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

On 12/15/2024 2:16 PM, WM wrote:

(1) E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
loses all content.

>
the set of common finite.ordinals is empty.

>
Fine.

 Each finite.cardinal
leaves after that.many steps,
with further steps to follow,
more steps than any other finite.cardinal

 

By the law
(2) ∀k ∈ ℕ :
∩{E(1),E(2),...,E(k+1)} =
∩{E(1),E(2),...,E(k)}\{k}
the sequence gets empty one by one.

If all natural numbers are
individually available for indexing
then they are available for
individually leaving the intersection.

 Yes.
Each finite.cardinal
indexes its own end.segment,
and leaves at the next end.segment.