Re: Calculus XOR Probability

Ross A. Finlayson said:

Virgil wrote:

Which it never does in any limiting process. There are NO limit
definitions in Cartesian geometry which even hint at infinitesimal
anything.

Isn't the idea of limit to "sweep the infinitesimals under the rug", as
it were, anyways?

The notion, or tool, method, of "limit" is used in what was formerly
called "infinitesimal analysis" because generally by consensus it was
seen as a way to remove ambiguities about infinitesimals from analysis,
where basically you get your Newtonian/Robinso(h)nian iterative or
recursive infinitesimal with the fluents and fluxions, or your
Leibnizian, in the sense of differential, nilpotent infinitesimal the
sum of which over the naturals is equal to one. That fits with the
Bishop and Cheng or Schmieden and Laugwitz or Palmgren or my
conceptions in a sense, towards a "rather restricted" transfer
principle, and obviously polydimensional points.

While the use of the limit as approximation by finite n-sets, with
domains of subsets of the naturals {1, ..., n} for finite natural n, is
used to establish an inductive guarantee of sorts of the existence of
limit as evaluation, those identities generally hold only in that
_infinite_ induction, where in delta-epsilonics neither delta nor
epsilon can be any positive _finite_ value, for where they are finite
then almost all results, that are perfect results from the
infinitesimal analysis, would be skewed in the finite differencing of
sorts.

So, there certainly _are_ not just hints of infinitesimals in geometry,
those ghosts of departed quantities that comprise arcs/curves, surfaces
and so on and so forth, in the rectilinear coordinate system of
Cartesian geometry, there is reason in the inductive guarantee that
those things exist, else the limit is not in evaluation good.

Your misapplied overgeneralizations are egregious.

Ross



Hi Ross. Long time, it seems. Hope you're doing well. Well said, by the way.
Thanks.
--
Smiles,

Tony
.

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