Proving that an injective function is bijective I am having a lot of trouble starting this proof. I would greatly appreciate any help I can get here. Thanks.
Let $n\in \mathbb{N}$. Prove that any injective function from $\{1,2,\ldots,n\}$ to $\{1,2,\ldots,n\}$ is bijective.

Hint: If $f:[n]\rightarrow [n]$ is injective (where $[n]= \{1,2,\dots,n\}$), all that remains to be shown is that $f$ is surjective. So, suppose it's not. How does the size of the image compare to the size of the domain, and what does this say about injectivity?
