# 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, $A \in \On$ if and only if $A$ 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

• Results about the class of all ordinals can be found here.