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

On 02.12.2024 20:06, joes wrote:

Am Mon, 02 Dec 2024 17:51:22 +0100 schrieb WM:

On 02.12.2024 16:46, FromTheRafters wrote:

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).

Non sequitur. That which is true for finite sequences is not
necessarily true for infinite sequences.

As easily can be obtaied from the above it is necessarily true that up
to every term and therefore also in the limit the sequences of
endsegments and of intersections are identical. Every contrary opinion
is matheology, outside of mathematics.

What is the limit?

If infinity is actual, then the FISONs {1, 2, 3, ..., n} have a limit, then the limit of the sequence of FISONs is ℕ. Then the limit of the complementary endsegments is the empty set.
Regards, WM