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Math Help - tough continuity problem need help

  1. #1
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    tough continuity problem need help

    g(x)=0 if x is rational
    g(x)=x if x is irrational

    for what values of x is g continuous?
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  2. #2
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    Quote Originally Posted by myoplex11 View Post
    g(x)=0 if x is rational
    g(x)=x if x is irrational

    for what values of x is g continuous?
    Have you ever heard of "Dirichelt" function?
    Same idea.

    The limit that we approach a point bt rationals needs to be the same as we approach the limit by irrationals. In that case x=0 is the only continous point.
    Look Heir
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  3. #3
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    i understand why it is continous a x=0 but i need to justify this mathematically
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  4. #4
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    Quote Originally Posted by myoplex11 View Post
    i understand why it is continous a x=0 but i need to justify this mathematically
    Choose any \delta>0 and set \epsilon=\delta, then |g(x)-g(0)|<\delta whenever |x|<\epsilon,
    hence g(x) is continuouse at x=0.

    RonL
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