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Math Help - Induction Proof

  1. #1
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    Induction Proof

    Prove by induction that, for all natural numbers, if 0 < x < y, then x^n < y^n.
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  2. #2
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    What have you attempted? I am guessing you're stuck on the k->k+1 step.
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  3. #3
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    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.
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  4. #4
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    Quote Originally Posted by bearej50 View Post
    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 0<x<y and x^n < y^n then it means x\cdot x^n < x\cdot y^n. Therefore, x^{n+1} < x\cdot y^n however, x\cdot y^n < y\cdot y^n = y^{n+1}. Putting this together we find that x^{n+1} < y^{n+1}.
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  5. #5
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    thank you! you enlightened me
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