Linear order

A linear order (or total order) on a set is a relation on that is:

1. irreflexive
2. transitive
3. trichotomous We say is linearly ordered by , or simply is a linearly ordered set.

Notation

For write for and for ” or ” This satisfies:

1. reflexivity
2. antisymmetric:
3. transitive:
4. trichotomous: