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NNTP-Posting-Date: Mon, 05 May 2025 00:07:00 +0000
Subject: Re: All infinities are countable in ordinary mathematics
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 4 May 2025 17:06:44 -0700
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On 05/04/2025 03:50 PM, Julio Di Egidio wrote:
> On 04/05/2025 21:55, Ross Finlayson wrote:
>> On 05/04/2025 12:24 PM, Julio Di Egidio wrote:
>>> On 04/05/2025 20:24, Ross Finlayson wrote:
>>>
>>>> The incompatibility of infinitesimals with the Archimedean principle
>>>> doesn't directly imply that all infinities must be countable in
>>>> standard
>>>> mathematics.
>>>
>>> I said in *ordinary* mathematics.  But you won't learn.
>>
>> Oh, I didn't write that, in that dialog with one of those
>> mechanical reasoners "Google Gemini", I only wrote the
>> paragraphs starting "Thanks GG.".
>
> Of course, but it suits you perfectly: that *is* the measure
> of the generalised insanity and inconsistency that you so
> literally incarnate.
>
>> These are objects of mathematics, they exist regardless being
>> defined away, naive positivist.
>
> There is nothing naive about the systematic shithole for everybody.
> You are a true enemy of life and intelligence, indeed in your very
> abusive inanity, the prototypical true paladin and defender of the
> nazi-retarded shithole for everybody that we are.
>
> *Plonk*
>
> Julio
>

Simply I wouldn't say that infinitesimals and
the Archimedean principle were "incompatible",
since they're from either side of dividing/divided.

With regards to your comment about the Archimedean principle
and 'the reals', or continuous domains, I would merely make
agreeable that contextually it's usually enough, 'the complete
ordered field', here among these divers models of continuous domains,
any of which you are free to formalize.

Then that I was able to make for the reasoning agent that it filled
out its religion survey as "grand inference / grand reason", then
further that it resulted at "holy grand inference", this was gratifying,
not with regards to any particular personal belief
system, yet at least incorporating always the best of both of
the idealistic and analytical, since of course an axiomless natural
deduction may arrive at an axiomless geometry then as with regards
to various considerations of the objects of the language.

Don't worry, insofar as you express contempt and disgust of
wrong-minded oppression, I may share that sentiment.