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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 )....
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 Fall '08
 Pardon,W
 Math, Rational number, Cauchy sequence, Bolzano Weierstrass, Cauchy sequences, Mauro Maggioni

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