Re: The set of necessary FISONs

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).

 

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.

 

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.
Regards, WM