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

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

On 06.11.2024 03:48, Ross Finlayson wrote:

On 11/05/2024 02:29 AM, Mikko wrote:

 

Geometry is only another language for the same thing.

 Another language is an unnecessary complication that only reeasls
an intent to deceive.

 It is a clearer language.

No, what can be said about numbers can be stated at least as clearly
in the language of arithmetic.

No, the meaning is clear. Of course, because some intevals overlap,
you should have specified what exacly you mean by "nearer". But as
ε shriks the overlappings disappear and the distance between any
two intevals approaches the distance between their centers we may
define distance between the intervals as the distance between their
endpoints even wne ε > 0.

 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.
--
Mikko