Results 1 to 4 of 4

Math Help - Prove x^2 < y^2

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    158

    Prove x^2 < y^2

    The question:
    x,y integers, 0 < x < y ==> x^2< y^2

    I used closure of the positive integers to show that x^2 and y^2 are both greater than 0.

    Before this question, I proved a few statements involving the transitivity of the < relation. I can prove the statement above quite easily using the induction postulate for the positive integers, but I would like to see a proof involving the transitivity of the order relation as I can't seem to come up with one on my own. Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Noxide View Post
    The question:
    x,y integers, 0 < x < y ==> x^2< y^2

    I used closure of the positive integers to show that x^2 and y^2 are both greater than 0.

    Before this question, I proved a few statements involving the transitivity of the < relation. I can prove the statement above quite easily using the induction postulate for the positive integers, but I would like to see a proof involving the transitivity of the order relation as I can't seem to come up with one on my own. Thanks.
    Hint:

    x < y \implies (x)x <(x)y  \iff x^2 < xy

    Can you finish from here?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    If we know that 0<x<y then we know that x^2<xy and xy<y^2.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Sep 2009
    Posts
    158
    Haha, I had this on my page for the longest time. Thanks for pointing it out.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove that
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: May 21st 2010, 05:48 AM
  2. Prove n^2<= ......
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: November 17th 2009, 05:52 AM
  3. Replies: 2
    Last Post: August 28th 2009, 02:59 AM
  4. prove that
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 7th 2008, 05:14 PM
  5. prove
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 7th 2008, 01:45 PM

/mathhelpforum @mathhelpforum