Results 1 to 5 of 5

Math Help - supremum

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    9

    Post supremum

    let inf S=m and sup S=M.
    if T={|x-y| :x,y belong to S},
    then prove that sup T= M-m
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by luckylawrance View Post
    let inf S=m and sup S=M.
    if T={|x-y| :x,y belong to S},
    then prove that sup T= M-m
    What ideas do you have?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    CSM
    CSM is offline
    Junior Member
    Joined
    Oct 2010
    Posts
    56
    Intuitively the difference between to elements in S is the biggest when one is the biggest element while the other one is the smallest (or vice versa).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2010
    Posts
    9
    Respected, the idea i have is that difference between two numbers is greatest when one is largest and other is smallest in S. but i don't know how to write the proof in proper way.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by luckylawrance View Post
    Respected, the idea i have is that difference between two numbers is greatest when one is largest and other is smallest in S. but i don't know how to write the proof in proper way.
    Use the characterization that if A\subseteq\mathbb{R} is bounded then \sup A=\alpha if and only if \alpha is an upper bound of A and for every \varepsilon>0 there exists a\in A such that \alpha-\varepsilon<\alpha.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Supremum
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: January 5th 2011, 05:12 PM
  2. Supremum
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 3rd 2008, 12:35 AM
  3. Supremum
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 22nd 2008, 12:29 PM
  4. Supremum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 13th 2008, 08:21 AM
  5. Supremum example
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 30th 2008, 12:22 AM

Search Tags


/mathhelpforum @mathhelpforum