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Math Help - map (m,n) to N

  1. #16
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    Re: map (m,n) to N

    Surjective is academic.

    All that is required for countabilty of g(m,n), m,n countable, is for g(m,n) to be a mapping, any mapping, even countably multi-valued, for ex, g(m,n) = +/-sqrt(mn), mn positive and countable.

    Hmmm. Got through after multiple tries. Thanks
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  2. #17
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    Re: map (m,n) to N

    Quote Originally Posted by Hartlw View Post
    Surjective is academic.

    All that is required for countabilty of g(m,n), m,n countable, is for g(m,n) to be a mapping, any mapping, even countably multi-valued, for ex, g(m,n) = +/-sqrt(mn), mn positive and countable.

    Hmmm. Got through after multiple tries. Thanks
    The OP (of the other topic) was not trying to show g(m,n) is countable. The OP was trying to show \mathbb{Q}\times \mathbb{Q} is countable. So I have no clue what you are trying to say.
    Last edited by SlipEternal; November 12th 2013 at 09:26 AM.
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