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

On 14.12.2024 11:26, joes wrote:

Am Fri, 13 Dec 2024 11:55:16 +0100 schrieb WM:

Just imagine all of the inf.many steps as a whole - y’know, ACTUAL
infinity.

Those who try to forbid the detailed analysis are dishonest swindlers and tricksters and not worth to participate in scientific discussion.

If not every natural number has left the endsegment and is applied
as an index of a line of the list, the list is useless.

Then the list were finite. It isn’t, though.

Therefore the sequence of intersections loses all content.
E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ... --> { }

But if every natural number has left the endsegments, then the
intersection of all endsegments is empty.

Yes.

Then the infinite sequence of
endegments has a last term (and many finite predecessors, because of ∀k
∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}).

No. It is literally „without an end”,

The end is reached when all content has gone because more cannot go. Then the intersection of endsegments which was not empty before has become empty. This cannot happen other than by the law
∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}

and yet can be „completed”, if
only you were able to conceive of infinity.

That is not a property of infinity but illogical nonsense.
Regards, WM