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

On 2024-11-06 17:55:15 +0000, WM said:

On 06.11.2024 16:04, Mikko wrote:

On 2024-11-06 10:01:21 +0000, WM said:

 

I leave ε = 1. No shrinking. Every point outside of the intervals is nearer to an endpoint than to the contents.

 This discussion started with message that clearly discussed limits when
ε approaches 0. The case ε = 1 was only about a specific unimportant
question.

 When ε approaches 0 then the measure of the real axis is, according to Cantor's results, 0. That shows that his results are wrong.

It is not the measure of the real axis but the set of rationals. The
real axis more than just the rationals. The irrationals are also a
part of the real axis.

But the important question is also covered by ε = 1. The measure of the real axis is, according to Cantor's results, less than 3. That shows that his results are wrong.

No, that is not Cantor's result, so all we can say about it is that
you are wrong about Cantor's result.
--
Mikko