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Thread: 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 $\displaystyle \mathbb{Q}\times \mathbb{Q}$ is countable. So I have no clue what you are trying to say.
    Last edited by SlipEternal; Nov 12th 2013 at 09:26 AM.
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