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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Mon, 3 Feb 2025 12:59:15 +0100
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On 02.02.2025 18:41, joes wrote:
> Am Sun, 02 Feb 2025 12:06:26 +0100 schrieb WM:
>> On 01.02.2025 19:42, joes wrote:
>>> Am Sat, 01 Feb 2025 14:40:12 +0100 schrieb WM:

>> 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]
> And you want the wrong P(ω) to hold, but you cannot remove infinitely
> many segments.

What does Peano create by n => n+1? Is it all natural numbers?
Why does induction n => n+1 not cover all FISONs.

> This is different from all P(n) which together say
> you can remove any finite *number of* segments (not the segments
> themselves).

What is the difference to Peano?

> Do you get that?

Not yet. I cannot see a difference between Peano's application of n => 
n+1 and my application of n => n+1.

> There is no infinite segment, but
> there *are* infinitely many.

Like the natural numbers created by Peano? Does he create the set ℕ? 
Does Zermelo by the same technique create the set ℕ?

Regards, WM