FOM: Re: Berkeley and nonstandard analysis
Martin Davis
martin at eipye.com
Fri Jan 28 13:32:00 EST 2000
At 08:57 AM 1/28/00 -0800, Charles Silver wrote:
> I have another question ... Isn't it true that it is *easier* and
> **clearer**
>to teach calculus using infinitesimals than the standard way ...That is,
>aren't the main reasons for the abandonment of infinitesimals in the
>teaching of beginning calculus historical rather than mathematical?
Probably. Jerry Keisler wrote an excellent elementary calculus textbook
based on infinitesimals. He elegantly put the needed model theory in a very
digestible form: any system of equations and inequalities is satisfiable in
the reals if and only if it is in the hyperreals. A colleague of mine
(Hausner) used the book quite successfully at NYU. But it never caught on.
Martin
Martin Davis
Visiting Scholar UC Berkeley
Professor Emeritus, NYU
martin at eipye.com
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http://www.eipye.com
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