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3 cards from this section. Quick, good the night before a test.
Define a countably infinite set. Give an example.
Remember what it means to list elements in a sequence.
What distinguishes uncountable sets from countable sets?
Think about the definitions of countability.
What is the main purpose of Cantor's diagonalization argument?
Think about what Cantor aimed to show with his argument.
True or False: The set of all integers is uncountably infinite.
Consider how integers can be listed.
What would happen if you tried to apply Cantor's diagonal argument to the set of rational numbers? Explain why it would fail.
Think about the characteristics of rational versus irrational numbers.
Create a new string using Cantor's diagonalization method based on the binary strings: 000, 111, 010, 110. What are the implications?
Focus on the method of flipping bits along the diagonal.
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