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4 cards from this section. Quick, good the night before a test.
What is a countable set?
Think about sets we can list out completely.
Are all finite sets countable?
Recall the definition of countability.
What is the definition of a countable set?
Think about positive integers as a reference.
True or False: The union of two uncountable sets is countable.
Recall properties of countable and uncountable sets.
Demonstrate that the set of all finite binary strings is countably infinite.
Think about each string as a unique arrangement of 0s and 1s.
Using the Schr"{o}der-Bernstein theorem, show that if A has a proper subset that is uncountable, then A must also be uncountable.
Consider what happens if both cannot contain the same finite elements.
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