\section{Dichotomies and choices}
There are some perspectives

Each is valuable, and gives the instructor choices: perhaps you'll use one or
the other throughout, perhaps you'll find one perspective more suitable than
the other at some times but not others, etc.
I'd also strongly recommend making the students aware of these different
perspectives at \emph{some} point -- they deepen and enrich their
understanding.

choices:

- functions
  (graphs vs. paths in plane)

- topology on reals
  (order vs. metric)

- transcendental functions
  early presentation so you have -something- to work with, but can't
  really present them well,
  or late presentation so you can present them well, but don't have examples
  at first
  (my opinion is that they should be introduced informally early,
   and formally later -- they are a main theme!)

