Re: The set of necessary FISONs

Am Wed, 26 Feb 2025 15:42:03 +0100 schrieb WM:

On 26.02.2025 15:21, joes wrote:

Am Wed, 26 Feb 2025 13:49:49 +0100 schrieb WM:

 

The power of induction proves ∀n ∈ U(F): |ℕ \ {1, 2, 3, ..., n}| = ℵo

It does not prove |N \ U{F(n): n e U(F)}| = oo.

Then U(F) must contain more than all n ∈ U(F). But it does not. And you
cannot find a difference.

No, it must not. That is simply an invalid inference, as you can see by
the differing structure of the formulas. You are the one unable to see
the difference between N missing a FISON and N missing everything, i.e.
not a FISON.

The *set* is not in the set.

No, why should it? But the set is proven to exist by induction.

Indeed, that you keep referring to removing |N| elements instead of n e
N is a mistake on your part. The existence has never been disputed.

Then show what remains after removing all n ∈ U(F).

Induction only allows you to remove a natural number of FISONs, not
infinitely many.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.