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

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.