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

On 12/24/2024 06:36 AM, FromTheRafters wrote:

Ross Finlayson wrote on 12/24/2024 :

On 12/24/2024 02:45 AM, WM wrote:

On 23.12.2024 15:32, Richard Damon wrote:

On 12/23/24 4:31 AM, WM wrote:

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No, I do as Cantor did.

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No, you do what you THINK Cantor did,

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Show an n that I do not use with all intervals [1, n].

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The LAST one, which you say must exist to use your logic.

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I do what Cantor did. There is no last one. You cannot show an n that I
do not use. There is none. Therefore all your arguing breaks down.
>
Regards, WM
>

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Cantor went insane, ....

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Irrelevant.

Well, a bit irreverant, yet Georg's constant
self-aggrandizing and inconstancy with regards
his collection of existing results and re-writing
them un-attributedly in Mengenlehre then had that
Skolem really put a bee in his bonnet then about
the Continuum Hypothesis that these days it rests
rather un-easily as for Cohen and "let's just say
it's un-decide-able".
So, students of set theory and axiomatic set theory
about foundations must of course consider things
like the cardinal continuum hypothesis of Cantor,
then Skolem shows up with "how about both", that
more-or-less gently Cohen "forces" "how about neither".
Anyways it's said that that's what Cantor had as
his long-standing un-achieved goal, CH, because
here after Cohen, and long after Skolem, it's
both or neither, and maybe Cantor just wanted
to have come up with a theorem for himself.
Then, Cohen sort of sits with Goedel, yet Cohen
definitely has the extra-ordinary as what
he "forces" in his model theory, though it's
deemed to be arrived at via comprehension simply
enough, if you actually read "The Independence
of the Continuum Hypothesis" or 1 and 2, it
sort of is similar to Goedelian incompleteness,
yet as well makes for that there are both,
just, "outside", the theory, say.
So, of course in at least theory it's both
after disambiguating the differences.
Then, it's not so different from the trolls
here, cranking along in theories that are
at best incomplete with neither, yet always
the objects of the theories repairing themselves
both, why such cranks are insane long ago.
The ordinals, and the cardinals:
are two quite altogether elementary objects
in two quite altogether fundamental theories
of two quite altogether opposite accounts
of "theories of one relation".