Real Analysis - Orderings

A Partial Ordering is a relation ≤ such that

1. a ≤ a (refective property)
2. a ≤ b and b ≤ c ⇒ a ≤ c (transitive property)

We call a partial ordering antisymmetric if

• a ≤ b and b ≤ a ⇒ a = b

A partial ordering ≤ is called a total ordering if

• Either a ≤ b or b ≤ a
• A total ordering ≤ is called a linear ordering if it is antisymmetric.