# Math Help - Realtion - Find function

1. ## 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!

2. Could this be somewhat of a start:

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

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