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

On 21.11.2024 12:01, Mikko wrote:

On 2024-11-21 10:50:32 +0000, WM said:
 

On 21.11.2024 10:21, Mikko wrote:

On 2024-11-04 10:47:39 +0000, WM said:
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That is wrong. The measure outside of the intervals is infinite. Hence there exists a point outside. This point has two nearest intervals

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No, it hasn't.

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In geometry it has.

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Depends on the set of intervals.

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No. Every point in the complement is closer to the end of an interval than to its contents of rationals.

 True but irrelevant because it may be even closer to the end of
another interval.

Every end of any interval is irrational.

In particular with Cantor's set of intervals
where there is no nearest interval.

For every point of the complement, every interval has irrational ends.
Regards, WM