is a [[computer software]] firm based in [[Manchester, England]] and [[Los Gatos]], [[California]].
+[[de:Transitivit%C3%A4t_%28Mathematik%29]]
+[[uk:&#1058;&#1088;&#1072;&#1085;&#1079;&#1080;&#1090;&#1080;&#1074;&#1085;&#1110;&#1089;&#1090;&#1100;]]
-{{disambig}}
-[[de:Transitivität]]