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Homework Help: Cardinality and countable

  1. Oct 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine whether or not the set is countable or not. Justify your answer.

    The set Bn of all functions f:{1,2,...,n}[itex]\rightarrow[/itex]N,

    where N is the natural numbers.

    2. Relevant equations

    1.)A countable union of countable sets is countable

    2.)A finite product of countable sets is countable

    3. The attempt at a solution

    In the solution, a theorem is used that is not in my book.

    It goes something like this Cardinality(A)=c and f:A[itex]\rightarrow[/itex]B, then the set of functions is Ba.

    I was wondering if anyone could help me figure out what information I was supposed to derive this from?

    Thank you.
  2. jcsd
  3. Oct 20, 2011 #2
    Maybe you can find a bijection between the set of all functions

    [tex]\{1,2\}\rightarrow \mathbb{N}[/tex]

    and [itex]\mathbb{N}\times \mathbb{N}[/itex]. Generalize.
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