On Saturday, May 22, 2021 at 6:50:51 PM UTC-7, mitchr...@gmail.com wrote:
> what finite do you choose and why
> are they different?
>
> The continuity bridge is starting
> at a size of infinity for the continuum
> hypothesis. You must build the
> whole bridge before you use it.
>
> Mitchell Raemsch

It's more like it's built itself and accesses you
than the other way around (which, though,
while "finite", is still "whole").

A continuum hypothesis vis-a-vis the cardinal
continuum hypothesis and 2^w = Aleph_1,
some continuum hypothesis that "integer
effectively large is infinite, in terms of that
a true infinite of course would have even
effectively infinite larger the effectively large
finite", that what all matters is that continuous
terms like area and volume result in the
products of the various increasing dimensions
of a usual Euclidean (or infinite dimensional)
vector space.

Otherwise no one will bother to attach a relevant
"correct" meaning besides what you generally bother
to observe what you perceive as relevant salient facts,
what result after foundations a simple classical with
plainly 3 space dimensions at rest.

Of course if I ask myself how to define real numbers
for real analysis, I know Dedekind-Cauchy for having
a working knowledge of mathematics as it's "usually"
practiced (or, formalized), then call that field-continuity
and introduce besides what are true alternate forms of
real numbers in continuity, then for the rest of the usual
fundamental theorems, line-continuity for field-continuity
then signal-continuity, for general linear motion and ratio
and density, that the rationals are large as a continuum
hypothesis, I answer myself.

Then, where it is the usual problems in mathematics
that there are finite and infinite, and line and area and
so on, usual conceptual hurdles, they are very strong
so I was lucky to be able in the course and already have
my own idea of things so borne out usually, including that
when the branches resulted like ".999", or, ..., mostly ".999",
I kept since that both the line continuity and field continuity
notions, what so result in clock arithmetic and the closure of
rational approximations what make roots in the modular.

Seems in answer to your question that it's the effective,
for example whether it is in length or depth some infinite,
or just how line segments are in vector spaces.

It's like "how fast do you drive your car?" "Miles/hour".

Infinite....

....spring in me some memories of the terminology that a guy used :

He believed in discrete as AP, but, in contrast, he
believed just in round shapes as the basis of geometry, circle, sphere, cone, cylinder.
The anatomy of a "discrete line segment" what composed of the "bound points" and the
"flesh points". The flesh points are the "length" of the "discrete line segment".
The "discrete line segment" always have at least two points, the bound points, and never
can be equal to one point alone. When he build a "discrete circle", the bound points
were were not adding to the arclenth of the "discrete circle", but still there.
He didnt believe in grids. He used other flamboyant words for his objects and operatiions.

Back to the topic, like number systems in ancient times, 1, 2 and many, infinity
as a reminicence of many.

On Monday, May 24, 2021 at 5:08:20 PM UTC-7, michael Rodriguez wrote:
> ...spring in me some memories of the terminology that a guy used :
>
> He believed in discrete as AP, but, in contrast, he
> believed just in round shapes as the basis of geometry, circle, sphere, cone, cylinder.
> The anatomy of a "discrete line segment" what composed of the "bound points" and the
> "flesh points". The flesh points are the "length" of the "discrete line segment".
> The "discrete line segment" always have at least two points, the bound points, and never
> can be equal to one point alone. When he build a "discrete circle", the bound points
> were were not adding to the arclenth of the "discrete circle", but still there.
> He didnt believe in grids. He used other flamboyant words for his objects and operatiions.
>
> Back to the topic, like number systems in ancient times, 1, 2 and many, infinity
> as a reminicence of many.

The arc of an infinite circle is infinitely close to being straight...
The infinite is the finite increasing forever never coming back down.

Mitchell Raemsch