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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 2 Feb 2025 17:39:51 +0100
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On 02.02.2025 14:47, joes wrote:
> 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.

Mathematical induction is a method for proving that a statement
P(n) is true for every natural number n that is, that the infinitely 
many cases P(0),P(1),P(2),P(3),... all hold. [Wikipedia]

>> Peano does not describe the set ℕ?
> N is not a natural number.

Not described by the Peano axioms?
> 
>> Anyhow all natural numbers n and all A(n) are discarded.
> No, there are more than any finite number.

Name one?

Regards, WM