I've recently started a unit on algebra, but it's been a while since I finished high school and I haven't used any of this stuff since then so I'm struggling to remember what I'm supposed to do.
The question reads:
(i) Prove that a > 1 implies a^2 > 1.
(ii) Prove that a^2 > 1 does not imply a > 1 by giving a counterexample.
(Hint: You may use the following property of positive numbers a, b, c: If a < b then a + c < b + c and ca < cb. )
I think I've done part (i) correctly by saying:
therefore, a>1 implies a^2>1
However I'm getting really confused with part (ii). I'm assuming my last line needs to read something along the lines of a^2>1>a, but I just can't wrap my head around how b and/or c fit in and what formula I need to show to get to that point.
Any help would be greatly appreciated.