Question
Problem 1. Let A = {5k : k N}. Prove |A| = |N| by constructing an explicit bijectionbetween A and N and proving that it
Problem 1. Let A = {5k : k N}. Prove |A| = |N| by constructing an explicit bijectionbetween A and N and proving that it is indeed a bijection.
Problem 2. Assume A and B are two non-empty sets such that A B = . Assume |A| = nfor some n N and |B| = |N|. Prove that |A B| = |N|.For this problem specify and explicit bijection between A B and N, but you do notneed to prove it is a bijection in a rigorous way.
Problem 3. Assume A and B are two non-empty sets such that A B = . Assume |A| = Nand |B| = |N|. Prove that |A B| = |N|.For this problem specify and explicit bijection between A B and N, but you do notneed to prove it is a bijection in a rigorous way. Looking at the proof we did in class for|N| = |Z| might be useful.
N = all natural numbers (0,1,2,3,4,..etc)
Z = all integers(positive and negative)
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