FOM: Another question on infinitesimals

[Vaughan R. Pratt]

>My question:  given that you can't go "all the way" with constructive
>infinitesimals, how far can you go?  Could you get all the way through first
>year college calculus, rigorously replacing epsilondelta with them?

Quite right, this is one of the reasons to be interested in my question

>(i) What functions on R are compatible with a suitably constructive
>notion of infinitesimal?

In particular what can be said about what is or is not possible for a
constructive notion of infinitesimal in the presence of the trig and
hyperbolic functions, a sine qua non of elementary calculus.

Vaughan