Re: The set of necessary FISONs

On 30.01.2025 15:30, Richard Damon wrote:

On 1/30/25 4:05 AM, WM wrote:

On 29.01.2025 15:00, FromTheRafters wrote:

WM was thinking very hard :

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It is Cantor's theorem that every set of ordinals has a first element. FISONs are v. Neumann ordinals.

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Yes, but some infinite sets don't have a first element.

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Every finite or infinite set of ordinals or FISONs has a first element! Other sets are irrelevant in the present context.
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Right, but the "Set of Neccessary FISONs" isn't actually a set,

But a set that has union ℕ is a set.

A set that doesn't exist doesn't need to have a first element.

A not existing set is not an infinite set. You said that some infinite sets don't have a first element.
Regards, WM