Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 16.11.2024 20:30, Jim Burns wrote:

On 11/15/2024 7:00 AM, WM wrote:

On 15.11.2024 11:43, Mikko wrote:

 

Translated intervals are not
the same as the original ones.
Not only their order
but also their positions can be different
as demonstrated by your example and mine, too.

>
If they do not cover the whole figure
 in their initial order,
then they cannot do so in any other order.

 Sets for which that is true
are finite sets.

Sets for which that is true are sets which obey geometrical rules.

⎝ And our sets do not change.

Therefore the set of intervals cannot grow. The average density is and remains 1/5, i.e., less than 1.
Regards, WM
Regards, WM