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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Thu, 7 Nov 2024 18:59:02 +0100
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On 07.11.2024 16:29, Jim Burns wrote:

> ⎛ The boundary of a set S holds
> ⎜ those points x′ such that
> ⎜ each interval [x,x″] with
> ⎜ x′ in its interior, x < x′ <  x″,
> ⎝ holds points in S and points not.in S
> 
Do you think you need the boundary in my last example?

When we cover the real axis by intervals
--------_1_--------_2_--------_3_--------_4_--------_5_--------_...
J(n) = [n - √2/10, n + √2/10]
and shuffle them in a clever way, then all rational numbers are 
midpoints of intervals and no irrational number is outside of all intervals.
Do you believe this???

Regards, WM