   Chapter 11.2, Problem 21ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Prove Theorem 11.2.4: If f is a real-valued function defined on a set of nonnegative integers and f ( n ) is Ω ( n m ) . where m is a positive integer, then f ( n ) is not O ( n p ) for any positive real number p < m .

To determine

The proof of the given statement.

Explanation

Given information:

The given statement is,

“A real valued functions f is defined on the set of non-negative if f(n) is Ω(nm) where m is a positive integer, then f(n) is not f(n) is Ο(np) for any positive real number p<m ”.

Proof:

Let’s assume f(n)=

Ο(np) ,

Then, by the definition of Ο (Big oh notation) there exists two constants c1, n0 such that,

f(n)c1np for some nn0 -----------

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 