Monotonically increasing function of natural numbers Given a function f, where for all $x\in \mathbb{N}$ we have $f(k+1) > f(k)$. Should i use induction to prove that for any $x_1 > x_2$, $f(x_1) > f(x_2)$ will be verified?
Additionally, how can we prove that f is injective, surjective?
Thanks a lot for any hints.

Induction is suitable, yes. That said, unless you're really going basic, it is rather obvious.
If you prove that $f$ is increasing, injectivity follows automatically.
$f$ definitely need not be surjective. For instance, take $f(n)=2n$.
