Practice - Conclusion
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Practice Questions
Test your understanding with targeted questions
What is a countably infinite set? Provide an example.
💡 Hint: Think of numbers you can count!
What does it mean for a set to be uncountable?
💡 Hint: Remember Cantor's work?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is true about uncountable sets?
💡 Hint: Think of sets that go beyond counting.
Cantor's diagonalization argument is used to prove that which of the following is uncountable?
💡 Hint: Which example did we focus on when applying this argument?
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Prove that the set of all subsets of the natural numbers is uncountable using Cantor's diagonalization argument.
💡 Hint: Consider how every subset can relate back to Cantor's argument.
Discuss how Cantor’s argument implies the existence of different 'sizes' of infinity.
💡 Hint: Think about the relationships between sets established.
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