# Definition:Ordinal Class

## Definition

The **Ordinal Class** is defined as the class of all ordinals:

- $\operatorname{On} = \{ x : x$ is an ordinal $\}$

Therefore, by this definition, $A \in \operatorname{On}$ if and only if $A$ is an ordinal.

## Also see

## Sources

- 1971: Gaisi Takeuti and Wilson M. Zaring:
*Introduction to Axiomatic Set Theory*: $7.11$