There's a huge fetish with punctured discs in intro calc;
that's because it's the necessary/correct domain for taking limits for
the derivative (which is the removable discontinuity par excellence),
but it's a bad way of looking at continuity, and is confusing and
picky.

(especially that obnoxious $0 < \abs{x-a} < \delta$)

...and makes people confused later (it made -me- confused...)

(note all the contorsions in L'H\^opital's rule to deal with
-punctured- neighborhoods, i.e., you don't need to assume that $f'(a)$
and $g'(a)$ exist)
