Union of Set of Ordinals is Ordinal/Proof 1
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Theorem
Then $\bigcup A$ is an ordinal.
Proof
By Class of All Ordinals is Well-Ordered by Subset Relation, a set of ordinals forms a chain.
The result then follows from Union of Chain of Ordinals is Ordinal.
Sources
- 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: Corollary $1.4$