Definition:Ordinal/Notation

Notation for Ordinal
The class of all ordinals can be found denoted $\On$.

In order to indicate that a set $S$ is an ordinal, this notation is often seen:
 * $\Ord S$

whose meaning is:
 * $S$ is an ordinal.

Thus $\operatorname {Ord}$ can be used as a propositional function whose domain is the class of all sets.

A tradition has grown up in set theory to use lowercase Greek letters $\alpha, \ \beta, \ \gamma, \ldots$ as symbols to represent variables over ordinals.

It is also customary to denote the ordering relation between ordinals as $\le$ rather than $\subseteq$ or $\preceq$.