Due Fri. 10/6: 1.4, 1.10, 2.4, 3.6 b,f,j,i,k, 4.19,
4.20
Due Wed. 10/11: 5.11, 5.21, 5.22, 10.10, 10.22
Due Fri. 10/13: 10.15, 10.30
Hints for 10.30:
- Use proof by contradiction. (So, you will assume the
negation of the well-ordering property and get a contradiction --
and remember that you are also assuming the principle of mathematical
induction!)
-
You will probably want to use the fact that 1 <= n
for all natural numbers n -- prove this as a lemma (by induction)!
Due Wed. 10/18:
11.11 (a) (show just O2), (b), and (c);
11.12 (a) (show just M2, M4, M5), (b)
Due Fri. 10/20:
11.2 (b),(c) (find counterexamples!); 11.4; 11.6
Due Fri. 10/27:
12.4, 12.5 12.6(a), 12.16 (Also, read the proof of 12.10 and prove 12.13)
Due Wed. 11/1:
12.7(a); 12.9; 12.13; 12.14(a)
Due Wed. 11/8:
13.2, 13.4, 13.5, 13.6, 13.7, 13.10, 13.18, 13.19, 13.20
Due Wed. 11/22:
14.2(a)-(d), 14.3, 14.5, 14.8, 14.11(a)
Due by Mon. 11/27:
You may turn in 14.13 separately for extra credit on the homework.
Make sure to justify your answers!
Due Wed. 11/29:
14.6, 14.12, 16.1, 16.3
Due Mon. 12/4:
16.6(b),(c); 16.7(a),(b),(c),(d); 16.8(a) (hint: try using contradiction);
16.9; 16.14
Due Wed. 12/6:
17.3(a),(b); 17.4; 17.5(b),(d),(h),(l);
17.6(a) (find a counterexample), (c)
(prove using Theorem 17.1!); 17.8