Practice - Module No # 05
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Practice Questions
Test your understanding with targeted questions
List three examples of countably infinite sets.
💡 Hint: Think about sets that can be listed or counted.
True or False: The set of real numbers is countable.
💡 Hint: Consider whether you can list all real numbers.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which of the following sets is uncountable?
💡 Hint: Recall Cantor's diagonal argument.
True or False: The rational numbers can be listed in a sequential manner.
💡 Hint: Think about how you could express fractions as sequences.
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Challenge Problems
Push your limits with advanced challenges
Considering Cantor's arguments, generate an enumeration of the real numbers between 0 and 1, and demonstrate why this enumeration is incomplete.
💡 Hint: Pay close attention to how the new number differs from your enumeration.
Use Cantor’s diagonalization argument to attempt to prove that the set of all finite binary strings is uncountable, and analyze where your reasoning fails.
💡 Hint: Reflect on the nature of finite versus infinite sets.
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Reference links
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