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.

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.
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".
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.
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.
So, there's a complete account.
"Cantor Pairing" isn't two integers,
it's two copies of the all the integers.
It's called a "subset of a Cartesian Product,
including book-keeping which domain is which".
Also it's usually called being Galilean,
or having the same cardinal.
Imagine a fountain of soap.
A tower of rain, ....