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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What makes a set countable?
💡 Hint: Think about natural numbers.
Question 2
Easy
Is the set of all integers countable?
💡 Hint: How do we list numbers?
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
Which of the following sets is countable?
- The set of all real numbers
- The set of all integers
- The set of all points in a plane
💡 Hint: Think about whether you can list these numbers.
Question 2
True or False: A union of two countable sets is also countable.
- True
- False
💡 Hint: Reflect on combining two lists.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Explain the process of proving that the Cartesian product ℤ x ℤ is countable. Detail each step involved.
💡 Hint: Visualize the spiral; how would you traverse the plane?
Question 2
Demonstrate how to prove two countable sets A and B have the same cardinality through the use of the Schroder-Bernstein theorem.
💡 Hint: Map elements carefully; consider which sets you could use.
Challenge and get performance evaluation