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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

    Hurkyl

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    So your goal is to find

    {discontinuous} + {discontinuous} = {continuous}.

    I bet you're doing it the hard way: you're trying to pick the two discontinuous functions.

    It's much harder to be continuous than it is to be discontinuous -- so you should pick the continuous function first, and then worry about what the discontinuous functions are.
     
    Last edited: Oct 17, 2006
  4. Oct 17, 2006 #3
    we were just asked to show that the sum of 2 discontinuous functions is not always discontinuous...
     
  5. Oct 17, 2006 #4

    StatusX

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    Think about how the sum of two irrational numbers can be rational. It's a similar idea.
     
  6. Oct 17, 2006 #5

    Hurkyl

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    If it's not discontinuous at a, then it's continuous at a.
     
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