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

On 07.01.2025 12:36, Alan Mackenzie wrote:
 

If there were such
things as "potential" and "actual" infinity in maths,

 Your comments about my quotes show that you have lost all contact with mathematics.

   then they would

make a difference to some mathematical result.

 Of course. Here is a simple example, accessible to every student who is not yet stultified by matheology.

 For the inclusion-monotonic sequence of endsegments of natural numbers E(k) = {k+1, k+2, k+3, ...} the intersection of all terms is empty. But if every number k has infinitely many successors, as ZF claims, then the intersection is not empty. Therefore set theory, claiming both, is false.
 Inclusion monotonic sequences can only have an empty intersection if they have an empty term. Therefore the empty intersection of all requires the existence of finite terms which must be dark.
 Further there are not infinitely many infinite endsegments possible because the indices of an actually infinite set of endsegements without gaps must be all natural numbers.
 Regards, WM