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

On 2024-11-21 19:22:39 +0000, WM said:

On 21.11.2024 12:01, Mikko wrote:

On 2024-11-21 10:50:32 +0000, WM said:
 

On 21.11.2024 10:21, Mikko wrote:

On 2024-11-04 10:47:39 +0000, WM said:

 

That is wrong. The measure outside of the intervals is infinite. Hence there exists a point outside. This point has two nearest intervals

 No, it hasn't.

 In geometry it has.

 Depends on the set of intervals.

 No. Every point in the complement is closer to the end of an interval than to its contents of rationals.

 True but irrelevant because it may be even closer to the end of
another interval.

 Every end of any interval is irrational.

Irrelevant to the claim that a point outside of all intervals has two
nearest intervals and also to the claim that there is a point outside
of all intervals and also to the topic specified on the subjec line.
All those claims are true for some sets of intervals and false for others.
--
Mikko