MATH 3220 § 1	SECOND HOMEWORK ASSIGNMENT	Due Tuesday,
A. Treibergs		September 4, 2007.

Remember that the  First Midterm Exam  will be in class, Wednesday, September 5.

The exam will be CLOSED BOOK except that you will be allowed to bring a single page "cheat sheet" of notes.

You are responsible for knowing how to solve the following exercises. Please hand in the starred "*" problems.
Exercises from the text "Foundations of Analysis" by Joseph L. Taylor. 7.2 [ !*, 2, 3, 4, 5, 8*, 11* ] Additional exercises. A*. Let (X,δ) be a metric space. Suppose x, y are points in X and {xn} and {yn} are sequences in X such that xn → x and yn → y as n → ∞. Show that δ(xn,yn) →  δ(x,y) as n → ∞. B*. Let {un} be a sequence in Ed and let u be a point in Ed. Suppose that for all vectors v in Ed we have v⋅un → v⋅u as n→∞. Show that un → u as n → ∞.