For $f(n)$ to be in $O(g(n))$, there must exist a $c > 0$ and $n_0 > 0$ such that
$$0 \leq f(n) \leq cg(n) \text{ for all }n \geq n_0\,.$$
I found a solution to a question where my $c$ is in terms of $n$, but my friend says you can't have that. I'd like to understand why. My thought process is: if I am given an $n$, I can pick a distinct $c$ that will satisfy the requirements above by using the $c$ in terms of $n$ relationship.
Thank you.