Joseph Fehribach

Syllabus of Homework Assignments

1a | * | Due 10 January | Please show that the rationals are countably infinite. | ||||

1b | p. 12 | Due 14 January | # 1a,b, 2a,c, 3c, 4d | ||||

2 | p. 12 | Due 17 January | # 7, 8, 9 | ||||

3 | pp. 29-30 | Due 23 January | # 1, 3, 4b, 5a,c,d, 6 | ||||

4 | pp. 30-31 | Due 27 January | # 7, 9, 10, 11, 13, 14 (find a rational x) | ||||

5a | p. 61 | Due 30 January | # 1a,c | ||||

5b | p. 61 | Due 4 February | # 2, 3, 4 | ||||

* | Due 7 February | A. Prove that the intersection
of a finite number of open set G is open. _{i} | |||||

6 | * | Due 7 February | B. Give an example
where the countably infinite
union of closed sets is not closed. | ||||

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

7 | p. 62 | Due 12 February | # 9, 11, 12, 13 | ||||

8 | p. 62 | Due 19 February | # 15, 16a, 17a,b | ||||

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

* | Due 20 | Any bounded sequence in R^{m} has a convergent
subsequence. | |||||

9 | * | February | 2. Please give an example to show why the nesting property fails | ||||

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

p. 64 | # 27, 30 | ||||||

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

pp. 90-92 | February | # 1b, 9a, 10, 11, 14a | |||||

Final Exam Solutions, C02:

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Final Exam Solutions, C03:

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Last Updated: Monday 10 March 2003

Copyright 2003, Joseph D. Fehribach