Re: The set of necessary FISONs

Am Sat, 01 Feb 2025 13:46:50 +0100 schrieb WM:

On 31.01.2025 18:51, joes wrote:

Am Fri, 31 Jan 2025 13:28:35 +0100 schrieb WM:

 

then all can be discarded,

No, only finitely consecutive ones.

Induction concerns all natural numbers n as well as all A(n).

ω, corresponding to „all”, is not natural.

But all F(n) can be shown to be completely useless because
infinitely many natnumbers are missing.

Again: every single one, or even an arbitrary finite number.
If you have inf. many segments, you obviously have inf. many numbers.

All finite natural numbers as well as all FISONs obey the Peano
axioms.

All naturals are finite. FISONs are not naturals but sets and can’t be
added together.

FISONs represent ordinals.

There is no FISON for ω (duh).

Removing all leaves nothing, in particular no sufficient set for
U(F(n)) = ℕ.

It is obvious that N is not empty.

But the set claimed to have the union ℕ gets empty without changing its
union.

Wrong. Finite sets of FISONs do not result in N.

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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.