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Decimal Expansion, 1-1 onto

  1. Sep 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Use the fact that every real number has a decimal expansion to produce a 1-1 function that maps S into (0,1). Discuss whether the formulated function is onto.

    2. Relevant equations

    S={(0,1):0<x, y<1}

    3. The attempt at a solution
    I don't even know where to begin. The whole decimal expansion business has me confused.
  2. jcsd
  3. Sep 14, 2010 #2
    Oops, I made a typo. That (0,1) in S should have been a (x,y).
  4. Sep 15, 2010 #3


    Staff: Mentor

    Just to be clear, S is the quarter plane whose left edge is the y-axis and whose upper edge is the line y = 1, right?

    Or did you mean that both x and y are between 0 and 1? If that's what you meant, your description for S should have been written as S = {(x, y) | 0 < x < 1, 0 < x < 1}.
  5. Sep 15, 2010 #4
    Yeah, that's what I meant.
  6. Sep 15, 2010 #5


    Staff: Mentor

    (.5, .25) is in S, right? .5205 is in (0, 1).
  7. Sep 15, 2010 #6
    yeah. Ok, so then we have z=x1y1x2y2....
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