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

WM presented the following explanation :

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.

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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.

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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.

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But size matters, or so I've heard.

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In sequences of sets only sets matter.

 The why are you averse to the emptyset?