Definition 2.3.1: Ordered and Well-Ordered Set
A set S is called partially ordered if there exists a relation r (usually denoted by the symbol ) between S and itself such that the following conditions are satisfied:
- reflexive: a a for any element a in S
- transitive: if a b and b c then a c
- antisymmetric: if a b and b a then a = b
A set S is called well-ordered if it is an ordered set for which every non-empty subset contains a smallest element.