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

On 12/02/2024 11:13 AM, FromTheRafters wrote:

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.

Try to avoid the second person - framing things in terms
of states and actions instead of personalities.
Because I'm like, there's not much reason here to care
at all, and it would work out best if nobody ever replied
to "Dumb-em" (Dumb-em-down, soft-ball straw-man), again.
Which has been among the greatest wastes of times ever
since it was launched at sci.math.
This is "news", if it's not "new", it's "old".
Mirimanoff, who introduces the extra-ordinary, is a
much more profound insight into isses of ordinarity
and regularity in set theory, then that there's an
entire sort of infinitary reasoning involved since
antiquity, still surprising and delighting thinkers
and even shaking the foundations, to this day.
As if there is one, ....
So, boycott that guy and find something better to
wax on about.