MATH 355 Final: MATH 355 Amherst F14M355Final

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

Document Summary

Rules: you may use your notes and textbook, but no other resources. For each positive integer k, let nk bk = J), then f is continuous on i. (b) prove that if f continuous on i and one-to-one then f is monotone. (you might. Also, suppose these functions are all bounded, and let m = sup{f (x) : x r} and. Mn = sup{fn(x) : x r}. (a) suppose that (fn) n=1 converges pointwise to f . One of the following statements is always true, and the other isn"t. 1: (8 points each part) suppose that a r and a 6= . C = {x : a ( , x) is nite or countable}, D = {x : a (x, ) is nite or countable}. (a) show that there is some real number c such that c = ( , c].