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

On 18.12.2024 19:22, Jim Burns wrote:

On 12/18/2024 7:40 AM, WM wrote:

The infinite end.segments of finite.cardinals
do not include any finite end.segments and
they have an empty intersection.

>
Explicitly wrong.
As long as only infinite endsegments are concerned their intersection is infinite.
>
There are no limits involved.

 Then it would be great if you (WM)
stopped calling things 'limit sets'

The sets described here are not limit sets.
f(k) = ∩{E(1), E(2), ..., E(k)} with E(1) = ℕ
∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k},
∩{E(1), E(2), ...} is empty.
Other sets are not in the argument.
Regards, WM