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Show that the set of functions from the positive integers

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 38E Chapter 2.5

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 38E

Show that the set of functions from the positive integers to the set {0. 1. 2, 3, 4. 5. 6. 7. 8, 9} is uncountable. [Hint: First set up a one-to-one correspondence between the set of real numbers between 0 and 1 and a subset of these functions. Do this by associating to the real number 0.   the function f with f(n) = dn.]

Step-by-Step Solution:

Step 1</p>

We have to show that the set of functions from the set of positive integers to the set

 { 0,1,2,3,4,5,6,7,8,9}  is uncountable.

Step 2</p>

 Proof

Let F be the set of all functions from the set of positive integers to the set {0,1,2,3,4,5,6,7,8,9}

We have to prove F is uncountable.

Step 3 of 3

Chapter 2.5, Problem 38E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 38E from chapter: 2.5 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “Show that the set of functions from the positive integers to the set {0. 1. 2, 3, 4. 5. 6. 7. 8, 9} is uncountable. [Hint: First set up a one-to-one correspondence between the set of real numbers between 0 and 1 and a subset of these functions. Do this by associating to the real number 0. the function f with f(n) = dn.]” is broken down into a number of easy to follow steps, and 64 words. Since the solution to 38E from 2.5 chapter was answered, more than 241 students have viewed the full step-by-step answer. This full solution covers the following key subjects: set, functions, real, Positive, hint. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.

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