[FOM] Infinitesimal calculus

[hendrik@topoi.pooq.com]

On Mon, May 25, 2009 at 08:21:05PM -0700, Monroe Eskew wrote:
> If the idea is just to teach calculus techniques to high school
> students,

you could use an intuitive understanding of continuity (can draw the 
graph without taking the pencil from the paper), and define a limit of a 
function to be the value it needs to have to be continuous.  Epsilons 
and deltas, or even "this approaches that" would only be needed if one 
wished to explain the underlying concept of continuity more thoroughly.

> If on the other hand we are talking about teaching mathematical theory
> to undergraduates,

this would be the place to use epsilons and deltas to explain 
continuity, be it Bishop-style uniform continuity or classical 
point-wise continuity.

-- hendrik