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

On 12/2/2024 6:53 AM, FromTheRafters wrote:

Chris M. Thomasson brought next idea :

On 11/30/2024 3:12 AM, WM wrote:

Endsegment E(n) = {n, n+1, n+2, ...}

>
This is his definition of endsegment, which
as almost anyone can see,
has no last element, so
yes it is infinite.

Yes.
Obviously and also provably.
For each finite cardinal k
k < |{n,n+1,n+2,...,n+k}| ≤ |n,n+1,n+2,...}|
No finite cardinal is |{n,n+1,n+2,...}|

He says 'infinite endsegment' as if
there were a choice,
only to add confusion.

I suspect that, sometime in the distant past,
  WM decided that 'infinite' meant
'extremely, unusably large but not (what others mean by) infinite',
  which is an error.
Famously, to err is human, and error, by itself,
  would never have ever aroused much interest.
One corrects oneself,
  nods to the great mathematicians who have also erred,
  and moves on.
However,
WM decided to go another way,
and he has spent the last 30(?) years
trying to make reality conform to his error.
Yes, 'infinite endsegment' adds confusion.
And that pleases Mückenheim, I suspect.
That confusion is the only impact his writings will ever make.
But, in Mückenreich,
first.infinite ω is countable.to and countable.past.
There, ω merely serves as a marker between
arbitrary (and changeable!) stretches of countable.to numbers.
If 'infinite endsegment' isn't merely trolling
  (which a 30.year troll seems a bit extreme),
I see "infinite endsegment" as one indicator that
  WM refuses to learn what 'infinite' means.