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

On 11.11.2024 19:23, Jim Burns wrote:

On 11/11/2024 3:41 AM, WM wrote:

But it will never complete
an infinite set of claims.

>
We do not need an infinite 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 of 𝗰𝗹𝗮𝗶𝗺𝘀 completed.
We do not want an infinite 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 of 𝗰𝗹𝗮𝗶𝗺𝘀 completed.

>
But you claim that
_all_ fractions are in bijection with
all natural numbers,
don't you?

 Yes, I claim that.

For that claim you need an infinite set of claims.

This is one 𝗰𝗹𝗮𝗶𝗺:
⎛ All fractions are in bijection with
⎝ all natural numbers.

It is wrong.

My intervals I(n) = [n - 1/10, n + 1/10]
must be translated to all the midpoints
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5,
2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1, ...
if you want to contradict my claim.

 Your 𝗰𝗹𝗮𝗶𝗺𝘀 start with "Sets change".

No, I claim that intervals can be translated. (The set of intervals remains constant in size and multitude.) For every finite subset this is possible.
Regards, WM