Re: how come calculus can be exact?
From: Robert Israel (israel_at_math.ubc.ca)
Date: 09/05/04
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Date: 5 Sep 2004 18:36:08 GMT
In article <1dc813f.0409051006.f35afef@posting.google.com>,
ashok <arjdombivli@indiatimes.com> wrote:
>How come calculus gives the exact results despite we are making
>approximations(neglecting the infinitesimal which tends to zero) at
>its basic definition level?
>I am getting very much frustated over it.
>Can someone please convince me over the exclusion of the infinitesimal
>terms from the definition and still getting the correct results.??
The main idea is that of a limit. You aren't just making approximations,
you are taking a limit of approximations as something (e.g. Delta x) goes
to 0. In any good approximation method, the limit of the approximations
is the exact result.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
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