Question: 1. Show that ℵ0 · ℵ0 = ℵ0.
2. What should ℵ2 mean?
3. What is the cardinality of the subset of [0,1] consisting of infinite decimal expansions with only the digits 2 and 5?
4. What is the cardinality of the set {1/k | k ∈ N}?
5. What is the cardinality of the set {P/Q | p,q ∈ N}?