Joseph Fehribach

Syllabus of Homework Assignments

1a | * | Due 16 January | Please show that the rationals are countably infinite. | ||||

1b | p. 12 | Due 20 January | # 2a, 3b, 4b,d | ||||

2 | pp. 12-13 | Due 23 January | # 7a,c,e,f, 8, 9 | ||||

3 | pp. 29-30 | Due 27 January | # 1, 2, 5, 6 | ||||

4 | pp. 30-31 | Due 2 February | # 7, 9, 10, 11, 12, 14 (find only a rational x)
| ||||

5a | p. 61 | Due 5 February | # 1a,b | ||||

5b | p. 61 | Due 10 February | # 3, 4, 6 | ||||

* | A. Prove that the intersection
of a finite number of open set G is open. _{i} | ||||||

6 | * | Due 13 February | B. Give an example
where the countably infinite
union of closed sets is not closed. | ||||

p. 61 | # 5, 7 | ||||||

7 | p. 62 | Due 17 February | # 8, 10, 12, 13 | ||||

8 | p. 62 | Due 23 February | # 15, 16a,c, 17c | ||||

* | A. Prove the in-class version of Corollary 1, p. 56: | ||||||

* | Due 27 | Any bounded sequence in R^{n} has a convergent
subsequence. | |||||

9 | * | February | B. Please give an example to show why the nesting property fails | ||||

* | for a sequence of nonempty, closed, but unbounded sets in R^{n} . | ||||||

p. 64 | # 27, 29 | ||||||

10 | p. 64 | Due 25 | # 28 | ||||

pp. 90-92 | February | # 1b,d, 9a, 10, 11 | |||||

Final Exam Solutions, C02:

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Final Exam Solutions, C03:

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Final Exam Solutions, C04:

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Last Updated: Friday 27 February 2004

Copyright 2004, Joseph D. Fehribach