Practice - Proof by Contradiction
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Practice Questions
Test your understanding with targeted questions
What is a countable set?
💡 Hint: Think about how you could list its elements.
Give an example of an uncountable set.
💡 Hint: Recall Cantor's diagonalization argument.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Cantor's diagonal argument demonstrate?
💡 Hint: Focus on the distinction between listing and counting.
Is the set of all finite binary strings countable?
💡 Hint: Consider how you can list finite strings.
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Challenge Problems
Push your limits with advanced challenges
If you had a list of all binary strings ranging up to a certain length, how might Cantor's argument show that there are still strings missing?
💡 Hint: Consider how flipping bits reveals unseen elements.
Why can’t we use Cantor’s diagonalization for rational numbers?
💡 Hint: Reflect on the definitions of rational and irrational.
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Reference links
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