Re: Incompleteness of Cantor's enumeration of the rational numbers

On 12/1/2024 3:33 PM, WM wrote:

On 01.12.2024 21:02, Jim Burns wrote:

On 12/1/2024 5:02 AM, WM wrote:

E(1), E(2), E(3), ...
and
E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
are identical for every n and in the limit
because
E(1)∩E(2)∩...∩E(n) = E(n).

>
Identical sequences without an empty end.segment.
Identical empty set of common finite.cardinals.
>
Inclusion monotony does not prevent
an empty set of common finite.cardinals
  without an empty end.segment.

ENDS⁺ is the set of
  non.empty end.segments of finite.cardinals.
⎛ ℕ,E(1),E(2),... ∈ ENDS⁺
⎝ {} ∉ ENDS⁺
For each end.segment E(k) ∈ ENDS⁺
for each finite.cardinal j
|E(k)| > j
For each finite.cardinal j
|ENDS⁺| > j
For each finite.cardinal j
⎛ j is only in each of ⟨ℕ,E(1),...,E(j)⟩ ⊆ ENDS⁺
⎜ |⟨ℕ,E(1),...,E(j)⟩| < |ENDS⁺|
⎜ j is not.in.common.with each E(k) ∈ ENDS⁺
⎝ j ∉ ⋂ENDS⁺
For each finite.cardinal j
j ∉ ⋂ENDS⁺
⋂ENDS⁺ = {}

Stupid or impudent. No reason to continue.