   Chapter 7.4, Problem 15ES ### 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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# Show that the set of all bit string (string of 0’s and 1’s) is countable.

To determine

To show that the set of all bit strings (strings of 0's and 1's ) is countable.

Explanation

Given information:

N={1,2,3...}S={the set of all bit string}

Concept used:

One to one: Every element in domain must be mapped with element in codomain.

Calculation:

Let the set of all bit strings be S then show that there exists a bijective function from N to S to show that the S is countable.

N={1,2,3,.....}S={the set of all bit strings}

Define a map f from N to S and show that ¡t is both one-one and onto to show that the set S is countable.

f(n)=Binary representation of n,where nN.

Now show that the function f defined above is a bijective function.

Firstly, show that the function f is one-one

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