Re: Incompleteness of Cantor's enumeration of the rational numbers

After serious thinking WM wrote :

On 20.11.2024 21:05, FromTheRafters wrote:

WM wrote on 11/20/2024 :

On 20.11.2024 15:14, FromTheRafters wrote:

WM formulated on Wednesday :

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It does not make it wrong, but it unmasks it at imprecise. That's why I don't like it. We can do better.

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It works well enough.

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Really? Then you can answer the following questions:
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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.

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Thank you. You are the first person not bewitched by set theory.

The real line is infinitely long in both directions. Your shifted intervals are all on the positive real axis.

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.

See above.

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.

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Recidivistic?

I recognize McDuck in disguise, or your notion that there are fewer primes than there are natural numbers. You keep finding different ways to say the same wrong thing.