I have been given a task to find afunction$\displaystyle f$ which satisfies:

1. Definition area for $\displaystyle f$ is $\displaystyle \mathbb{J}$

2. Value area for $\displaystyle f$ is the amount/quantity by the equivalentclass of~

3. f is injective

4. f is surjectiv

5. $\displaystyle f(a+b) = f(a)+f(b)$ for all $\displaystyle a$ og $\displaystyle b$ in $\displaystyle \mathbb{J}$

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!