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Homework Help: Cantor's Theorem (real analysis)

  1. Sep 12, 2010 #1
    Google has my particular homework online. I am doing 1.5.6, 1.5.7, 1.5.8

    On 1.5.6 a), I created a function f(x) such that {a} if x = a, {b} if x = b, {c} if x=c. This is 1-1 since each element of A gets mapped to something different. Its obviously not onto.

    Skipping down to 1.5.7, I need to create the set B for this function. For any a, it cant be an element of f(a). Does this mean B = the empty set?

    If so, I think I can tackle the rest...
  2. jcsd
  3. Sep 12, 2010 #2


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    Homework Helper

    If you want help, then I suggest you post your question here. We're not going to do an in depth google search to find your homework.
  4. Sep 12, 2010 #3
    Last edited by a moderator: Apr 25, 2017
  5. Sep 12, 2010 #4


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    In this case B is going to be the empty set
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