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

On 12.11.2024 16:58, Jim Burns wrote:

On 11/11/2024 3:33 PM, WM wrote:

On 11.11.2024 19:23, Jim Burns wrote:

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

 

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.

 By which, you mean that translation changes intervals.

No, the intervals remain constant in size and multitude.

(The set of intervals remains constant
in size and multitude.)

 The set of intervals remains constant. Absolutely.
Sets do not change.
Intervals do not change.
Mathematical objects do not change.

Therefore the intervals covering all naturals cannot cover more. But the rationals are more in the sense that they include all naturals and 1/2. By your argument Cantor has been falsified.
Regards, WM
Regards, WM