If a and b are both positive and , then (multiplying the inequality by b on both sides) and (multiplying the inequality by a on both sides). Then by transitivity, implies . The proof that is similar.
I've a couple of problems that are driving me crazy:
Prove or disprove that if a,b ε D and a > b, then a² > b².
Prove or disprove that if a,b ε D and a > b, then a³ > b³.
Should I start with a² > b² and try and disprove it for a²=b², and a² < b²? I have been trying it that way but no success as of yet.
Any help would be much appreciated.