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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: Mon, 16 Dec 2024 20:32:32 -0800
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On 12/16/2024 3:52 PM, Richard Damon wrote:
> On 12/16/24 3:30 AM, WM wrote:
>> On 15.12.2024 21:21, joes wrote:
>>> Am Sun, 15 Dec 2024 16:25:55 +0100 schrieb WM:
>>>> On 15.12.2024 12:15, joes wrote:
>>>>> Am Sat, 14 Dec 2024 17:00:43 +0100 schrieb WM:
>>>>
>>>>>>>>>> That pairs the elements of D with the elements of ℕ. Alas, it can
>>>>>>>>>> be proved that for every interval [1, n] the deficit of hats
>>>>>>>>>> amounts to at least 90 %. And beyond all n, there are no further
>>>>>>>>>> hats.
>>>>>>>>> But we aren't dealing with intervals of [1, n] but of the full 
>>>>>>>>> set.
>>>>>>>> Those who try to forbid the detailed analysis are dishonest
>>>>>>>> swindlers and tricksters and not worth to participate in scientific
>>>>>>>> discussion.
>>>>>>> No, we are not forbiding "detailed" analysis
>>>>>> Then deal with all infinitely many intervals [1, n].
>>>>> ??? The bijection is not finite.
>>>> Therefore we use all [1, n].
>>> Those are all finite.
>>
>> All n are finite.
> 
> But N isn't, so the sets [1, n] aren't what the bijection is defined on.
> 
>>>
>>>>>>>>> The problem is that you can't GET to "beyond all n" in the 
>>>>>>>>> pairing,
>>>>>>>>> as there are always more n to get to.
>>>>>>>> If this is impossible, then also Cantor cannot use all n.
>>>>>>> Why can't he? The problem is in the space of the full set, not the
>>>>>>> finite sub sets.
>>>>>> The intervals [1, n] cover the full set.
>>>>> Only in the limit.
>>>> With and without limit.
>>> Wonrg. There is no natural n that „covers N”.
>>
>> All intervals do it because there is no n outside of all intervals [1, 
>> n]. My proof applies all intervals.
> 
> And all the intervals are finite, and thus not the INFINITE set N, which 
> is where the bijection occurs.
> 
> Thus your "proof" is just a LIE.

Seems to be so. Unless I am missing something, WM seems to suggest that 
Cantor Pairing does not work with all natural numbers. 0 aside for a 
moment. Even though it works with 0 as well, anyway... WM has a personal 
issue here? For him to overcome? Can he see the "light" so to speak?