Many things in calculus make more sense if you introduce limits over
-nets-, not just sequences.
...it also clarifies order relations and their use

In particular:
- integrals
 using nets, you can take limits over the set of partitions and thus
 define integrals without using sups and infs!

- oscillation/continuity
 here you take the limit over the neighborhoods of a point
 (since this is a metric space, hence uniform space, you can just take the
  limit over basic open neighborhoods $\epsilon=1/n$)
