Re: All infinities are countable in ordinary mathematics

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.