Due date: Monday, 10/26/15
Last update made by D. Groisser Wed Oct 21 22:57 EDT 2015
You are required to do all of the problems and reading below. You will not be required to hand in all the problems. I’ve indicated below which problems 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. 61–65/ 8,10,12,13,14,23. Prior to doing #13, do non-book problem B1. Of these, hand in all EXCEPT #14. In #s 12 and 13, the Proposition on p. 48 (“Sequences in R `behave well’ with respect to arithmetic”) is helpful.
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 problem (there is only one, B1). Hand in B1.
Back to general homework page
Back to class home page