This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Office Problem 1  Math 139 Due Oct 13th Instructor Mauro Maggioni Office 293 Physics Bldg. Office hours Monday 1:30pm3:30pm. Web page www.math.duke.edu/ mauro/teaching.html Office consultation: Oct. 7th, 8th, 1pm3pm, usual office hours on Oct. 11th. Possibly other times on demand (pls. write me an email in advance). Let C ( Q )(resp., C ( R )) denote the set of equivalence classes of Cauchy sequences of rational (resp., real) numbers as defined in Homework 5; C will denote either one in cases where a statement is valid for both. (It is in fact the case that C ( Q ) = CR ). The purpose of this office problem is to complete the construction of the real numbers from the set C ( Q )of equivalence classes [ a n ] of Cauchy sequences { a n } of rational numbers, which was begun in the Additional Problems of Assignment 5. In particular, you will show that C is ordered, define completeness in C and show that each decimal gives rise to an element of C ( Q )....
View Full
Document
 Fall '08
 Pardon,W
 Math

Click to edit the document details