def2:

Let

$$f:N\rightarrow R^{*}$$

$$g:N\rightarrow R^{*}$$

$$g(n)= O(f(n))$$

, ie.,

$$g(n) \in O(f(n))$$

,
if for some $c\in R^{+}$ and some $n_{0} \in N$

$$g(n)\leq cf(n)$$

for all $n\geq n_{0},$ where
$R^{*}=R^{+}\cup \{0\}$,
$R^{+}=$set of positive reals
$N=\{0,1,2,3,\ldots\}$.