Prove by induction that, for all natural numbers, if 0 < x < y, then x^n < y^n.
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What have you attempted? I am guessing you're stuck on the k->k+1 step.
That is exactly where I am stuck. I have never wrote a proof of this knid using mathematical induction. I just dont know how to go about it.
Originally Posted by bearej50 Prove by induction that, for all natural numbers, if 0 < x < y, then x^n < y^n. I write out the most imporant step in this solution but you need to complete all the steps of the proof thyself. If and then it means . Therefore, however, . Putting this together we find that .
thank you! you enlightened me
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