Practice - Examples of Countably Infinite Sets
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What defines a countably infinite set?
💡 Hint: Think about how you could make a pairing with the number line.
How many rational numbers are between 1 and 2?
💡 Hint: Consider how you can divide 1 and 2 into different fractions.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
Is the set of rational numbers countable?
💡 Hint: Think about how you could list fractions systematically.
What is the term for a set that can be put into a one-to-one correspondence with positive integers?
💡 Hint: Consider how you might measure the size of a set.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Prove that the union of countably infinite sets A and B is also countable.
💡 Hint: What would happen if you outlined one set's items and then went through the other?
How can you demonstrate that any subset of a countably infinite set is either finite or countably infinite?
💡 Hint: Consider how a small class can still join together with a larger class!
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.