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Difference between revisions of "Transitive relation"

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One of the most important properties of a [[Binary relation|binary relation]]. A relation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t093/t093810/t0938101.png" /> on a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t093/t093810/t0938102.png" /> is called transitive if, for any <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t093/t093810/t0938103.png" />, the conditions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t093/t093810/t0938104.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t093/t093810/t0938105.png" /> imply <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t093/t093810/t0938106.png" />. Equivalence relations and orderings are examples of transitive relations.
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One of the most important properties of a [[Binary relation|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 are examples of transitive relations.

Revision as of 21:04, 14 April 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 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=11202
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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