Preorder and Posets

Poset

A poset is a set equipped with a binary relation such that the following conditions hold for all :

• reflexivity:
• transitivity: if and , then
• antisymmetry: if and , then .

e.g. The real numbers with their usual ordering form a partially ordered set that is also linearly ordered: either or for any .

Definition

Def Monotone Poset Function A function with posets and is monotone if