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4 cards from this section. Quick, good the night before a test.
List three examples of countably infinite sets.
Think about sets that can be listed or counted.
True or False: The set of real numbers is countable.
Consider whether you can list all real numbers.
Which of the following sets is uncountable?
Recall Cantor's diagonal argument.
True or False: The rational numbers can be listed in a sequential manner.
Think about how you could express fractions as sequences.
Considering Cantor's arguments, generate an enumeration of the real numbers between 0 and 1, and demonstrate why this enumeration is incomplete.
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.
Reflect on the nature of finite versus infinite sets.
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