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Math Help - Relation given by function

  1. #1
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    Relation given by function

    I'm having some difficulties on how to show/prove this relation.

    Defined function:
    ⊕:
    by


    Show that,
    ~ and ~
    then
    ~

    Grateful for any pointers, elaboration!

    Bit sorry for the wrong title...
    Last edited by jokke22; May 12th 2009 at 05:01 AM. Reason: Misleading title
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  2. #2
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    your defined function looks fishy to me as its written N^2 x N -> N, although it takes N^2 x N^2 -> N^2 input...

    however, the relation to prove is easy as it's just addition of "vectors" or a coupled pair...
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  3. #3
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    Sorry, a typo there it should be N^2*N^2->N^2
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  4. #4
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    Quote Originally Posted by TiRune View Post
    your defined function looks fishy to me as its written N^2 x N -> N, although it takes N^2 x N^2 -> N^2 input...

    however, the relation to prove is easy as it's just addition of "vectors" or a coupled pair...
    Would you then just show that, since ⊕: \mathbb{N}^2 * \mathbb{N}^2 \rightarrow \mathbb{N}^2
    And
    (n,m) (k,l) = (n+k, m+l)

    That
    (n,m) (k,l)~(n_1,m_1) (k_1,l_1)

    I'm bad at proving these things.... Be gentle...
    Which is by defenition

    (n^2*k^2, m^2*l^2) which is the same as (n_1^2*k_1^2, m_1^2*l_1^2)
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