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MATH 501 FALL 2006 Supplementary Homework 1 1. Show that (a, b) ∼ R for any nonempty interval (a, b) ⊂ R by finding an explicit one-to-one correspondence between the two sets. 2. Let S denote the set of all finite subsets of N. What is the cardinality of S? 3. Let A = {1, 2, . . . n}, B = Z and let S denote the set of all functions from A to B. What is the cardinality of S?