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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: A question for set-theorists
Date: Wed, 20 Nov 2024 18:02:40 +0100
Organization: A noiseless patient Spider
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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?

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