MATH 355 Final: MATH 355 Amherst S10M28Final

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 355
• Professor: All

Document Summary

Instructions: this exam is to be turned in no later than tuesday may 11th at 10am. You may use your book, your notes from class, and your problem sets, but no additional resources or discussion are permitted. If you need clari cation on a problem, please ask me. There are a total of 50 points on this exam. Let a, b r be bounded and de ne a b = {a b | a a, b b}. Show that sup(a b) = sup(a) inf(b). Show that if a r is dense, then a = r. Let a, b o be in r. recall that we de ne. Ab = {ab | a a, b b with a, b 0} {q q, q < 0}. Show that i = {t q | t < 1} is a cut and the multiplicative identity. (i. e. that ai = a for all a r with a o).