Upsetting problems in math

- 0.999... = 1
- Monty Hall
- birthdays paradox (sp?)

The math in each of these is interesting but easy;
the main interest is in *psychology*:
+ why are they counter-intuitive?
+ why do people resist so strongly?

Details:
- 0.999... = 1
  Presentation vs. value; limit of a sequence.

- Monty Hall
  Apparent symmetry.
  (Arguments from symmetry are good!)

- birthdays
  Restated as "no 2 people in room have same birthday"
  it's more believable.
  Many things in probability are counter-intuitive
  to ordinary intuition; this is just most known.
  (People opine b/c the answers are a number,
   so they can grasp the answers, but not the reasoning;
   lotta stuff in math is completely alien.)