1549901369-Elements_of_Real_Analysis__Denlinger_

10 Chapter 1 • The Real Number System

(h) Exercise 18.

(i) Exercise 1 9.

(j) Exercise 20. •

EXERCISE SET 1.1-B

1. Prove Theorem 1.1.2 (b).
   2. Prove Theorem 1.1.3 (b). [Hint: see how Part (a) was proved.]


2. Prove Theorem 1.1.3 (d). [Hint: see how Part (c) was proved.]


3. Prove Theorem 1.1.4 (c). [Hint: compare with the proof of (a).]


4. Prove Theorem 1.1.4 (f). [Hint: use Part (d) and Theorem 1.1.3 (d),
   and compare with the proof of (b).]


5. Prove Theorem 1.1.4 (g). [Hint: use Part (e) and prove that x-^1 y-^1 is
   a multiplicative inverse of xy.]


6. Prove Theorem 1.1.4 (i). [Hint: apply (h).]


7. Prove Theorem 1.1.4 (j).


8. Prove Theorem 1.1.4 (k).


9. Prove Theorem 1.1.7 (a).


10. Prove Theorem 1.1. 7 ( c).


11. Prove Theorem 1.1. 7 ( d).

13. Prove Theorem 1.1.8 (a).

14. Prove Theorem 1.1.8 (b).

15. Prove Theorem 1.1.8 (c).

1 6. Prove Theorem 1.1.8 (f).

17. Prove Theorem 1.1.8 (g).

18. Prove Theorem 1.1.8 (h).

19. Prove Theorem 1.1.8 (i).

20. Prove Theorem 1.1.8 (j). [Note that this requires a two-part proof: first,
    b
    that --is a solution and then, that it is the only so lution.]
    a