Re: The set of necessary FISONs

Am Sun, 02 Feb 2025 12:43:49 +0100 schrieb WM:

On 02.02.2025 05:55, joes wrote:

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

 

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

But to all numbers.

No, to *a* number, though which is arbitrary. Not to a *set* of numbers.

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.

Peano does not describe the set ℕ?

N is not a natural number.

Anyhow all natural numbers n and all A(n) are discarded.

No, there are more than any finite number.

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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.