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 Gi is open. | ||||||
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 Rn 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 Rn . | ||||||
p. 64 | # 27, 29 | ||||||
10 | p. 64 | Due 25 | # 28 | ||||
pp. 90-92 | February | # 1b,d, 9a, 10, 11 | |||||
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