MATH 355 Final: MATH 380 Amherst S08Math27Final

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

Document Summary

Rules: you may use your notes and your textbook, but no other resources. Point values for each problem are indicated in brackets at the beginning of the problem: for a, b , we de ne a b to mean: a b is nite and b a is in nite. More formally, we could say that is the relation on p( ) de ned as follows: = {, b% p( ) p( ) | a b is nite and b a is in nite}. (more informally, you might think of a b as meaning that a is almost a subset of. In this problem you will prove that there is a set a such that for all n , an a, and a . First, for each n , let cn = a0 a1 an = ! {ai | i n}. (i) [5] prove that for all n , cn an+1.