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

On 04.11.2024 18:49, Mikko wrote:

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.

Geometry is only another language for the same thing.

 

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.

Nonsense.

 

Therefore the
point has no nearest interval.

>
That is an unfounded assertions and therefore not accepted.

 It is not unfounded.

Of course it is. It is the purest nonsense. Starting at a point outside of the intervals we move and stop as soon as the first interval is reached. If that is declared as impossible then your theory is irrelevant.
Regards, WM
  Your conterclaim is unfounded (or at least its

foundation is not in anythhing relevant).