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?