Re: how come calculus can be exact?

From: Norm Dresner (ndrez_at_att.net)
Date: 09/07/04 

Date: Tue, 07 Sep 2004 06:05:24 GMT

> In <1dc813f.0409051006.f35afef@posting.google.com>, on 09/05/2004
> at 11:06 AM, arjdombivli@indiatimes.com (ashok) said:
>
> >How come calculus gives the exact results despite we are making
> >approximations(neglecting the infinitesimal which tends to zero) at
> >its basic definition level?
>

You're reading the equations of calculus wrong. They're not (precisely)
equations but rather shorthand statements about limiting processes.
Calculus gives precise results only in the context of these limits. There
is, as another poster remarked, something called Nonstandard Analysis in
which these infinitesimal quantities are presumed to exist and then Calculus
presents true equations within that context. It is, however, non-standard.

    Norm

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