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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 19 Dec 2024 13:25:31 -0800
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On 12/19/2024 6:58 AM, WM wrote:
> 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,

Cantor Pairing does not deal with rationals. It can create a unique pair 
of unsigned integers from any unsigned integer. Then we can use that 
unique pair to go back to the original unsigned integer.


> 
> 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
>