Re: Calculus XOR Probability

Virgil wrote:
In article <MPG.1eadc6b84b9328e298ac3a@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:


How do you know that there are any infinite n in the first place?

Because there are sets with infinite numbers of elements, such as any
set of all reals in a finite interval.

Whether there are infinite sets is quite irrelevant to whether some
member of one of them is itself infinite.

No, that's not quite so.

There is no universe in ZF, however.

It's good to see you use a word from philosophy, "noumenon", what would
you say that one of those is?

(It's noumena, a thing _and_ a multitude, or aggregate, indviduum and
continua.)

Points and lines or points and all possible spaces or scalars and
composites and so forth are in a sense defined in terms of each other.
In a quite similar and as more fundamental more fundamentally obvious
so are the void and universe, yet those totally comprehensive and
totally, basically incomprehensive notions of eternity, comprehensive,
and null incomprehensive, as a reduction to mutually agreeable truths
in, for example, an axiomless system of natural deduction, lead to a
variety of simple theorems about the finite and hereditarily finite
basically validating fact.

Then, in the infinite, there are a variety of definitions of sizes and
sizings and hierarchies and patterns, and lack thereof in various cases
eg where trichotomy fails or the vague fugue or tempus fugit.

Ha ha ha ha.

There are counterexamples in real analysis that there are
infinitesimals in the reals, and correspondingly there are
counterexamples, standardly, to that they exist. That's about some
facets of the real numbers, those of the continuum of real numbers,
complete and gapless between zero and one, where it can be said that
standard definitions don't adequately describe those things, for all
that is expected of them.

In ZF, there is no set of numbers.

The consideration of infinite values in the natural integers, or
continuum of natural integers, has been addressed by many. There are
many things to note about them, and few. Consider infinitesimal
analysis, for no finite number of terms is the sum a correct
expression, except for regular polygons and so forth, but then the
circle is, in smooth infinitesimal analysis, a regular polygon with
infinitely many sides. Thus, in a way, that can be seen as a simple
counterexample to that nilpotent infinitesimals don't actually exist,
and to Zeno stall, basically that the limit is a sedative.

I'm reminded of octants and so forth and rays from the origin and
squares and circles in the small and large, very small, and very large.

There's much more said about it.

The universe is infinite.

Ross

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