This would seem to be a common question, but I am surprised not to see it already asked and answered on MO!
I am teaching an undergraduate course, and I want to teach them to construct basic epsilon-delta proofs, say, of $\lim_{x \rightarrow 3} x^2 = 9$ and $\lim_{x \rightarrow 4} x^2 \neq 17$. (Elementary, continuous functions only.) This is a serious stumbling block for many students, with good reason, and I anticipate it will be for mine as well.
Do other MO'ers have suggestions (beyond what I can find in typical calculus books) for presenting epsilon-delta for the first time? Any success stories to share?
Thank you very much! --Frank
(Background: I am teaching a discrete math course to American undergraduates who have already had a year of calculus. Whether $\epsilon-\delta$ is on topic for discrete math is perhaps questionable, but we did material on making sense of statements with lots of quantifiers, and also an introduction to techniques of proof, and so the material seemed like a natural fit. I should also mention that I intend to test the students on this material and not just expose them to it.)
