Give a direct proof that for every real number x: if x > 0, then x 2 > 0. Remember what I said in the lecture about applying some of the inequality assumptions: you need to make sure the hypotheses of the assumptions are satisfied as given in the notes (so, for example, you can't just quote assumption (8) to say that if a > b and b > c then a > c; you'd first convert to b < a and c < b. NOW you can use assumption (8) to conclude that c < a)