Practice Lecture No # 29: Cantor’s Diagonalization Argument (6.1)

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6 sample questions

Question 1.
What is a countably infinite set?
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Think about how we can list numbers.
Question 2.
Give an example of an uncountable set.
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Consider the type of list that can't be completed.
3Question 3.
What is the main implication of Cantor's Diagonal Argument?
- It proves all sets are countable.
- It shows some sets are uncountable.
- It only applies to finite sets.
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Think about the consequences of constructing new strings.
4Question 4.
True or False: The set of integers is countably infinite.
- True
- False
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Reflect on how integers can be arranged in order.
Question 5.
Using Cantor’s diagonalization argument, prove that the set of sequences of rational numbers is countable.
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Think about listing each rational number as a fraction.
Question 6.
Discuss why Cantor’s argument fails when applied to finite strings.
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Consider the essential property of length in finite strings.

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