I'm reading Data Structures and Algorithms by Goodrich. The explanation that he gives for Big Oh notation is given below:
Let $f(n)$ and $g(n)$ be functions mapping positive integers to positive real numbers. We say that $f(n)$ is $O(g(n))$ if there is a real constant $c > 0$ and integer constant $n_0\geq1$ such that $|f(n)| \leq cg(n)$, for $n\geq n_0$. This definition is referred to as the "big-oh" notation, and is sometimes pronounced as "$f(n)$ is big-oh of $g(n)$".
If I understood this definition right, it would mean that I can say; for a function $f(n) = n$ then $n$ is big-oh of $n^2$ because $n \leq 1\cdot n^2$ for any $n_0$. But, that is not accurate because big-oh notation for a function '$n$' is $O(n)$. What am I missing here? Would it be accurate for me to say that '$n$' is big-oh of $n^2$?