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

On 12/22/24 8:07 AM, WM wrote:

On 22.12.2024 13:28, Richard Damon wrote:

On 12/21/24 4:58 PM, WM wrote:

 

Finite endsegments have a natural number of elements.

>
SO, none of your E(n) are finite endsegments, since they all have an INFINITE number of elements, being the INFINITE set of
{ n+1, n+2, n+3, ... } by your definition.

 The intersection of all endsegments is empty. It cannot get empty other than by one element per endsegment.
 Regards, WM

Your problem is you need to intersect *ALL* the sets, and that is an infinite amount, but your logic only allow the processing of a finite number of set.
Since and infinte number is bigger than a finite number, your problem comes down to the fact that you tools just can't do the job.
That is shown by the fact that if you try to build the set of Natural Numbers one at a time by adding each number individually, you never reach the end, so your tools could never have the set of the Natural Numbers to work with in the first place.
All you are doing is proving that you brain is just broken and has exploded into a dark hole by the contradictions you have inflected upon it by using it for things it is just incapable of handling.