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 Assignment Assigned Due Problems HW1 9/4/18 9/11/18 Read Sections 1.1-1.3. 1. Do Exercise 1.2.4. 2. Do Exercise 1.2.7(b) and 1.2.7(c). 3. Do Exercise 1.2.8. HW2 9/11/18 9/18/18 Read Sections 1.4-1.5. Read the following problems, but do not turn them in: 1.3.3, 1.3.6(a)(b)(c), 1.4.3, 1.4.8. 1. Do Exercise 1.3.2. 2. Do Exercise 1.3.9. 3. Does the non-Archimedean field $\mathbb R(t)$ satisfy the Nested Interval Property? Explain. HW3 9/18/18 9/25/18 Read Sections 1.5-1.6. Read the following problems, but do not turn them in: 1.5.4, 1.5.5, 1.5.9, 1.6.10. 1. Do Exercise 1.5.2. 2. Do Exercise 1.5.8. 3. Show that if $S\subseteq [0,1]$ is uncountable, then there is a real number $r\in[0,1]$ such that both $[0,r]\cap S$ and $[r,1]\cap S$ are uncountable. HW4 9/25/18 New Due Date! 10/4/18 Read Sections 2.1-2.4. 1. Do Exercise 2.2.4. 2. Do Exercise 2.3.7 (a), (b), (c). 3. Do Exercise 2.4.4 (a). HW5 10/2/18 10/9/18 Read Sections 2.5-2.6. 1. Do Exercise 2.4.2. (Hint for (b): use MCT to prove $(y_n)$ converges.) 2. Do Exercise 2.4.3 (a). (Hint: use MCT to prove the sequence converges. To find the limit, show that it must satisfy $L^2-2=L$ and $L>0$.) 3. Do Exercise 2.5.1 (a), (b), (c). HW6 10/16/18 10/23/18 Read Section 2.7. 1. Do Exercise 2.6.2 (a) (c). 2. Do Exercise 2.6.4 (c). (Where the author says Decide whether each of the following sequences is a Cauchy sequence'', interpret this to mean Decide whether each of the following sequences MUST BE a Cauchy sequence''.) 3. Do Exercise 2.7.4 (a) (d).