Re: The set of necessary FISONs

On 13.03.2025 12:15, FromTheRafters wrote:

WM formulated on Thursday :

On 13.03.2025 10:59, FromTheRafters wrote:

I happen to know that the naturals are exemplary of the smallest inductive set.

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The naturals defined by Cantor have more elements than any natural number can measure. Inductive sets never can leave the domain measured by natural numbers.

 So, now you are saying that the superset of the naturals has cardinality aleph_zero and as such is only countably infinite

It is not countable. Countable is only the inductive set. (I use ℵ₀ only as symbol of actual infinity in honour of Cantor.)

but bigger than the set of naturals?

It is bigger than the set of such natural numbers which have infinite distance from ω or |ℕ|.
Regards, WM