# 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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