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Math 139, Exam 2 Review Sheet

Chapter 2, Section 2.6:
Know what a rational number is
● Know a couple of examples of irrational numbers
● HW assigned from 2.6: #22, 23, 26, 27, 33, 34, 35

Section 2.7:
● What are the Natural numbers ? Rational numbers ? Irrational numbers? Real numbers ?
● Given a decimal expansion for a rational number, how do you express the number as a fraction?
(Try working homework not assigned: 2.7 # 17, 19, 21, 22, 24)
● Sec 2.7 HW assigned: # 18, 20, 23, 31, 32

Chapter 3, Section 3.1:
● What is infinity?
● What are some examples of finite sets? Infinite sets?
● What is a one to one correspondence between two sets ? Given two sets, can you find a one to
one correspondence between them?
● Sec 3.1 HW assigned: # 10, 11, 12

Section 3.2:
● What is the cardinality of a set?
● How do you know if two sets have the same cardinality? (Try working homework not assigned:
3.2 # 8, 9, 10, 14, 15)
● Sec 3.2 HW assigned: # 6, 11, 16, 17, 18, 19, 35

Section 3.3:
● Cantor's proof that there are more real numbers than natural numbers (Try 3.3 # 8)
● Dodgeball: What are the rules of the game ? What happens when we increase the size of the
playing board?
● Sec 3.3 HW assigned: # 7, 10, 11, 13, 14, 22

Chapter 4, Section 4.1:
● What is the Pythagorean Theorem?
● How do you use the Pythagorean Theorem?
● Sec 4.1 HW assigned: # 8, 11, 12, 14, 15, 18

Section 4.2:
● What is a closed polygonal curve ?
● Given a floor plan of an art gallery that is a closed polygonal curve , can you place cameras (or
guards) at appropriate vertices so that every point in the gallery is within view? Can you do so
using a minimal number of cameras ?
● What is the Art Gallery Theorem?
● Sec 4.2 HW assigned: #7, 8, 14, 15, 19, 20

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