Results 1 to 2 of 2

Math Help - analysis!!

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    172

    analysis!!

     let \ f:R \to  R  \  be \ continuous \ at \ some \ point \ x_0 \in R . prove
     that \ if \ f(x+y) = f(x)+ f(y) , \forall x,y \in R ,  \ then \  f  \ is  \ continuous  \ at \ every \ point \ of <br />
\  R
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1
    Quote Originally Posted by flower3 View Post
     let \ f:R \to  R  \  be \ continuous \ at \ some \ point \ x_0 \in R . prove
     that \ if \ f(x+y) = f(x)+ f(y) , \forall x,y \in R ,  \ then \  f  \ is  \ continuous  \ at \ every \ point \ of <br />
\  R
    |f(x_0 + h) - f(x_0)| = |f(x_0) + f(h) - f(x_0)| = |f(h)|,

    so given an \epsilon > 0, there is a \delta > 0 such that whenever |h| < \delta, |f(h)| < \epsilon.

    Then if x \in R,
    |f(x + h) - f(x)| = |f(x) + f(h) - f(x)| = |f(h)|,
    so...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. analysis help
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 16th 2010, 05:30 PM
  2. analysis!!
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 9th 2009, 01:52 PM
  3. analysis 4.1.1
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2008, 08:57 PM
  4. analysis 4.1.3
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2008, 08:51 PM
  5. Please help with a bit of analysis!!!
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 16th 2008, 10:12 AM

Search Tags


/mathhelpforum @mathhelpforum