@EliahKagan What impressed me was the idea that if you can get as close as you want but you can't get quite there, then there's a there you're getting closer to.
@Zanna With the limit, or with the derivative, or something else?
The symbols $\forall$ and $\exists$ are not the issue; lectures and introductory calculus books don't typically use them. But the logic of nested quantifiers is there whether one writes it in a formal language or not. Also, I found it quite helpful to the quantifiers out; that is, to translate it into those symbols.
