Exercise 0. The well-ordering principle said that every nonempty set of non-negative integers has a least element. The point of this exercise is to use other related ordering principles as a proof technique. Why, for instance, do we use sets of integers? Let's use rational numbers instead (a) Debug the faulty statement, "every nonempty set of non-negative rationals has a least ele- 12 ment. OK, that won't work. To fix it, let's also change what "less than" means, using an ordering