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

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?

and also to the claim that there is a point outside
of all intervals

That is proven by the measure of the intervals being less than 3.

and also to the topic specified on the subjec line.

That is concerned by the fact that in the complement of measure oo - 3 rational numbers must exist.

All those claims are true for some sets of intervals and false for others.

Let me know what else than an irrational number could be next to a point in the complement, if there were no rational numbers.
Regards, WM