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Discontinuity math help

  1. Dec 18, 2009 #1
    1. The problem statement, all variables and given/known data
    f is a function with the property that every point of discontinuity is removable. There are infinitely many such points in f's domain. Define [tex] g(x) = \lim_{ y \to x } f(y) [/tex]. Prove g is continuous

    3. The attempt at a solution
    I wanted to maybe conclude something from showing g is bounded but I didn't really get anything there. I was wondering if you could give me a hint, but DON'T GIVE ME A SOLUTION yet. Should I be using straight forward definition or take some other route?
     
  2. jcsd
  3. Dec 18, 2009 #2
    Re: Discontinuity

    You should be able to do this by following the definitions in a straightforward manner, more or less using only the concepts of limit and continuity. The key is that when you are examining the behavior of [tex]g[/tex] on an interval, you can transfer statements about [tex]g[/tex] at a point to statements about [tex]f[/tex] on a smaller interval.
     
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