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

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

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.

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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

So?
You are making the error of assuming that the infinite set is just like a finite set that has part of it.
The problem is that the actual problem is defined on the INFINITE set, and in that case, there ARE enough hats to cover.
All you are doing is showing that you finite set logic doesn't work on the infinite sets, and when you try to make it work, if just blows up your logic.
Sorry, you are just proving your stupidity,