Transitivity: Difference between revisions

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In grammar, a verb is transitive if it takes an object. See Transitive verb.

In mathematics, a binary relation R is transitive if xRy and yRz together imply xRz. For example, the less-than relation is transitive. See transitivity.

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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 * In [[grammar]], a verb is '''transitive''' if it takes an object.  See [[Transitive verb]].
-* In [[mathematics]], a [[binary relation]] is '''transitive''' if <math>xRy</math> and <math>yRz</math> together imply <math>xRz</math>.  For example, the ''less-than'' relation is transitive.  See [[Transitivity]]. A [[group action]] is '''transitive''' if it has just one [[orbit (mathematics)|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 [[mathematics]], a [[binary relation]] ''R'' is '''transitive''' if ''xRy'' and ''yRz'' together imply ''xRz''.  For example, the ''less-than'' relation is transitive.  See [[transitivity]].
+* In [[mathematics]], a [[group action]] is '''transitive''' if it has just one [[orbit (mathematics)|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''.