Assignments for Week 4

Math 139

Assignments for Week 4
Week 4 (February 2-6). On Monday we will complete our discussion of the completeness axiom and Cauchy sequences. On Wednesday, we will discuss subsequences and the Bolzano-Weierstrass Theorem. On Friday we will move on to discuss continuity in Section 3.1.

Assignment for Wednesday, February 4
Problems 1 and 5 in Section 2.4 and Problem 1 in Section 2.5.

Assignment for Friday, February 6 Note: These problems have been postponed until Monday, Feb. 9.
Problems 1, 2, 4, 8, and 9 in Section 2.6

Assignment for Monday, February 9

Complete the assignment above.
Show that for all x and y abs(abs(x) - abs(y)) <= abs(x - y).
Show that if a_n converges to a, then abs(a_n) converges to abs(a).
Show that the absolute value function is continuous.
Show that if f is a continuous function on Dom(f), then abs(f) is also a continuous function on Dom(f), where abs(f)(x) = abs(f(x)).

Lawrence C. Moore < lang@math.duke.edu>

Last modified: February 6, 1998