Definition:Usual Ordering of Ordinals
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Let $\On$ denote the class of all ordinals.
The usual ordering $\le$ on $\On$ is the subset relation:
- $a \le b \iff a \subseteq b$
and its corresponding strict version:
- $a < b \iff a \subsetneqq b$
- Well-Ordering of Class of All Ordinals under Subset Relation, demonstrating that $\le$ is a well-ordering.
- 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