f(n) = O(g(n)), g(n) is an Asymptotic Upper Bound for f(n)

O(g(n)) = {f(n): there exist positive constants c and *n*_{0} such that
0 f(n) c*g(n) for all
}

See Figure 2.1b, page 25, for graphical depiction of O.

**Examples:**

*n*^{2}- 2n = O(*n*^{2})- 200
*n*^{2}- 100n = O(*n*^{2}) = O(*n*^{3}) = ... - n = O(
*n*^{2}) - Does f(n) = imply f(n) = O(g(n))? Yes
- Does f(n) = O(g(n)) imply f(n) = ? No