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2 cards from this section. Quick, good the night before a test.
Define a countable set with an example.
Think of listing elements in a sequence.
What is the significance of the union of two countable sets?
Consider the definition of countability.
What is a countable set?
Consider how lists of elements are structured.
The union of two countable sets is what type of set?
Remember the definitions discussed.
If you have three countable sets, S₁, S₂, and S₃, how can you show their union remains countable?
Think about how each element can be represented by its indices.
Provide a counterexample to show that the union of an uncountable set with a countable set is uncountable.
Reflect on the definitions of countable versus uncountable.
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