# Definition:Class of All Ordinals

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## 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**.

## Sources

- 1971: Gaisi Takeuti and Wilson M. Zaring:
*Introduction to Axiomatic Set Theory*: $7.11$ - 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 1$ Ordinal numbers