3:46 AM
@EliahKagan we can do the impossible with this widget

4:20 AM
@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?

I don't know enough to know what I mean, but that was my feeling about it

4:40 AM
The $\varepsilon$–$\delta$ definition of the limit is something many students find difficult. I had the advantage, at the time, of already having studied formal logic, and thus being familiar with quantifiers.
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.
It was only many years later that I learned that a major motivation for the development of quantification theory in the history of logic was to formalize analysis and, in particular, to define the limit rigorously.

1 hour later…
5:45 AM
@EliahKagan * to write the quantifiers out