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

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.

In other news,
the sum of two numbers is
the sum of one of the numbers and the other number.

This set is defined by
the sequence of cardinalities from
∀k ∈ ℕ : E(k+1) = E(k) \ {k}
and by nothing else.

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