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Homework Help: Is the function continoous?

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data

    I have the function f(x) = x if x= 1/n and n is an integers / {0)
    = 1- x otherwise

    and the function g(x) = x if x is rational
    =1- x if x is irrational

    The problems is to find if the above functions are continuous at x=0 and x=1/2 each.
    I am really struggling and am not sure how to go about this. Can someone help me figure it out. Please?

    2. Relevant equations

    3. The attempt at a solution

    For x=0, I believe f(x) is not coninuous as n is an integer and so x cannot equal 0 for x=1/n
    However I know that is the worng way of seeing things and I just don't know the steps to take to figuring something like this out.
  2. jcsd
  3. Nov 24, 2012 #2


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    Science Advisor
    Homework Helper
    Gold Member

    f is defined as
    f(x) = x if x= 1/n for some nonzero integer n
    = 1- x otherwise (i.e. for all other x)
    So first question is, what is f(0)?
    Next question: does f(δ) get ever closer to that value as δ approaches 0?
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