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.

>
Maybe. In this case it is precisely this.
>
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