Introduction to Mathematical ReasoningMath 310 Spring 2006
Assignment #9
Due 5/31/06
Reading
•None this week. No reading report required.
Part I
A. Page 143, Exercise 11.6.
B. Page 181, Exercises 14.1, 14.2.
Part II
Give a complete proof for each of the following problems.
C. If Xcontains an infinite subset, prove that Xis infinite.
D. If Xcontains an uncountable subset, prove that Xis uncountable.
E. If Xis uncountable and Ais a countable subset of X, show that X−Ais uncountable.
F. Determine whether each of the following sets is empty, finite but nonempty, denumerable, or uncount-
able. No proofs necessary.
(a) {1/n :n∈Z+}.
(b) R−Q.
(c) Z×R.
(d) [0,∞).
(e) {x∈R:x2∈Z}.
Part III
With your writing group, write final drafts of all portfolio problems that have been assigned so far. Each
group should bring one copy of their writeups to class on Friday, June 2 (the last day of class), along with
all marked-up previous drafts.
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