# Talk:Intersection of Two Ordinals is Ordinal

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## Proof not quite complete, and can be generalized

The proof isn't quite complete; it is using Definition 3 of an ordinal (implicitly) to conclude, however this definition doesn't just require elements to be equal to their initial segments, but also that the set be well-ordered.

There is also no reason the proof can't be generalized to the intersection of a family of ordinals $\bigcap_{i \in I} A_i$. Joelbrennan (talk) 18:28, 5 April 2023 (UTC)

- How's that? Well-orderedness follows from them being ordinals.
- The generalisation can of course be done by anyone with the patience. Best to be done on a separate page. --prime mover (talk) 23:40, 5 April 2023 (UTC)