Question

can anyone sum up the general idea behind the epsilon delta proof? My instructor introduced the topic in class, and was quite intrigued about it.

Answer 1

\[\forall \epsilon > 0 \exists \delta > 0: \forall x(0<|x-c|<\delta \implies |f(x)-L|<\epsilon)\]
Imagine taking a box of length epsilon and height delta, it's basically saying you can close that box in as small as you want such that the function minus its limit is smaller than epsilon. I.e., the smaller you make the box the closer you get to the actual limit. At least, this is how my advanced calc teacher explained it.

Answer 2

Thanks a lot, will mull over your answer a bit.