# what is the meaning of $a_n$ grows as for example $O(n\log n)$ or $O(n^2)$

Given a positive and increasing sequence $\{a_n\}$, what is the meaning of $a_n$ grows as for example $O(n\log n)$ or $O(n^2)$. I have read this in some books but the google search did not yield anything.

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$$f: \mathbb{N} \longrightarrow \mathbb{R}, f(n):=a_n$$
and for example $a_n$ grows $O(n^2)$ now means that there are constants $k, n_0$ such that $$\forall n>n_0 \; |f(n)| \leq |n^2\cdot k|$$
I would have said: $|f(n)| \le k\;n^2$. –  GEdgar Jun 11 '11 at 16:54