Chapter 5.3, Problem 109E

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 between as 0.2430, and 0.244 can be written as 0.2440. There are many numbers between these two numbers. Some of them are 0.2431, 0.2435, and 0.243912. In Exercises 107-110, find a rational number between the two numbers in each pair Many answers are possible.

109. −2.176 and −2.175