Quasi-order is not defined uniformly

In the literature, some authors define “quasi order” as transitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmath and reflexiveMathworldPlanetmathPlanetmathPlanetmath, others define it as transitive and irreflexiveMathworldPlanetmath.

No such discrepancy seems to exist in using “preorderMathworldPlanetmath” for the former (transitive and reflexive) and “strict partial orderMathworldPlanetmath” for the latter (transitive and irreflexive).

It seems wise to use only the unambiguous terminology, and start any text where the term “quasi order” is felt with a proper warning.

Just for completeness: a partial order is transitive, reflexive and antisymmetric.

Title Quasi-order is not defined uniformly
Canonical name QuasiorderIsNotDefinedUniformly
Date of creation 2013-03-22 15:35:18
Last modified on 2013-03-22 15:35:18
Owner boute (11676)
Last modified by boute (11676)
Numerical id 5
Author boute (11676)
Entry type Definition
Classification msc 06A99