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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 19 Dec 2024 15:58:21 +0100
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On 19.12.2024 04:29, Richard Damon wrote:
> 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."
>>
> How is your f(n) an "infinite sequence, since n is a finite number in 
> each instance.

How is Cantor's sequence infinite since every positive rational number 
is finite?
> 
> NONE of your f(n) contains *ALL* natural numbers, since no "n" is the 
> highest natural number,

None of Cantor's terms q_n contains all rational numbers, sice no n is 
the highest natural number.

> Your problem is you just don't understand what "infinity" is

Your problem is that you believe to understand it.

Regards, WM