Due Fri. 4/13: 4.2, 4.4, 4.8, 4.11, 4.18(c)

Due Wed. 4/18: 5.2, 5.14, 5.18, 5.20, 5.25, 10.15, 10.22

Due Fri. 4/20: Prove 10.25 in two ways: First, use the principle of mathematical induction (Theorem 10.2). Second, prove 10.25 using the well-ordering property of N (and not Theorem 10.2!)

Due Wed. 4/25: 11.2, 11.4 (prove without using the result of Theorem 11.7!), 11.5, 11.7, 11.10 (refer to the field axioms that you use in the proof), 11.11(c) (show your work!)
Also, turn in your proof of the well-ordering property of N, using the following outline: Proof of the WOP

Due Fri. 4/27: 11.6(a), 12.4, 12.7(a) (Prove only the first part: if k >= 0, then sup(k S) = k sup(S).)
Also, prove: If D is a natural number that is not a perfect square, then there exists a natural number L (or Lambda) such that L^2 < D < (L + 1)^2. (See the hint for Exercise 12.9 in the book; however, you should consider the set {m in N : D < (m+1)^2} instead.)

Due Wed. 5/2: 12.5; 12.6(a); 12.16; 13.4(a),(b),and (c); 13.5; 13.12; 13.19; 13.21(c).

Due Fri. 5/4: 13.2, 13.7, 13.9(a), 13.10

Due Wed. 5/9: 14.3(a),(b),(d) (For (a) and (d), just write down the open cover; for (b) also write a proof that there is no finite subcover.); 14.5; 14.8(a); 14.9

Due Fri. 5/18: 14.2, 14.6, 14.8 (redo (a) and also do (b)), 14.12, 14.13, 16.1, 16.3(b),(d)

Due Wed. 5/23: 16.2; 16.6 (b),(c),(e); 16.7 (c),(e),(f); 16.9

Due Fri. 5/25: 16.8 (c),(d); 16.12; 16.14; 16.15

Due Fri. 6/1: 17.4(a); 17.5(a), (b), (d), (e), (g), (h) (prove the convergence or divergence using any result you know); 17.6; 17.8; 17.10; 17.14; 17.16

Due Wed. 6/6: 18.3(b); 18.4; 18.7; 18.9; 18.11; 18.14