Chapter 4, Problem 37C

Program Plan Intro

Big-Oh notation:

In big-Oh notation, let “f” and “g” be functions from the integers or the real numbers to the real numbers. It means that f(x) is “$\text{O}\left(\text{g}\left(\text{x}\right)\right)$” if there are constants “C” and “k” such that,

$\left|\text{f}\left(\text{x}\right)\right|\le \text{C}\left|\text{g}\left(\text{x}\right)\right|\text{where}\text{x > k}$

Big-Omega notation:

In asymptotic notation for lower bound, let “f” and “g” be functions from the integers or the real numbers to the real numbers. It means that $\Omega \left(g\left(n\right)\right)= f\left(n\right)$ if there exist positive constants “$c$”$\left(c>0\right)$ in real numbers, such that $0\le cg\left(n\right)\le f\left(n\right)$ for all $n\ge n_0$.