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

On 11/29/24 8:44 AM, WM wrote:

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.

You are looking at FINITE sets, and then trying to extrapolate to an infinte set, which doesn't work.

>
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.

And 0^x is 0, and x^0 is 1, which shows that just because you have a constant sequence, it limit is not necessarily the final value.
Your logic is just faulty becuase it makes the INCORRECT assumption that infinite sets just act like finite set, but are just "bigger".
That error is what has exploded your mind to the point you can't see that you mind has been exploded.
You are not just potentially stupid, you have acheived actual stupidity.

 Regards, WM