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Show that if r is an irrational number, there is a unique

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

Problem 18E Chapter 1.8

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 18E

Show that if r is an irrational number, there is a unique integer n such that the distance between r and n is less than I/2.

Step-by-Step Solution:
Step 1 of 3

Solution:Step-1: In this problem we need to show that if r is an irrational number , there is a unique integer n such that the distance between r and n is less than . We know that irrational number is not an integer. Given that , r is an irrational number. Therefore , it must lie between two integers , So there exist an integer n such that n < r < n+1. Given r is an irrational number . So , . Now , there are two cases .Step-2: Case(1) : Therefore , the distance between r and n is less than .Step-3: Case(2) : , since...

Step 2 of 3

Chapter 1.8, Problem 18E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7th
Author: Kenneth Rosen
ISBN: 9780073383095

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