Re: Replacement of Cardinality (analytische bruecken)

On 08/11/2024 05:24 AM, WM wrote:

Le 10/08/2024 à 19:16, FromTheRafters a écrit :

WM expressed precisely :

Le 09/08/2024 à 05:34, Jim Burns a écrit :
>

and he thinks that
a set ordered with two ends is
more complete than
the same set with one or zero ends.

>
The set of unit fractions has two ends, namely at 1 and before 0.

>
Wrong,

>
Name unit fractions larger than 1 or smaller than 0.
Note: Before domains without unit fractions the set has ended.
>
Regards, WM
>
>

What's missing is a fuller dialectic of deductive inference
of the geometric space and integer lattice and that there
are the multiple regularities/rulialities of the modular.
Otherwise you just get "degenerate intervals".
The Sorites/heap reflects on finite means,
to frame it in the finite again as always modular.
This way deductive inference can build into the
finite modular for the unbounded and actually infinite modular,
like from "a sober mind speaks" when it's pointed out that
mathematics really does have mathematical infinity in it.
The "infinite limit" and "completions" are two things,
it seems better to complete the geometric series first,
than to just axiomatize least-upper-bound and measure 1.0,
that the geometric series naturally gives completion.
(Of an infinitary or infinite expression, that's also
specifically _not_ finite.)