Practice - 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 is a countably infinite set?
💡 Hint: Think of how integers relate to naturals.
Can you list an example of a countably infinite set?
💡 Hint: What can be matched with 1, 2, 3, etc.?
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a countably infinite set?
💡 Hint: Consider counting the elements.
True or False: The set of binary strings of infinite length is countable.
💡 Hint: Remember Cantor's argument.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Using Cantor's argument, prove that the decimal representation of any irrational number is infinite and does not repeat.
💡 Hint: Focus on how equating with rationals fails.
Suppose you are asked to list the set of all real numbers. Describe why this is impossible.
💡 Hint: Connect to the earlier discussions about the diagonal.
Get performance evaluation