   Chapter 11.4, Problem 31ES ### 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

# Show that 4 n is not O ( 2 n ) .

To determine

Show that 4n is not O(2n).

Explanation

Given information:

4n

Proof:

Let b and B be positive real numbers. f(x) is not O(g(x)) if and only if for all positive real numbers b and B, there exists some number x that is greater than b and that has the property |f(x)|>B|g(x)|.

Let n= max (b,B,log2B).

We then note that n > b and n > log2B.

|4n|=4n                                    4n is always positive=( 2 2)n                                                4=22=22n

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