Prove That Finite Cross Product of Countable Set Is Countable - Search Videos

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Suppose that A is a countable set. Show that the set B is also counta…

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Prove that the collection ℱ(ℕ) of all finite subsets of ℕ is countable.

Prove that the collection ℱ(ℕ) of all finite subsets of ℕ is countable.

If A and B are two countable sets, prove that the set consisting of all elements from A or B (or both) is also countable. Since A is countable, there is a 1-1 correspondence between elements of A and the natural numbers so that we can denote these elements by a1, a2, a3, …Similarly, we can denote the elements of B by b1, b2, b3, …Case 1: Suppose elements of A are all distinct from elements of B. Then the set consisting of elements from A or B is countable, since we can establish the following 1-

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