# Pre-order

From Encyclopedia of Mathematics

*quasi-order, pre-ordering, quasi-ordering*

A reflexive and transitive binary relation on a set. If is a pre-order on a set , then the relation if and only if and , , is an equivalence on . The pre-order induces an order relation (cf. also Order (on a set)) on the quotient set .

**How to Cite This Entry:**

Pre-order.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Pre-order&oldid=15209

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