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Math Help - Intersection of two countably infinite sets

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    Intersection of two countably infinite sets

    If A and B are countably infinite, is A \bigcap B countably infinite?

    I'm working on this problem with my friend and we know that with countably infinite sets there is a bijection of each of the sets however we are not sure where to go from there.
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    Quote Originally Posted by andirc5192 View Post
    If A and B are countably infinite, is A \bigcap B countably infinite?

    I'm working on this problem with my friend and we know that with countably infinite sets there is a bijection of each of the sets however we are not sure where to go from there.
    It does not have to be for

    let A=\{1,3,5,7,\cdots\} the odd integers and
    B=\{2,4,6,8,\cdots\} the even integers

    both of these are countably infinite what does this say?
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