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

On 12/24/2024 12:27 PM, Chris M. Thomasson wrote:

On 12/24/2024 4:48 AM, Ross Finlayson wrote:

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.
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Regards, WM
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Cantor went insane, ....
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Cantor Pairing works with any unsigned integer.

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No, it works with two copies of the all the integers,
a left-hand-side and right-hand-side,
with regards to pairs
one from column A and one from column B.
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It reminds me of Prof. R., one time I
told him "I'm studying infinity" and
he laughed and said "infinity makes
people nuts" and I laughed and said
"yeah, it does".
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Point being that the incongruities of
what so many times is merely lax book-keeping
of "mathematical paradox" _seem_ to arise
from infinity, when it's really that there
are none, there are no mathematical paradoxes,
that point is to arrive at a theory for
mathematical objects, infinity and continuity
and all, and especially continuity and infinity,
that is sane.
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That lazy, forgetful mathematicians confuse and
confound and conjoin and conflate various abstractions
and generalizations that are not due, has that
partial accounts are not sound.
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So, there's a complete account.
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"Cantor Pairing" isn't two integers,
it's two copies of the all the integers.
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It's called a "subset of a Cartesian Product,
including book-keeping which domain is which".
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Also it's usually called being Galilean,
or having the same cardinal.
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Imagine a fountain of soap.
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A tower of rain, ....
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