Definition:Class of All Ordinals

Definition
The class of all ordinals is defined, obviously enough, as the class of all ordinals:
 * $\On = \leftset {x: x}$ is an ordinal $\rightset {}$

Therefore, by this definition, $A \in \On$ $A$ is an ordinal.

Also known as
The class of all ordinals is often referred to as the ordinal class, but this can be misconstrued as an ordinal class, which misrepresents it.

Also see

 * Class of All Ordinals is Ordinal