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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Wed, 18 Dec 2024 22:29:12 -0500
Organization: i2pn2 (i2pn.org)
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On 12/18/24 2:06 PM, WM wrote:
> On 18.12.2024 13:29, Richard Damon wrote:
>> On 12/17/24 4:57 PM, WM wrote:
> 
>>>
>>> You claimed that he uses more than I do, namely all natural numbers.
>>
>> Right, you never use ALL the natural numbers, only a finite subset of 
>> them.
> 
> Please give the quote from which you obtain a difference between
> "The infinite sequence thus defined has the peculiar property to contain 
> the positive rational numbers completely, and each of them only once at 
> a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]
> and my "the infinite sequence f(n) = [1, n] contains all natural numbers 
> n completely, and each of them only once at a determined place."
> 
> Regards, WM
> 
> 

How is your f(n) an "infinite sequence, since n is a finite number in 
each instance.

NONE of your f(n) contains *ALL* natural numbers, since no "n" is the 
highest natural number, since suc a number doesn't exist,

Your problem is you just don't understand what "infinity" is, and seem 
to think it is just some unimaginably bit but finite number, which is 
just wrong.