At the moment I am hearing the lecture named geometric group theory. In the last exercise we got the following exercise: Let $f,g:\mathbb{N}\mapsto \mathbb{R}_{\geq 0}$. We say that $f\leq g$ if there exists a constant $C$, such that
$f(n)\leq C*g(C*n+C)+C*n+C$
We say that $f\sim g$ if $f\leq g$ and $g\leq f$. The exercise is to show that this defines an equivalence realtion on these functions. My problem is to show the reflexivity, because I have no idea how I can choose the C such that I can easy see that $f\sim f$. Maybe I have to use that $C*(n+1)$ is also a monotone function. I think I forgot something important out of the lectures Analysis I+II, which I have to use for a solution. Thanks for help.