Principles of Analysis

Homework Assignment #4

Due Wednesday, October 2, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Bilodeau and Thie's book, the required text for the course. You should write up solutions neatly to all problems, paying particular attention to your arguments and proofs. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.

Problems on Cardinality and Infinite Sets:
Do problems 1, 3, 5, 6, 7, 8 from the handout Cardinality and Infinite Sets.

Section 2.1
Problems:   1, 2 (parts b, c, d, h), 7, 13a, 14

Note: For problem #1, be sure to explain your answer carefully, referring to the definition of a convergent sequence. For problem #14, think about how we negate the definition of a convergent sequence. (What is the negation of "for any" and "there exists"?)