# Does physics need an epsilon-delta definition for the concept of limit?

This question has been inspired by a question asked on Mathoverflow about "effectiveness of (epsilon, delta) definition". Most mathematicians have a strong opinion about the need of such definitions: They are a must for mathematics as a discipline and accordingly, they are a must for whom studies mathematics. But, It happens (like the current term) that I do teach calculus to physics students where I cannot come up with a straightforward decision about the use of such definitions. The question is: To what extent are they also a "must" for a person who studies physics?

-
Not at all. I think I've never used that formalism in the context of physics; proofs in the mathematics sense aren't all too popular in most branches. –  Danu Feb 23 at 13:26
I agree with the math people -- those definitions are essential to what you mean by a limit and by continuity, as well as foundational for the whole field of topology, which is critical for several higher-level physics diciplines. Discounting them is silly. Difficulty level is irrelevant. –  Jerry Schirmer Feb 23 at 13:45
Frankly, this definition isn't really all that hard if when saying it you also make a drawing, denoting $\varepsilon$, $\delta$ and the neighborhood of limit point. (I realized this when I first studied analysis at university and tried to understand all this epsilon-delta — it appeared really simple as compared to non-rigorous handwaving). –  Ruslan Feb 23 at 14:27
Possible duplicate: physics.stackexchange.com/q/234/2451 –  Qmechanic Feb 23 at 15:04
(IMO this is not a duplicate question.) At the very least epsilon and delta give some flavor of rigor, and that's valuable, even to engineers and experimentalists. But it's not essential for that audience. I think that if there's any chance that a student will make a career in physics, then yes, include it. Apocryphal story-- Student: How much math does a physics student need to know? Victor Weiskopf: More. –  garyp Feb 23 at 17:11