I have a function:
$\displaystyle f(m,n) = mn$
The domain for this is $\displaystyle Z \times Z$. The range is $\displaystyle Z$. How can I prove if it is one-to-one, onto, or both?
It is clearly not one-to-one: $\displaystyle f(2,3)=f(3,2)$.
Is it onto? If $\displaystyle z\in \mathbb{Z}$ then is it possible that $\displaystyle f(?,?)=z$?