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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 2 Feb 2025 13:47:11 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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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.

-- 
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.