Prove that the union of infinitely many countable sets is countable.

Expert Solution

Colby Messinger answered 2 years ago

1) a) Prove that the union of two countable sets is countable. b) Prove that the...

1) a) Prove that the union of two countable sets is countable. b) Prove that the union of a finite collection of countable sets is countable.

(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...

4: \textbf{Proof} Prove that if $A$ and $B$ are countable sets, then $A \cup B$ is...

4: \textbf{Proof} Prove that if $A$ and $B$ are countable sets, then $A \cup B$ is countable. 5: Use induction and problem 4 to prove that if $A_1, A_2, ..., A_m$ are each countable sets, then the union $A_1 \cup A_2 \cup ... \cup A_m$ is countable. #5 please

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Prove that the union of infinitely many countable sets is countable.

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