Prove that [n / 3] = O (n)

Question

How should I start by proving this? I know that for very large N values ​​the difference between the two numbers will be minimal, but I do not know how to prove it to my concrete math teacher.

Answer 1

Hint:

$$\forall n\in\mathbb{N},\quad \lfloor{n\over3}\rfloor\le {n\over 3}\le n$$