Results 1 to 2 of 2

Math Help - Subadditive Proof

  1. #1
    Apr 2010

    Subadditive Proof

    Suppose that a function f is a subadditive prove that if f(0)=0 and if f is continuous at x=0 then f is continuous on all of R ?

    how can i solve it ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Apr 2010
    A function f(x) is continuous at a point a if \lim_{x\to a}f(x)=f(a). Another characterization of continuity at a (which is useful in your case) is that \limsup_{x\to a}f(x)-\liminf_{s\to a}f(x)=0. ( \limsup of course is defined as \limsup_{x\to a}f(x)=\lim_{\epsilon\to0}\ \sup\{f(x):\lvert x-a\rvert<\epsilon,x\neq a\}

    I would use the subadditivity of f along with the above characterization to show continuity at an arbitrary point.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 19th 2010, 11:50 AM
  2. Replies: 0
    Last Post: June 29th 2010, 09:48 AM
  3. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 27th 2010, 11:07 PM
  4. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 02:20 PM
  5. proof that the proof that .999_ = 1 is not a proof (version)
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: April 14th 2008, 05:07 PM

Search Tags

/mathhelpforum @mathhelpforum