1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Order relation question