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Order relation question

  1. Feb 6, 2004 #1
    How do you go about proving a statement like n^3>n^2 for n is equal to or greater than 2? I can prove this using mathematical induction, but I am unsure how to show n^3-n^2 is an element of the set of natural numbers without just saying in general that this must always yield a number equal to or greater than 1.
     
  2. jcsd
  3. Feb 6, 2004 #2
    Can't you just say that because

    [tex]\forall\alpha>1:\alpha n^2 > n^2[/tex]

    we must conclude that

    [tex]\forall n>1: n^3 > n^2[/tex]
     
  4. Feb 6, 2004 #3

    HallsofIvy

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    Why not just note that n3- n2= n2(n-1)? As long as n> 1, this will be a positive integer.
     
  5. Feb 6, 2004 #4
    Yeah, Halls of Ivy, thats what I was thinking. It just looked like too short a proof so I thought I was missing something. Thanks dudes.
     
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