Let $A$ be a set.
Then $A$ is an ordinal if and only if $A$ is:
The class of all ordinals can be found denoted $\On$.
- $\Ord S$
whose meaning is:
- $S$ is an ordinal.
According to 1993: Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (2nd ed.), it is common practice in set theory to use lowercase Greek letters $\alpha, \ \beta, \ \gamma, \ldots$ for ordinals.