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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: Sun, 15 Dec 2024 16:25:55 +0100
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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].
> 
>>>>> 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.
> 
>>>>> Yes, there are only 1/10th as many Black Hats as White Hats, but
>>>>> since that number is Aleph_0/10, which just happens to also equal
>>>>> Aleph_0, there is no "deficit" in the set of Natual Numbers.
>>>> This example proves that aleph_0 is nonsense.
>>> Nope, it proves it is incompatible with finite logic.
>> There is no other logic.
> There is the logic of the infinite.
> 
All logic is finite.

Regards, WM