5. (P19, Page 12) Define S = {r € R | ² < x}. Do the following. (a) Use properties of real numbers to prove that 1 is an upper bound for S. [Properties needed: (i) If a ± 0, a² > 0. (ii) If a > 0, then a¯1> 0. (iii) If a < b and 0 < c, then ac < bc.]

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