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Homework Help: Prove is countable

  1. Sep 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that [tex] \mathbb Z^{+} X \: \mathbb Z^{+} X \: \mathbb Z^{+} [/tex] is countable, where X is the Cartesian product.

    2. Relevant equations

    3. The attempt at a solution
    I'm lost as to where to start proving this.
  2. jcsd
  3. Sep 17, 2010 #2
    do you know how to prove this

    [tex] \mathbb Z^{+} X \: \mathbb Z^{+} [/tex]

    is countable?
  4. Sep 17, 2010 #3
    There are many ways to do this you show that there it bijection from N to ZxZ ,that is , ZxZ is countable. Then show that there is bijection from ZxZ to ZxZxZ.

    someone beat me to it.
  5. Sep 17, 2010 #4
    I had to prove that [tex] \mathbb Z^{+} \: X \: Z^{+} \: \rightarrow \: Z^{+} [/tex] was one-one and onto using [tex] f(a,b)=2^{a-1}(2b-1)[/tex], does that count for proving it's countable, and if it's not, no I don't know how to prove it's countable.

    The class I'm taking is a giant leap from Calc 4, and Abstract Algebra isn't even pre-req though it probably should be because the professor keeps asking who's taking it before.
  6. Sep 17, 2010 #5
    Yes, that is a bijection. So you have already shown the first part all you need to do provide a bijection from ZxZxZ to ZxZ .
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