Recall that a set B is dense in R if an element of B can befound between any two real numbers a < b. Which of the following sets aredense in R? Take p ∈ Z and q ∈ N in every case. (b) The set of all rational numbers p/q with q a power of 2.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.1: Ideals And Quotient Rings
Problem 3E: Prove or disprove each of the following statements. The set Q of rational numbers is an ideal of the...
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Recall that a set B is dense in R if an element of B can be
found between any two real numbers a < b. Which of the following sets are
dense in R? Take p ∈ Z and q ∈ N in every case.

(b) The set of all rational numbers p/q with q a power of 2.

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