Re: Replacement of Cardinality (effective bounds)

On 08/24/2024 11:08 AM, FromTheRafters wrote:

WM has brought this to us :

Le 23/08/2024 à 20:06, joes a écrit :

Am Fri, 23 Aug 2024 14:27:11 +0000 schrieb WM:

Le 22/08/2024 à 16:19, FromTheRafters a écrit :

WM formulated the question :

>

*If there is a complete chain*, then it has a last member.

Just as the last saucer completes the tea set?

No, just as there is a border between populated and empty domains.

The unit fractions don’t reach 0.

>
Of course not. Therefore they must cease before.

>
Why must they cease at all?

He can just axiomatize it so, saying that
there's a rule.
Or, imagine for example there's a mathematical cripple
of sorts, he's got finite means. So, instead of more
or less axiomatizing his accessibility to infinite induction,
he has to cope with his limited means, so he makes models
where there's an effective infinity and an effective
infinitesimal, then also has that the analytical bridges
go through, i.e. that the limit exists and has a well-defined sum.
Let's call him A.P. So, on this world where most of the
mathematical cripples simply axiomatize that their way
is ordinary, making it regular this way, he confronts the
otherwise paradoxes of mathematical infinity by staying
away from them at all.
Then you might call him AP or WM or any of these other
finite-means retro-finitist howler-trolls of sorts that
find their mirror images in, ..., finite-means retro-Russellian
end-of-discussion sorts, yet, in a sense, his pastiche of
pieces of broken mirror and the fetish of here a, ...,
"complete chain", can be a model of closure in completion
even though it leaves out many and most of the results
in the middle, which one may aver that the other kind
of "one of us" end-thinkers don't complete, anyways.