I am facing the following problem. I have proven by induction that if x, y are positive then x < y => x^n < y^n but now I have to prove the converse (not specified using which kind of proof) ie. that if both x, y are positive then x^n < y^n => x<y and I'm not really sure how I should start. I have thought of proving that it is true for n-1 and therefore it must be true for n=1. But then there would be no base step. Could I do it like that? Or is there another way?