Definition:Usual Ordering of Ordinals

Definition
Let $\On$ denote the class of all ordinals.

The usual ordering $\le$ on $\On$ is the subset relation:
 * $a \le b \iff a \subseteq b$

and its corresponding strict version:


 * $a < b \iff a \subsetneqq b$

Also see

 * Well-Ordering of Class of All Ordinals under Subset Relation, demonstrating that $\le$ is a well-ordering.