On injections and surjections Let $f:N^2 \rightarrow N$ be defined by $f(x, y) = x^3 + y^3$.
I can tell that $f$ is not injective, but would it be surjective?
Any intuitive explanations would be greatly appreciated!

Calculate the values for (0,0), (0,1), (1,1), (1,2), (2,2). None of them is 3 (for example).
If either $n_k$ in $(n_1 , n_2)$ is bigger than 2, you'll get values bigger than you got by calculating those, so none of them can be 3 either.
If you have $\mathbb{N} = \{ 1,2,...\}$, the proof is even easier.
