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

On 12/02/2024 05:22 PM, Jim Burns wrote:

On 12/2/2024 7:43 PM, Ross Finlayson wrote:

On 12/02/2024 04:32 PM, Jim Burns wrote:

On 12/2/2024 9:28 AM, WM wrote:

>

Infinite endsegments contain an infinite set each,
infinitely many elements of which
 are in the intersection.

>
Yes to:
⎛ regarding finite.cardinals,
⎜ for  each  end.segment   E(k)
⎜ there is a subset S such that
⎝ for each finite cardinal j, j < |S| ≤ |E(k)|
>
No to:
⛔⎛ regarding finite.cardinals,
⛔⎜ ⮣ there is a subset S such that ⮧
⛔⎜ ⮤ for  each  end.segment   E(k) ⮠
⛔⎝ for each finite cardinal j, j < |S| ≤ |E(k)|
>
A quantifier shift tells you (WM) what you (WM) _expect_
  but a quantifier shift is untrustworthy.
>

An empty intersection cannot come before
an empty endsegment has been produced by
losing one element at every step.

>
No.
Because see below. [redacted by JB]

>

The usual idea of wrestling with a pig is
that you both get dirty, and the pig likes it.

>
However it seems to you,
I'm not really hostile to the pig,
even if it does piss me off sometimes.
Let it like the wrestling.
Am I hurt by that?
>
I get dirty.
Oh! I get dirty! Oh my! Oh my! Oh my!
Have you never gotten dirty, Ross?
One gets dirty,and then one gets clean again.
And then, one gets dirty.
Welcome to life.
>

Quit letting that pig dirty things.

>
Refresh my memory, Ross.
Was it you, Ross, who told me that,
even though I tell you
I'm talking about standard integers,
you will take me to be talking about _everything_
?
>
In what way is talking with you (RF)
different from wrestling with a pig
?
>
Oh, wait. I forgot.
You (RF) don't answer questions.
Never mind.
>
>

You mean like "do you pick?".
Remember "do you pick?".
See, in mathematics, all of which are mathematical
objects, in one theory called mathematics, there's
the anti-diagonal argument, which here used to be
called the diagonal argument which is the wrong name,
has after an only-diagonal argument, what results
that you either get both or none, though that the
only-diagonal itself is constructive for itself
while the anti-diagonal is a non-constructive argument
when you look at it that way.
So, "do you pick?".
I think us long-term readers can generously,
generously, aver the "Burse's memories", are,
at best, regularly erased.
Many of which elicited a spark of thought
then out-went-the-lights. Most of which
went starkers bat-shit.
So, do you even remember? Or did you just get told again?