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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What defines a countably infinite set?
💡 Hint: Think about how you could make a pairing with the number line.
Question 2
Easy
How many rational numbers are between 1 and 2?
💡 Hint: Consider how you can divide 1 and 2 into different fractions.
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
Is the set of rational numbers countable?
- True
- False
💡 Hint: Think about how you could list fractions systematically.
Question 2
What is the term for a set that can be put into a one-to-one correspondence with positive integers?
- Countable
- Finite
- Uncountable
💡 Hint: Consider how you might measure the size of a set.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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?
Question 2
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!
Challenge and get performance evaluation