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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a countable set in your own words.
💡 Hint: Remember the definition of natural numbers.
Question 2
Easy
What is the significance of the Cartesian product in enumerating rational numbers?
💡 Hint: Think about how ordered pairs work.
Practice 1 more question and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What distinguishes countable sets from uncountable sets?
- Countable sets are finite
- Countable sets can be listed with natural numbers
- Countable sets have a finite number of elements
💡 Hint: Think about how we defined countability.
Question 2
Are the rational numbers countably infinite?
- True
- False
💡 Hint: Recall the enumeration discussion about rational numbers.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the union of two countable sets A and B is also countable.
💡 Hint: Think about listing elements alternately from both sets.
Question 2
Demonstrate why the set of real numbers is uncountable.
💡 Hint: Consider how to list real numbers and where the diagonal argument comes into play.
Challenge and get performance evaluation