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Homework Help: Discontinuous functions

  1. Oct 17, 2006 #1
    can you give me an example of two discontinuous functions at a number a whose sum is not discontinuous at a? :confused: thanks!!!:shy:
     
  2. jcsd
  3. Oct 17, 2006 #2
    i was just about to ask a question about dis. functions, and express each function as a composition, and i dont know how to do that??

    if you give me a prob, i might help to see what you mean.
     
  4. Oct 17, 2006 #3
    huh?

    If the functions are discontinuous at a, then their sums are not going to be continuous at a. I suppose you could have two step functions, one going up and one going down, but I don't think that is really fair because there is still a discontinunity at a.... Mathematicians?
     
  5. Oct 18, 2006 #4

    arildno

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    Let f(x)=0 when x is not zero, and 1 when x is zero.
    Let g(x)=0 when x is not zero, and -1 when x is zero.

    then f+g is continuous everywhere.
     
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