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

On 11/23/2024 3:45 PM, WM wrote:

On 23.11.2024 21:18, Jim Burns wrote:

On 11/23/2024 5:30 AM, WM wrote:

It is impossible to shift the red hats
so that all unit intervals of
the whole real axis get red hats.
There are too few prime numbers.

>
No.
>
⎛ Assume that that is so.

>
That need not be assumed but
that is obviously so for every part of the real axis.

The obviously.so are best to assume.
However,
some of the seemingly.obviously.so
  require contradictions/gibberish
and, although they seem obvious, are NOT so.
Insufficient red hats require contradictions/gibberish.
So, it is NOT so.

⎜ Assume that there are
⎜ enough red hats for the first 𝔊 numbers
⎜ but not enough for the 𝔊+1ᵗʰ

>
That is a mistake.
If there are enough hats for G natnumbers,
then there are also enough for G^G^G natnumbers.

Thank you.

Alas they leave G^G^G unit intervals without hats.
That is the catch!

After all hat.shifts,
there is no first number without a hat.
After all hat.shifts,
the set of numbers without hats is empty.

There are too few prime numbers.

>
No,
there being too few primes
leads to contradiction.

>
Shall unit intervals disappear like Bob?

After all swaps,
Bob is not in any room (visible or dark)
which Bob has ever been in.