I know that to prove A is finite, I say:

$\displaystyle \exists$ a bijection $\displaystyle f : N_k \rightarrow A$

So to prove A is infinite would I say:

$\displaystyle \exists $ a bijection $\displaystyle f : \mathbb{N} \rightarrow A$

Our professor just said "not finite." So I am a little confused as to what to negate.