Re: No, David, you don't need limits (Was Energy)

[Jack Uretsky <jlu@HEP.ANL.GOV>]

On Sat, 22 Sep 2001, David Bowman wrote:

> Regarding Brian W.'s fearsome self-proclaimed mangling:
__________________________________________________
> OK, (except for the minor part about the volume per *unit area* per
> unit time).  Also, we of course need to properly take limits to
> find the instantaneous velocity, i.e.
> (zero displacement)/(zero time interval).

        Newton didn't need to take limits.  Leibniz didn't need to take
limits.  All Zeus's children don't need to take limits.  All you and
they need is a proper definition of infinitesimal.  For this, see
1. The references in the introduction to my Calculus text at
        www.hep.anl.gov/jlu/index.html
2. The notion of an infinitesimal as a quantity so small that its
        square is ("as good as") zero.
3. The definition of derivative as given in Chapter 3 of my text, which
        you will find at the same URL.
                See, also, math-gm/10065 in the (formerly Los Alamos, now
Cornell) arXiv.

--
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                     <The 5-MINUTE ILIAD and Other Classics>