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

On 09.12.2024 22:45, FromTheRafters wrote:

WM explained :

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.

 But size matters, or so I've heard.

>
In sequences of sets only sets matter.