I am a first year freshman at UC Berkeley, in Math 1A. We learned the delta-epsilon proof for proving the limit of functions. I won't go through a whole proof or anything, but the general idea is you have a delta that is less than |x-a| (and greater than zero) and an epsilon less than |f(x)-L|. The way we have learned to prove this is to find a delta in terms of epsilon, and then solve for epsilon. Here is my problem. This proof really just does simple algebra in one direction (to find delta in terms of epsilon), and then the reverse of that algebra to isolate epsilon. So, what goes wrong if you prove a limit that is not true? My graduate student instructor said you wouldn't know unless you plugged in epsilon values. My professor said it was a good question, and it would be hard to prove that you were doing an incorrect proof. The way he said to prove that that limit is incorrect would be to do the proof for the correct limit. A function can have only one limit, and so the wrong one would be supplanted. But I still think that there is a real problem with a proof that proves things that are incorrect. How is that a proof at all?