Results 1 to 9 of 9

Math Help - analysis homework

  1. #1
    Junior Member
    Joined
    Nov 2007
    Posts
    58

    analysis homework

    Let S be a nonempty set of real numbers that is bounded above, and let Beta be the least upper bound of S. Prove that for every Epsilon greater than 0, there exists an element x such that x is greater than Beta minus Epsilon.

    Any ideas or help would be appreciated. Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by eigenvector11 View Post
    Let S be a nonempty set of real numbers that is bounded above, and let Beta be the least upper bound of S. Prove that for every Epsilon greater than 0, there exists an element x such that x is greater than Beta minus Epsilon.

    Any ideas or help would be appreciated. Thanks.
    note that \beta - \epsilon < \beta  - \frac {\epsilon}2 < \beta
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2007
    Posts
    58
    I'm not sure where to go with your little hint. Are you saying that Beta minus (epsilon/2) will be my x value?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    Quote Originally Posted by eigenvector11 View Post
    I'm not sure where to go with your little hint. Are you saying that Beta minus (epsilon/2) will be my x value?
    Yes.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by eigenvector11 View Post
    I'm not sure where to go with your little hint. Are you saying that Beta minus (epsilon/2) will be my x value?
    yes

    EDIT: haha, jinx, topsquark! you owe me a soda!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by eigenvector11 View Post
    I'm not sure where to go with your little hint. Are you saying that Beta minus (epsilon/2) will be my x value?
    Sorry but that argument does not work.
    How do you know that \left( {\beta  - \frac{\varepsilon }{2}} \right) \in S? The fact is you do not know that.

    What does work is quite simple. What does least mean?
    If \beta is least then \beta  - \varepsilon is not.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Nov 2007
    Posts
    58
    But how do you know that there is another element other than Beta that is greater than (Beta - Epsilon)?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Plato View Post
    Sorry but that argument does not work.
    How do you know that \left( {\beta  - \frac{\varepsilon }{2}} \right) \in S? The fact is you do not know that.
    ah yes. i was thinking of S as an interval, but that might not be true
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Nov 2007
    Posts
    58
    Does anyone else have any ideas for this question? My assignment is due fairly soon. Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Real analysis homework help!!!!!!
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 30th 2009, 04:55 PM
  2. Real analysis homework help!!!!!!
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 27th 2009, 06:36 PM
  3. Homework Help with real analysis
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 26th 2009, 09:26 AM
  4. Real Analysis Homework Help!!!!!!
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 24th 2009, 08:25 PM
  5. Real Analysis Homework Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 11th 2006, 06:45 PM

Search Tags


/mathhelpforum @mathhelpforum