Determine if the following is surjective I need to determine if $f: \Bbb N\times\Bbb N \to \Bbb N$ such that $f(a,b) = a^b$ is a surjective (onto) function. My intuition is that it is but I don't know how to prove it. I don't even know how to represent this graphically. Help appreciated

Proof: Let $\eta$ be an arbitrary element in $\mathbb{N}$. Then
$$
f(\eta,1) = \eta^1 = \eta\in\mathbb{N}. \blacksquare
$$

This answer gives you the proof that the mapping $f\colon\mathbb{N}\times\mathbb{N}\to\mathbb{N}$ defined by $f(a,b)=a^b$ is onto, and it makes use of Cameron's hint. Can you see why the above constitutes a proof?
