Solutions to Homework Chapters 3.1 and 3.2.
3.1: 5,7,20,22
5) Bunch of balls. Most cans of tennis balls contain three balls, so there will NOT be a
one-to-one correspondence between cans and balls (unless you have very exclusive, individually packaged ten
Solutions to Homework 3.3: 1,2,3,4,5
1) Shake em up. Georg Cantor was the first mathematician to show that there are
more real numbers than natural numbers, demonstrating that there are different
sizes of infinity.
2) Detecting digits. The first digit of
Homework Solutions Section 4.5
1. It's nice to be regular. A polygon is regular if all sides are the same length and all angles have equal
measure. Here are regular polygons with 3, 4, 5, 6, 7, and 8 sides. (Note that the regular 7-gon is particularly
har
Answers to Homework 6.2: 1,2,3,4,5, 27,28,29
1. Any interest? At the end of one year you will have (1.03)($1000) = $1030. After two years youll have (1.03)2 ($1000) = $1060.90. After five years, youll
have (1.03)5($1000) = $1159.27.
2. Urban expansion. In
MATH 110
MIDTERM 2
FALL 2005
ANSWERS
1. [10 pts.] Suppose I claim that the following list will show that there is a one-to-one
correspondence between the natural numbers and the real numbers. Prove that I am
wrong by describing Cantors diagonalization arg