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

On 2024-11-04 10:47:19 +0000, WM said:

On 04.11.2024 11:31, Mikko wrote:

On 2024-11-04 09:55:24 +0000, WM said:
 

On 03.11.2024 23:18, Jim Burns wrote:
 

There aren't any neighboring intervals.
Any two intervals have intervals between them.

 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.

This discussion is about numbers, not geometry.

Between that point an an interval there are rational
numbers and therefore other intervals

 I said the nearest one. There is no interval nearer than the nearest one.

There is no nearesst one. There is always a nearer one.

Therefore the
point has no nearest interval.

 That is an unfounded assertions and therefore not accepted.

It is not unfounded. Your conterclaim is unfounded (or at least its
foundation is not in anythhing relevant).
--
Mikko