MAA 4211 Assignment 5
Due date: Friday 10/25/13.
Last update made by D. Groisser Tue Oct 22 00:54:22 EDT 2013
You are required to do all of the problems below. You will not be required to hand them all in. I’ve indicated which ones you do have to hand in. Don’t make the mistake of thinking that I’m collecting only the problems I think are important.The “due date” above is the date that your written-up problems should be handed in, but don’t wait to get started on the assignment. You should always get started on problems as soon as we cover the relevant material in class.
- A: Rosenlicht pp. 61–63/ 8,12,13,14,23. Of these, hand in only 8, 13, and 23. For #23, hand in only the proofs for “an + bn” and “cn an“; don’t hand in the proof for “an – bn“. Prior to doing #13, do B3 in the non-book problems. You may assume the result of B3 to do #13, whether or not you are successful with B3.Definition for #8: A reordering of a sequence {pn}{n=1}∞ is a sequence {qn}{n=1}∞ such that for some bijection f: N→ N we have qn = pf(n) for all n∈N. (In “{pn}{n=1}∞“, the superscript “∞” is meant to be sitting over the subscript “n=1“, but I don’t know how to achieve this in HTML.) Problem 8 is asking you to prove that if {qn}{n=1}∞ is a reordering of a convergent sequence {pn}{n=1}∞ in a metric space, then {qn}{n=1}∞ converges and limn →∞ qn = limn →∞ pn.
- B: Click here for non-book problems. Of these, hand in only B1ab, B2, B3, and B5b.