I have some difficulties understanding asymptotics in general.
Is $O(n)$ the same as $O(-n)$?
Is $O(f(n))$ the same as $O(cf(n))$ even though we know that $f(n)\leq 1$ for all $n$?
I know the general Standard rules you can find e.g. on Wikipedia, but I don't have a very good intuitive understanding of these things.