# Definition:Ordinal/Definition 2

Jump to navigation
Jump to search

## Definition

Let $A$ be a set.

Then $A$ is an **ordinal** if and only if $A$ is:

## Notation

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.

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**.