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NNTP-Posting-Date: Wed, 20 Nov 2024 20:10:33 +0000
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Wed, 20 Nov 2024 12:10:36 -0800
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On 11/20/2024 12:05 PM, FromTheRafters wrote:
> WM wrote on 11/20/2024 :
>> On 20.11.2024 15:14, FromTheRafters wrote:
>>> WM formulated on Wednesday :
>>
>>>>
>>>> It does not make it wrong, but it unmasks it at imprecise. That's
>>>> why I don't like it. We can do better.
>>>
>>> It works well enough.
>>
>> Really? Then you can answer the following questions:
>>
>> Let every unit interval after a natural number on the real axis be
>> coloured white with exception of the powers of 2 which are coloured
>> black. Is it possible to shift the black intervals so that the whole
>> real axis becomes black?
>
> No, of course not.
>
>> Or: Let every unit interval after a natural number on the real axis be
>> coloured as above with exception of the intervals after the odd prime
>> numbers which are coloured red. Is it possible to shift the red
>> intervals so that the whole real axis becomes red?
>
> No, of course not.
>
>> What colour has the real axis after you have solved both tasks?
>
> Depending on the order of the tasks. I think half red or half black.

Well you have to reference academic reference and describe "supertask"
besides "asymptotics" about where "the asymptotic density of black or
red respectively is 1 in the limit", that you point to "supertask"
instead of mumbling like it's not already considered by proper minds,
not just ketonic neck-flap gaspers of having failures altogether
of any sort of related-rates problems.

This is mathematics: humor is irrelevant, and so is what
anybody "thinks", or, "feels".

It only matters what "is", and there's a language of it,
so use it. (Or lose it.)

Good sir