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

On 22.11.2024 23:56, Jim Burns wrote:

On 11/22/2024 4:30 PM, WM wrote:

Remember:
The intersection of all endsegments is empty,
but the intersection of
endsegments which can be counted to
is infinite.

 No one should "remember" that.
It is incorrect.

∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k), |E(k)| = ℵ₀
∩{E(1), E(2), ...} = { }.

 

Note that every endsegment loses only one number.

 Finite cardinalities can lose one number.

For all endsegments:
∀k ∈ ℕ: |E(k+1)| = |E(k)| - 1

Therefore there must
exist infinitely many finite endsegments.

Regards, WM