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Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Tue, 24 Dec 2024 16:09:02 -0800
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On 12/24/2024 04:07 PM, Ross Finlayson wrote:
> 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:
>>>>
>>>>>>>> No, I do as Cantor did.
>>>>>>
>>>>>>> No, you do what you THINK Cantor did,
>>>>>>
>>>>>> Show an n that I do not use with all intervals [1, n].
>>>>
>>>>> The LAST one, which you say must exist to use your logic.
>>>>
>>>> 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
>>>>
>>>
>>> Cantor went insane, ....
>>>
>>
>> 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, ....
>
>

Behind the noodles, ....