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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 22 Feb 2025 22:38:40 -0500
Organization: i2pn2 (i2pn.org)
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On 2/22/25 9:04 AM, WM wrote:
> On 22.02.2025 13:15, Richard Damon wrote:
> 
>> Peano's successors are not induction.
>>
>> Induction is the axiom that lets your prove that a set contains the 
>> set of Natural Numbers. It isn't a "construction" technique.
> 
> Induction is the feature, proven or claimed, that an element exists in 
> the set and with any element also its successor.
> 
> Regards, WM
> 

Where do you get that from? The induction rule is the method used to 
prove that a statement P(n) is true for every natural number, by showing 
that P(0) is true, and that if P(n) is true, the P(n+1) must be true.

Your claim is just the opposite of induction.

All this shows is that you really don't understand what you are talking 
about. Perhaps it is a language issue, you just don't understand the 
language of actual Mathematics, but are trying to understand it form 
guesses an intuition to avoid the dangers of formal "Mathologies"