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Math Help - One to one and onto function from R^3 to N

  1. #1
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    One to one and onto function from R^3 to N

    Not sure if this is the appropriate place. Seems like an aglebraic topic.

    I would like a one to one and onto function f that goes from N^3 to N. Something like

    f(x,y,z) -> n.


    Any ideas?
    Last edited by mulaosmanovicben; February 28th 2012 at 05:29 PM.
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  2. #2
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    Re: One to one and onto function from R^3 to N

    For every bijection f:\mathbb{N}\times\mathbb{N}\to\mathbb{N}, g(x,y,z)=f(x,f(y,z)) is a bijection from \mathbb{N}\times\mathbb{N}\times\mathbb{N} to \mathbb{N}. For a bijection from \mathbb{N}\times\mathbb{N} to \mathbb{N} you can take the Cantor pairing function or f(x,y)=2^x(2y+1)-1.
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  3. #3
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    Re: One to one and onto function from R^3 to N

    Wow thank you so much! That is such a beautiful result
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