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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sat, 23 Nov 2024 13:47:30 +0100
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On 23.11.2024 13:35, FromTheRafters wrote:
> WM has brought this to us :
>> On 23.11.2024 13:20, FromTheRafters wrote:
>>> WM laid this down on his screen :
>>
>>>> Let every unit interval after a natural number on the real axis be 
>>>> coloured white with exception of the intervals after the prime 
>>>> numbers which are coloured red. It is impossible to shift the red 
>>>> intervals so that the whole real axis becomes red. Every interval 
>>>> (10n, 10 (n+1)] is deficient - on the whole real axis.
>>>
>>> So what? Your imaginings don't affect the fact that there is a 
>>> bijection.
>>
>> If there was a bijection,
> 
> There is.
> 
>> then the whole axis could become red.
> 
> What makes you think that?

A bijection proves that every prime number (and its colour) can be put 
to a natural number (and colour it).
> 
>> Do you believe that?
> 
> No, of course not.

Relieving.

Regards, WM