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

On 11/11/2024 4:00 AM, WM wrote:

On 10.11.2024 21:36, Chris M. Thomasson wrote:

On 11/10/2024 1:35 AM, WM wrote:

On 10.11.2024 00:27, Jim Burns wrote:

On 11/9/2024 6:45 AM, WM wrote:

Everybody who believes that the intervals
I(n) = [n - 1/10, n + 1/10]
could grow in length or number
to cover the whole real axis
is a fool or worse.

>
Our sets do not change.

>
But intervals on the real axis can be translated.

The interval [4-⅒,4+⅒] can be translated to
the interval [1/3-⅒,1/3+⅒].
[4-⅒,4+⅒] does not change to [1/3-⅒,1/3+⅒]
[4-⅒,4+⅒] will continue being after translation.
[1/3-⅒,1/3+⅒] has never been [4-⅒,4+⅒].
Our sets do not change.
Everybody who believes that
  intervals could grow in length or number
is deeply mistaken about
  what our whole project is.