Omega(g(n))

f(n) = $\Omega(g(n))$, g(n) is an Asymptotic Lower Bound for f(n)

$\Omega(g(n))$ = {f(n): there exist positive constants c and n₀ such that 0 $\leq$ c*g(n) $\leq$ f(n) for all $n \geq n_0$ }

See Figure 2.1c, page 25, for graphical depiction of $\Omega$.

Examples:

• n² - 2n = $\Omega(n^2)$
• 200 n² - 100 n = $\Omega(n^2)$ = $\Omega(n)$ = $\Omega(1)$
• n² = $\Omega(n)$
• Does f(n) = $\Theta(g(n))$ imply f(n) = $\Omega(g(n))$? Yes
• Does f(n) = $\Omega(g(n))$ imply f(n) = $\Theta(g(n))$? No