TITLE: Are there concepts in nonstandard analysis that are useful for an introductory calculus student to know?
QUESTION [6 upvotes]: Studying calculus I became aware that nonstandard analysis had some methods that that made the concept of infinitesimal concrete, so that $dx$ actually made sense.
Can someone elaborate on this concept and whether there are any other things that are useful to know for a student in introductory calculus?

REPLY [2 votes]: Short opinion answer.
I think the fact that the use of infinitesimals can be made rigorous is the most important contribution of nonstandard analysis at the elementary calculus level. That should free students and instructors to work confidently with the intuition infinitesimals provide. I don't think it's useful or necessary to work with formal nonstandard analysis, any more than it's necessary to provide a definition of the reals sufficient to work rigorously with ordinary analysis.