Practice - Lecture No # 29: Cantor’s Diagonalization Argument
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Practice Questions
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What is a countably infinite set?
💡 Hint: Think about how we can list numbers.
Give an example of an uncountable set.
💡 Hint: Consider the type of list that can't be completed.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main implication of Cantor's Diagonal Argument?
💡 Hint: Think about the consequences of constructing new strings.
True or False: The set of integers is countably infinite.
💡 Hint: Reflect on how integers can be arranged in order.
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Challenge Problems
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Using Cantor’s diagonalization argument, prove that the set of sequences of rational numbers is countable.
💡 Hint: Think about listing each rational number as a fraction.
Discuss why Cantor’s argument fails when applied to finite strings.
💡 Hint: Consider the essential property of length in finite strings.
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