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

On 2024-11-24 14:19:06 +0000, WM said:

On 24.11.2024 13:56, Mikko wrote:

On 2024-11-22 11:05:58 +0000, WM said:
 

On 22.11.2024 09:52, Mikko wrote:

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

 

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

 What else should it have?

 For every point that is neither an endpoint nor interior point of any
of the intervals there is no nearest interval because between that point
and any interval there is another interval.

 Wrong. Starting from that point a cursor, by simplest logic, will either touch nothing or something. If it touches something, it can only be an irrational endpoint.

Your "wrong" is wrong. It will either touch something or nothing. If it
touches nothing it cannot touch an irrational endpoint.
--
Mikko