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Homework Help: Bijective function

  1. Oct 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Is this function bijective ?

    f: [0,1] --> [0,1]

    f(x) = x if x E [0,1] intersection Q
    f(x) = 1-x if x E [0,1]\Q


    2. Relevant equations



    3. The attempt at a solution

    it is bijective for the rational numbers not sure about the irrationals.
     
  2. jcsd
  3. Oct 30, 2008 #2

    morphism

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    Just manually check whether it's 1-1 (consider the different meanings of "f(x)=f(y)") and onto (draw a graph; is there anything in [0,1] that f misses?).
     
  4. Oct 30, 2008 #3

    Dick

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    Why not? If x is irrational and in [0,1] then 1-x is irrational and in [0,1]. The function is pretty easy to invert.
     
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