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Math Help - Realtion - Find function

  1. #1
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    Realtion - Find function

    I have been given a task to find a function f which satisfies:

    1. Definition area for f is \mathbb{J}
    2. Value area for f is the amount/quantity by the equivalentclass of ~
    3. f is injective
    4. f is surjectiv
    5. f(a+b) = f(a)+f(b) for all a og b in \mathbb{J}

    What is done is actually to complete the quantity theoretical constuction of all integers from the natural numbers.

    I actually have no idea where to start! Feel free to point me in a direction, all help is gratefully accepted!
    Last edited by jokke22; May 13th 2009 at 10:57 AM. Reason: Forgot code
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  2. #2
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    Could this be somewhat of a start:

    f: \mathbb{J} \rightarrow \mathbb{J}
    j \rightarrow f(j)

    f(j) = j-1+2j   \quad \forall j \ge 2
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