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Solution: Dense Set of Numbers A set of numbers is said to

A Survey of Mathematics with Applications | 9th Edition | ISBN: 9780321759665 | Authors: Allen R. Angel, Christine D. Abbott, Dennis C. Runde ISBN: 9780321759665 194

Solution for problem 5.1.289 Chapter 5.3

A Survey of Mathematics with Applications | 9th Edition

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A Survey of Mathematics with Applications | 9th Edition | ISBN: 9780321759665 | Authors: Allen R. Angel, Christine D. Abbott, Dennis C. Runde

A Survey of Mathematics with Applications | 9th Edition

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Problem 5.1.289

Dense Set of Numbers A set of numbers is said to be a dense set if between any two distinct members of the set there exists a third distinct member of the set. The set of integers is not dense since between any two consecutive integers there is not another integer. For example, between 1 and 2 there are no other integers. The set of rational numbers is dense because between any two distinct rational numbers there exists a third distinct rational number. For example, we can find a rational number between 0.243 and 0.244. The number 0.243 can be written as 0.2430, and 0.244 can be written as 0.2440. There are many numbers between these two. Some of them are 0.2431, 0.2435, and 0.243912. In Exercises 109114, find a rational number between the two numbers in each pair. Many answers are possible. 1.3457 and 1.34571

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Chapter 5.3, Problem 5.1.289 is Solved
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Textbook: A Survey of Mathematics with Applications
Edition: 9
Author: Allen R. Angel, Christine D. Abbott, Dennis C. Runde
ISBN: 9780321759665

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Solution: Dense Set of Numbers A set of numbers is said to