# Transitivity

From Encyclopedia of Mathematics

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:**

Transitivity.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Transitivity&oldid=31686

This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article