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Tony Orlow wrote:
> Randy Poe said:
> >
> > Han de Bruijn wrote:
> > > Randy Poe wrote:
> > > > Ah, so when you said "physicists use infinitesimals" what you
> > > > really mean was "physicists use integrals".
> > >
> > > No. Physicists use "infinitely small element"s and "an infinite number
> > > of elements".
> >
> > In the form of integrals.
> >
> > > How can you possibly deny? Can't you just READ the above?
> >
> > Yes, I've read a thousand such passages, which are always deriving
> > an integral equation or differential equation.
> >
[snip]
> >
> > Your infinitesimals are only used under integral signs.
> >
> > - Randy
> >
> >
>
> I think that Han's whole point is that, while the final solution leads to an
> integral,
The final expression is an integral, yes.
> the derivation of the integral itself rests on the very notion of
> infinitesimals that he's trying to put forth, as the limit of 1/n as n->oo.
No it doesn't. Physicists know they aren't being rigorous
when they throw stuff like that around, they know they
aren't following a rigorous derivation. But they know that the
integral is valid, and it is that endpoint they are interested in.
Nobody cares about the actual "infinitesimals". They care about
the limit of the sum, i.e. the integral.
> So,
> if calculus itself is derived using this notion,
It isn't.
> the question becomes why this
> notion of the infinitesimal cannot be discussed in its own right.
It can. That's called NSA. And calculus can be developed within
NSA. But it doesn't have to be, and Han's claim is that physicists
are routinely doing something like NSA, or treating infinitesimals
separately from their sums.
- Randy
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