FOM: Examples of Infinitesimals

Vaughan R. Pratt pratt at cs.Stanford.EDU
Thu Nov 13 08:53:00 EST 1997

>From: Harvey Friedman <friedman at>
>By the way, I am interested in arguing that epsilon-delta calculus is
>better than infinitesimal calculus, and I find the epsilon-delta calculus
>so much easier and more fun to honestly teach that I only teach
>epilson-delta calculus. E.g., if I was in your class, I would ask you for
>an example of an infinitesimal. What would be your answer? Students are
>always asking me for examples of anything I talk about in calculus.

I would agree with Harvey that not being able to produce an example of
an infinitesimal would be a serious pedagogical flaw in the method.

But what's wrong with the example 1/oo, or -2/oo, where oo (or its
pedagogically optimal name) is the constant on which the method is

If you can't convey that 1/oo can be smaller than any standard positive
real yet be consistently interpreted as nonzero, then Harvey has a
point, you probably shouldn't be teaching calculus with this method.


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