Re: Replacement of Cardinality (infinite middle)

On 08/11/2024 11:30 AM, Jim Burns wrote:

On 8/10/2024 7:05 PM, Moebius wrote:

Am 11.08.2024 um 00:47 schrieb Chris M. Thomasson:

On 8/10/2024 3:43 PM, Moebius wrote:

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Hint: Let's "consider" the real line:
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...|-----|-----|-----|-----|--..
   0     1     2     3     4
>
[Now] omega is not a point on this line. :-P

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"Out of scope", perhaps? Is that okay?

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Somehow. :-P
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I guess, JB would say:
"If we don't consider omega,
we don't consider omega."
:-P

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I think I can make a good case for that.
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----
I propose that
each split F,H of the line is situated in the line
== the line has a point last.in.F or first.in.H
>
It follows that
each positive point is separated from 0
by some finite /n
otherwise, contradiction follows.
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If each positive point has a reciprocal,
then each point has a finite reciprocal,
and no point is ω
>
----
Georg Cantor did not get up one morning and ask,
"How can I piss off Wolfgang Mückenheim decades from now?"
>
We often have reasons for things being how they are,
the weirder they seem, the better the reasons,
because, no, those who made it that way
are not actually trying to piss you off.
They have (had) better things to do.
>
>
>

Did Cantor wake up on morning "why am I in an insane asylum?"
You know before the Mengenlehre the set theory, including
where Cantor pulled together the anti-diagonal argument of
duBois-Reymond and the nested-intervals which is like Zeno's
and what you have here, then also there's the "m-w" proof
and I'm not quite sure its provenance though perhaps it's really
G.L.P.C.'s, before the Mengenlehre, Cantor at Halle was in the
orbits of Dirichlet and about the formalization of Fourier-style
analysis showing a continuum limit of an infinite expression of
periodic functions the computed coefficients, that Heine showed
the uniqueness of this after Dirichlet had worked up after Fejer
after Fourier this kind of thing, that Cantor picked that up and
I forget if it was actually Heine or another, who made it so that
there is a unique series of pairs of coefficients the Fourier series,
that Cantor re-wrote that a bit, that before the Mengenlehre,
that had been the paper that Cantor wrote.
So, you know, there are some studies since the 50's and 60's or
Phythian, then for dynamics and turbulence, that have that it's
not necessarily so exactly this uniqueness.
Do you think that would aggravate him as much as that
the Continuum Hypothesis being broken both ways put him in the madhouse?