Do the following. (a) (6 pts) Use properties of real numbers to prove… Show more Define S = {x ∈ R | x 2 < x}. Do the following. (a) (6 pts) Use properties of real numbers to prove that 1 is an upper bound for S. [Properties needed: (i) If a 6= 0, a 2 > 0. (ii) If a > 0, then a −1 > 0. (iii) If a < b and 0 < c, then ac < bc.] • Show less