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Rational and Irrational numbers

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data
    Let f be the function defined on the real line by

    [tex]
    f(x)=
    \begin{cases} \frac{x}{3} & \text{if $x$ is rational }
    \\
    \frac{x}{4} &\text{if $x$ is irrational.}
    \end{cases}
    [/tex]

    Let D be the set of points of discontinuities of f. What is D?

    2. Relevant equations

    None

    3. The attempt at a solution

    How do you answer this?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 10, 2011 #2

    micromass

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    Well, perhaps it would be good if you would first try to "plot" the function. You can't plot it accurately, but you can get an idea. What does the plot look like? What can you conclude?
     
  4. Sep 10, 2011 #3
    Ok I got it, D is the entire real number set excluding 0.
     
  5. Sep 11, 2011 #4

    micromass

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    Yep, that's it!! :smile:
     
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