MATH 3210 § 1 SIXTH HOMEWORK ASSIGNMENT  Due Friday,
A. Treibergs    October 3, 2008.

A. Please hand in the following problems from Taylor's Foundations of Analysis.
  • 33[ 2, 8a, 9c ],
  • 40[ 5, 8, 11 ].
B. Please hand in the following additional problems.

  1. Prove that if a, b, x, y are real numbers such that

          |x - a| < 1, |y - b| < 2, |a - b| > 7.

    Then |x - y| > 4.

  2. Suppose that the functions f, g are defined on a set containing A as a subset, then

    supA(f + g) ≤ supA f + supA g.

    Give an example that shows that "<" may happen.