Solution Found!
Determine whether each of these sets is countable or
Chapter 2, Problem 3E(choose chapter or problem)
Determine whether each of these sets is countable or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.
a) all bit strings not containing the bit \(0\)
b) all positive rational numbers that cannot be written with denominators less than 4
c) the real numbers not containing \(0\) in their decimal representation
d) the real numbers containing only a finite number of \(1s\) in their decimal representation
Questions & Answers
QUESTION:
Determine whether each of these sets is countable or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.
a) all bit strings not containing the bit \(0\)
b) all positive rational numbers that cannot be written with denominators less than 4
c) the real numbers not containing \(0\) in their decimal representation
d) the real numbers containing only a finite number of \(1s\) in their decimal representation
ANSWER:Step 1 of 4
We have to determine the following sets are countable or uncountable.