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

On 11.12.2024 21:58, Jim Burns wrote:

On 12/11/2024 2:57 PM, WM wrote:

On 11.12.2024 20:27, Jim Burns wrote:

Each "leaves" by
not.being.in.common.with.all.end.segments.
 ∀k ∈ ℕ:
k ∉ E(k)\{k} = E(k+1) ⊇ ⋂{E(i):i} ∌ k
 ⋂{E(i):i} = {}.

Therefore,
one.element.emptier ℕ\{0}
is not.smaller.than ℕ

>
It is a smaller set.

>
For each k in ℕ
there is unique k+1 in ℕ\{0}
>

Cardinalities are not useful.

>
And yet, by ignoring them,
you (WM) end up wrong about
⎛ For each k in ℕ
⎝ there is unique k+1 in ℕ\{0}

Is the complete removal of natural numbers from the sequence of intersections
bound by the law
∀k ∈ ℕ :
∩{E(1), E(2), ..., E(k+1)} =
∩{E(1), E(2), ..., E(k)} \ {k}
or not?