   Chapter 11.2, Problem 42ES ### 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
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# What can you say about a function f with the property that f ( n ) is Θ ( 1 ) ?

To determine

To discuss:

The characteristics of a function of n if f(n) is Θ(1).

Explanation

Formula used:

Let f and g be real valued functions defined on the same nonnegative integers, with g(n)0 for every integer nr, where r is positive real number.

Then,

f is of order g, written f(n) is Θ(g(n)), if and only if, there exist positive real numbers A,B and kr such that

Ag(n)f(n)Bg(n) for every integer ka.

When f(n) is Θ(1), using the definition of Θ notation, we can consider A and B be any positive real numbersfor g(n)=1 such that

Ag(n)f(n)Bg(n)

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