(11) Prove that a union of two countable sets is countable. (Hint: the same idea used...

(11) Prove that a union of two countable sets is countable. (Hint: the same idea used to show that Z is countable might be useful.) (Don’t forget that countable sets can be finite.)

(12) We saw in class that N × N ∼ N is countable. Prove that A × B is is countable for any countable sets A, B. (Hint: If you can prove that A × B ∼ N × N then you can use what has already proved...) (Don’t forget that countable sets can be finite.)

Expert Solution

11)

12)

Colby Messinger answered 2 years ago

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