1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Extremely Simplistic Proof Check

  1. Oct 7, 2009 #1
    Doing this simplistic proof for one of my computer math classes. I've already taken Abstract Algebra and I'm having trouble with this lol. Actually, I just need someone to verify this is correct for me. It seems far too simple.

    1. The problem statement, all variables and given/known data

    Prove the following [tex]n^3 > n^2[/tex].

    2. Relevant equations

    None of importance...

    3. The attempt at a solution

    Well, I really just think it is something as simple as:

    [tex]\frac{n^3}{n^2}>\frac{n^2}{n^2} \Rightarrow n > 1 [/tex]

    ...unless I'm really missing something
  2. jcsd
  3. Oct 7, 2009 #2


    User Avatar
    Homework Helper

    could be wrong i think you might have used the original theorem

    [tex]\frac{1}{n^2} = \frac{1}{n^2} [/tex]
    then you effectively multiply the expression by
    [tex]n^2 > n^3 [/tex]

    however it only a slight tweak to change the proof, start with the assumption:
    then assuming you could use the following property:
    if a<b and c>0, then a.c < b.c

    otherwise this could be done by induction no worries
  4. Oct 7, 2009 #3
    Oh right, lol, I started with the wrong assumption! Yeah, so, is it really that simple? He he, awesome.
  5. Oct 7, 2009 #4


    User Avatar
    Homework Helper

    if you can assume the property

    i think induction would only need to assume 1<n
  6. Oct 7, 2009 #5


    User Avatar
    Science Advisor

    It would be convenient to explain what kind of number n is. A natural number greater than 1?
  7. Oct 7, 2009 #6


    User Avatar
    Homework Helper

    Induction is possible but not needed: if [tex] n > 1 [/tex] (which it must be for the desired inequality to be true)
    simply look at

    n^3 - n^2

    think how you show this difference is > 0.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook