FOM: Re: Berkeley and nonstandard analysis

Martin Davis martin at
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 Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at
                          (Add 1 and get 0)

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