Results 1 to 2 of 2

Math Help - Supremum

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    30

    Supremum

    (Let R represent the real numbers) Let D be a nonempty set and suppose f: D --> R and g: D-->R. Define f+g: D-->R by (f+g)(x) = f(x)+g(x). If f(D) and g(D) are bounded above then PROVE sup[(f+g)(D)] is less than or equal to sup f(D) + sup g(D).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,908
    Thanks
    1759
    Awards
    1
    From the given we know that these exist: \alpha  = \sup \left( {f(D)} \right)\,\& \,\beta  = \sup \left( {g(D)} \right).
    \left( {\forall z \in D} \right)\left[ {f(z) + g(z) \leqslant \alpha  + \beta } \right]<br />
.
    This means that {\alpha  + \beta } is an upper bound of \left[ {f + g} \right](D).
    Can you finish?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. supremum
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: January 15th 2011, 04:54 PM
  2. Supremum
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: January 5th 2011, 05:12 PM
  3. Supremum
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 3rd 2008, 12:35 AM
  4. Supremum
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 22nd 2008, 12:29 PM
  5. Supremum example
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 30th 2008, 12:22 AM

Search Tags


/mathhelpforum @mathhelpforum