Definition:Ordinal/Notation
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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.
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.
Sources
- 1993: Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (2nd ed.) ... (previous) ... (next): $\S 1$: Naive Set Theory: $\S 1.7$: Well-Orderings and Ordinals
