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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: A question for set-theorists
Date: Wed, 20 Nov 2024 13:46:35 -0800
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On 11/20/2024 1:42 PM, Chris M. Thomasson wrote:
> On 11/20/2024 9:02 AM, WM wrote:
>> 1) 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?
> 
> 1->(black)->2->(white)->3->(black)->4->(white)->...
> 
> That? Notice how the odd numbers are black. ;^)

Powers of 2?

2^1, 2^2, 2^3, ...

2->(black)->4->(white)->8->(black)->...






> 
> 
> 
>>
>> 2) 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?
>>
>> What colour has the real axis after you have solved both tasks?
>>
>> Regards, WM
>