(1) students don't know what a rational number is
  (best characterization/definition: ratio of two integers;
   alt char: terminating/repeating decimal expansion)
(2) People learn things better in context, for instance -rigor-
However, calculus is an -awful- context to learn rigor in:
 the questions feel uninteresting, there's lots of details, and it's a
 pain.
Much better is elementary number theory:
 easy, familiar, interesting
