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Help with Cantor-Schroder-Berstein theorem please!

  1. May 4, 2008 #1
    I really don't get this. Can someone please help me?

    Apply the proof of the Cantor-Schroder-Berstein theorem to this situatuion:
    A={2,3,4,5,...}, B={1/2,1/3,1/4,...}, F:A-->B where F(x)=1/(x+6)and G:B-->A where G(x)=(1/x)+5. Note that 1/3 and 1/4 are in B-Rng(F). Let f be the string that begins at 1/3, and let g be the string that begins at 1/4.

    a)Find f(1), f(2), f(3), f(4).
    For this one, f(1)=1/3, then f(2)=1/(1/3)+5=8, then f(3)=1/(8+6)=1/14, and f(4)=1/(1/14)+5=19? Is that right? and then I do the same for g? g(1)=1/4, g(2)=9, g(3)=1/15, and g(4)=20?
    b) Define H as in the proof of the Cantor-Schroder-Berstein theorem and find H(2), H(8), H(13), and H(20).
    I have no clue how to do this one at all. Can you help me please?

    Thanks for the help!
  2. jcsd
  3. May 8, 2008 #2
    There are many ways to prove this theorem. You have to tell us what H is, and what YOUR proof looks like, before we can apply it.
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