Re: Incompleteness of Cantor's enumeration of the rational numbers

On 06.11.2024 15:59, Mikko wrote:

On 2024-11-05 11:26:58 +0000, WM said:
 

  Cantor's results are

conclusions of proofs and you have not shown any error in the proofs.

 I have. This example for instance proves that he did not enumerate all rationals, because the rationals are dense, the intervals are not dense.

 You have not proven that. It is fairly easy to prove that there are
no positive rationals other than those enumerated by Cantor (if I
recall correctly he enumerated only positive rationals). To prove
that there are positive rationals that are not included in Cantor's
enumeration it suffices to show one but you have not shown any.

 I have shown that without rational numbers outside of the intervals with irrational endpoints covering 3 of infinitely many units the real axis has measure 3.