Union of Set of Ordinals is Ordinal/Proof 1

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $A$ be a set of ordinals.

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