Re: The set of necessary FISONs

On 01.02.2025 15:07, joes wrote:

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.

ω describes the order type but is not the set ℕ but greater than all natnumbers.

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.

Induction covers all natural numbers. Otherwise it would not be sufficient in the Peano axioms.
Regards, WM
Regards, WM