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

On 09.12.2024 21:55, Jim Burns wrote:

On 12/9/2024 2:45 PM, WM wrote:

On 09.12.2024 18:20, Jim Burns wrote:

 

Your two sequences as you have written them
are equal, and have equal limits: the empty set.
>
I suspect that it is the distinction between
cardinality of limit #⋂{E(i):i} = #{} = 0  and
limit of cardinalities ⋂{#E(i):i} = ⋂{ℵ₀:i} = ℵ₀

>
The cardinality of the limit is
the cardinality of the limit set.

By the way, we need no cardinality. We need only the sequence of sets with the empty set in the limit.

The limit set is
the set of numbers in common with each end.segment
and isn't anything else.

The limit set is the same for both sequences.
(E(1)∩E(2)∩...∩E(n)) and (E(n))
In order to stop tricksters we go without cardinality.
Regards, WM