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

On 28.11.2024 18:17, Richard Damon wrote:

On 11/28/24 11:09 AM, WM wrote:

The properties of the infinte set is not just the properties of the series of the finite sets that approach it.

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Maybe. In this case it is precisely this.
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Look: 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. Therefore only a fool could believe that infinitely many black hats were supplied after all. If you wish to be a fool you may claim that. My students would never come down that much.

 It is sort of like trying to figure out what 0^0 is.

No. 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.
Regards, WM