Practice - Set of Rational Numbers
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Practice Questions
Test your understanding with targeted questions
Define a countable set in your own words.
💡 Hint: Remember the definition of natural numbers.
What is the significance of the Cartesian product in enumerating rational numbers?
💡 Hint: Think about how ordered pairs work.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What distinguishes countable sets from uncountable sets?
💡 Hint: Think about how we defined countability.
Are the rational numbers countably infinite?
💡 Hint: Recall the enumeration discussion about rational numbers.
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Challenge Problems
Push your limits with advanced challenges
Prove that the union of two countable sets A and B is also countable.
💡 Hint: Think about listing elements alternately from both sets.
Demonstrate why the set of real numbers is uncountable.
💡 Hint: Consider how to list real numbers and where the diagonal argument comes into play.
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Reference links
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