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2 cards from this section. Quick, good the night before a test.
What is a countable set?
Think about how you could list its elements.
Give an example of an uncountable set.
Recall Cantor's diagonalization argument.
What does Cantor's diagonal argument demonstrate?
Focus on the distinction between listing and counting.
Is the set of all finite binary strings countable?
Consider how you can list finite strings.
If you had a list of all binary strings ranging up to a certain length, how might Cantor's argument show that there are still strings missing?
Consider how flipping bits reveals unseen elements.
Why can’t we use Cantor’s diagonalization for rational numbers?
Reflect on the definitions of rational and irrational.
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