(1) Show that the set { 1 m + 1 n : m, n ∈ N}...

(1) Show that the set { 1 m + 1 n : m, n ∈ N} is countable.

(2) Show that the set {a + b √ 2 : a, b ∈ Q} is countable.

(3) Show that the intersection of two countable sets is countable.

(4) Show that the set of all irrational numbers is uncountable.

(5) Let C = {0, 1, 2, . . . , 9}. Show that the set C ×C × · · · is uncountable. [Hint: Imitate the proof we had for E × E × · · ·, where E = {0, 1}.]

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Expert Solution

Colby Messinger answered 3 months ago

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