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

WM formulated on Monday :

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

Yes, your nth term is the term common to all previous sets as members of the sequence. This final 'n' is always a member of the naturals. For infinite sets of naturals, there is no last element to be common to all previous sets, so it, the intersection, is empty.

and therefore also in the limit the sequences of endsegments and of intersections are identical.

Says you, but you can't prove the conjecture.

Every contrary opinion is matheology, outside of mathematics.

Says you, but you have little credibility here concerning mathematics.