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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 3 Nov 2024 16:21:25 -0500
Organization: i2pn2 (i2pn.org)
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On 11/3/24 7:47 AM, WM wrote:
> On 03.11.2024 09:52, joes wrote:
>> Am Sat, 02 Nov 2024 18:42:15 +0100 schrieb WM:
>>> On 02.11.2024 14:50, Moebius wrote:
>>>> Am 02.11.2024 um 14:21 schrieb joes:
>>>>> Am Fri, 01 Nov 2024 18:03:26 +0100 schrieb WM:
>>>>
>>>>>> If an invariable set of numbers is there, then there is a smallest
>>>>>> and a largest number of those which are existing.
>>>> or each and every n e IN there is an n' e IN (say n' = n+1)
>>> Actual infinity is not based on claims for each and every, but concerns
>>> all.
>> Lol. That actually sheds some light on your thought process:
>> how do you suppose some property holds for all x, but not
>> for every?
> 
> Every natnumber is finite. But here I mean that not only induction can 
> be applied and that induction is not valid for all natnumbers.
> 
> Regards, WM
> 

But Induction *IS* valid for all Natural Numbers.

Or is your "natnumber" a code word for a number system that is supposed 
to be like the Natural Numbers, but missing something so it isn't the 
actual infinite number system it needs to be.