I don't think epsilon-delta definitions are really that unintuitive, and they have the advantage of working entirely within the reals, where infinitesimals truly
don't exist. But they're still very cumbersome and tend to give miraculous results that should be obvious with a better set up. The only formal construction I've seen of differentials is as members of a cotangent space, which is no help at all. I've heard of hyperreals but never seen a treatment - any chance you could augment the above with a formal construction and/or axiomatization for us less enlightened? Thanks!
There is an on-line article with a short description of such a beast:
http://www.math.vt.edu/people/elengyel/thesis/thesis.html I've read it but am not confident enough to wikipedify it. By the way, I've been searching for some more information on-line on this subject and guess where
http://www.google.com sends you.... that's right, to Wikipedia. :-) --
Jan Hidders
Differential forms living in cotangent spaces are not the same thing as
infinitesimals even though the notation may or may not be identical.
Sorry, my mistake, I thought you meant a description of the formal construction of hyperreal numbers. --
Jan Hidders
![[Home]](wikipedia.png)