I have a function $f_2: \mathbb Z \times \mathbb Z \to \mathbb Z $ defined by $f_2(m,n)=m^2+n$.
How do I know if it is one-to-one, onto or both?
What I am most confused about is what $\mathbb Z \times \mathbb Z \to \mathbb Z$ means and how that is different from just $\mathbb Z \to \mathbb Z$.
I know one-to-one means every $x$ has a unique $y$ and onto means for all $y$, there exists an $x$ such that $f(x)=y$.