FOM: Examples of Infinitesimals

[Vaughan R. Pratt]

>From: Harvey Friedman <friedman at math.ohio-state.edu>
>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
based?

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.

Vaughan