Preorder
A relation "<=" is called a preorder (or quasiorder) on a set S if it satisfies:
1. Reflexivity: a<=a for all a in S.
2. Transitivity: a<=b and b<=c implies a<=c.
A preorder that also has antisymmetry is a partial order.
See also
Partial Order, Total OrderThis entry contributed by Michael Clarkson
Explore with Wolfram|Alpha
WolframAlpha
References
Harel, D.; Kozen, D.; and Tiuryn, J. Dynamic Logic. Cambridge, MA: MIT Press, p. 6, 2000.Referenced on Wolfram|Alpha
PreorderCite this as:
Clarkson, Michael. "Preorder." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Preorder.html