Re: The set of necessary FISONs

Am Sat, 01 Feb 2025 19:23:29 +0100 schrieb WM:

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.

Induction proves a sentence for every number, not for the set.
You cannot extend a sentence about numbers to sets.

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.

It covers the elements of N, not the set itself.

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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.