Excercise Problem Real Analysis
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Homework #1 for MAA 5228, due Friday, September 3, 2010 1. Let B = {p ∈ Q : p > 0 and p2 > 2}. Prove that B has no smallest element. That is, prove that for every p ∈ B , there exists q ∈ B such that q < p. 2. Let E = {p ∈ Q : p ≤ 0}. Prove that sup E = 0. 3. Let E = {1/n : n ∈ N}. Prove that sup E = 1 and inf E = 0. 4. Exercise 1.1. 5. Exercise 1.2. 6. Exercise 1.4
