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Possible Duplicate:
Countable Sets and the Cartesian Product of them
Sum of two countably infinite sets

I want to solve a problem, this problem is the following:

Prove that if the sets $A$ and $B$ are countable then these sets are also countable:

  1. $Α \cap B$
  2. $A \cup B$
  3. $A \times B$ (Cartesian product of $A$ and $B$)

Thank you very much.

  • 4
    Does "numerous" mean "countable"?2012-01-05
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    Does "acts of" mean "operations on"?2012-01-05
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    @Srivatsan: I think "numerous" does mean "countable" because the result is true if it does and false if it means "uncountable"!2012-01-05
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    @Srivatsan OP probably intended "denumerable", which is sometimes used to mean "countably infinite".2012-01-05
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    I also believe that should be an uncountable collection of answers on this site in which those questions were answered. I know that the search function sucks, but even "countable product" should give you your desired thread.2012-01-05
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    @Austin Ah, yes. I'm not very used to the word, so it did not occur to me unfortunately. That would fit, except that the intersection of two countably infinite sets need not be countably infinite. Let's hope the OP clarifies. :)2012-01-05
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    The part about union of two sets is basically the same as [Sum of two countably infinite sets](http://math.stackexchange.com/questions/85612/sum-of-two-countably-infinite-sets)2012-01-07

2 Answers 2