Let f be a continuous function on [0, 1] and f(0)=f(1). Show that, for n=2, 3, 4, ..., there is some a in [0, 1-1/n] such that f(a)=f(a+1/n). Learn how to use the Intermediate Value Theorem to prove the above statement. This question appears on the transfer entrance exam at National Taiwan Univier...