Lester Zick wrote:
Tony, let me see if I can provide an alternative line of reasoning to
support my analysis.
Okely Dokums!
Over the past couple of years in addition to tautological analysis
I've also provided analysis of angular mechanics in corrected form.
And in that analysis I do make use of arithmetic combinations of
finites and infinitesimals. In particular I take finites such as the
radius of circles, r, and combine them with infinitesimal changes in
radius, dr, showing that for any finite multiple of dr, such as ndr,
the combination can change only infinitesimally such that r+ndr=r and
r remains finitely constant. I don't know if you followed that
discusion but the mechanics involved are identical to what you
suggest.
Yes, I thought it was encouraging to see the notion of a mixture there,
though it didn't seem like it followed necessarily. It was more like,
there could be an infinitesimal change, that wouldn't be detected. In
any case, do go on... ;)
Now the problem for you and your idea of combining finites and
infinitesimals arithmetically is that you can't combine finites and
infinitesimals directly.
Oh, then no dr/dt for you tonight, young man. And after you brushed your
teeth already...
In other words there is no way to say r+dr>r
Except you just did it.
as you're trying to suggest because finites and infinitesimals don't
lie together on a common line with the same metric.
Same line, different scale.
In the case of angular mechanics this is also true. However I provide
a common metric for them by definitely integrating a finite velocity,
dr/dt, between 0 and dt which provides a finite dr of infinitesimal
magnitude.
Uh, what? A finite dr of infinitesimal magnitude? What makes it finite?
In other words you can't provide an arithmetic sum for
finites and infintesimals directly without first providing a common
finite metric for them through definite integration of some kind.
Yeah. That's what IFR's about. The line, Man. That's the common metric.
_______________________________________________________________________
This is how we can know arithmetic combinations of finites of finite
magnitude and finites of infinitesimal magnitude. Mathematically
modern mathematikers incorrectly analyze the same problem in the
reciprocal terms of n/dr instead of ndr and wind up with various kinds
of 00 they like to pretend follow the finites on a common real number
line. However this makes the proper analysis of angular mechanics
impossible unless one takes r to be an infinite and ndr to be finite.
In any event I hope this clears up my perspective on analysis of the
arithmetic combination of finites and infinitesimals.
Actually I got lost at the end there. Infinitesimals are things that, if
you multiply them together, they disappear. *poof*
<snip diggy dig>
01oo
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