Difference between revisions of "Transitive relation"
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| − | One of the most important properties of a [[ | + | One of the most important properties of a [[binary relation]]. A relation $R$ on a set $A$ is called transitive if, for any $a,b,c\in A$, the conditions $aRb$ and $bRc$ imply $aRc$. [[Equivalence relation]]s and orderings (cf [[Partially ordered set]]) are examples of transitive relations. |
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Revision as of 18:24, 19 October 2014
One of the most important properties of a binary relation. A relation $R$ on a set $A$ is called transitive if, for any $a,b,c\in A$, the conditions $aRb$ and $bRc$ imply $aRc$. Equivalence relations and orderings (cf Partially ordered set) are examples of transitive relations.
How to Cite This Entry:
Transitive relation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transitive_relation&oldid=33953
Transitive relation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transitive_relation&oldid=33953
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article