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

On 29.11.2024 01:06, Richard Damon wrote:

On 11/28/24 12:50 PM, WM wrote:

If for all intervals 1, 2, 3, ..., n the covering is 1/10, then there are no natnumbers outside of all intervals and there are no hats
outside of all intervals.

You are making the error of assuming that the infinite set is just like a finite set that has part of it.

No. Analysis concerns infinite sequences and sets.

 The problem is that the actual problem is defined on the INFINITE set, and in that case, there ARE enough hats to cover.

No. The limit of the sequence f(n) of relative coverings in (0, n] is 1/10, not 1. Therefore the relative covering 1 would contradict analysis.
Regards, WM