1.2 Sets and set notation

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 4

Good afternoon!

Schedule: 

• Learning goals 
• Homework Padlet
• Sets and set notation 
• Worksheet / Homework

Learning goals 

At the end of this lessons I can:

• Classify the different kinds of real numbers 
• Represt the different kinds of real numbers
• Describe set in list form and with words
• Use set symbols to describe sets

What is a set? (definition)

Sets

Definition

A set (noun): a number of things of the same kind that belong or are used together.

Sets and set notation

A = { all even numbers between 1 and 10} 

A = { 2, 4, 6, 8, 10}

Set 

Description of the elements of A

Listing of the elements of A

You can also call this "Roster notation"

Types of numbers

You have different types of numbers: 

Natural numbers (counting numbers): Positive whole numbers

{0, 1, 2, 3, 4, ...}

All natural numbers = 

ℕ

Types of numbers

You have different types of numbers: 

Integers: Positive and negative whole numbers

{..., -2, -1, 0, 1, 2, 3, ...}

                 , 

                                    All integers = 

Every natural number is an integer !

ℤ

Types of numbers

You have different types of numbers: 

Rational numbers: Numbers you can write as a fraction 

for example           ,              , 4

                 , 

                           All rational numbers= 

Every integer is a rational number, therefore every natural number is also a rational number !

ℚ

​4​​3​​

0.2

Types of numbers

You have different types of numbers: 

Real numbers : All rational and irrational numbers 

For example          ,           , -2, 0.9999999....

 

               All real numbers =

​4​​3​​

√​2​​​

ℝ

Every number we've talked about so far is a real number

Types of numbers

Sets and set notation

if A = { -3, -2, 0, 1, 5}

Then

A+ = {.... }

A- = { ....}

A* = { .... }

Find the elements of these 3 sets.

Sets and set notation

if A = { -3, -2, 0, 1, 5}

Then

A+ = {1, 5}

A- = {-3, -2}

A* = {-3, -2, 1, 5}

Worksheet

1. Work on the worksheet 

2. When you finish, start on the homework: 

Homework

Standard:

P. 22: Practice 1 ALL

P. 24: Practice 2 (1, 2)

Extended:

P. 24: Practice 2 (3)

Sets and set notation

 Read this as: 

U is the set of all x such that x is an integer larger or equal to 0 and smaller or equal than 20.

Listing of the elements: 

U = {0, 1, 2, 3, 4, 5, ... , 19, 20}

You call this "Set builder notation"

Subsets and proper subsets

B = {1, 2,} 

The subsets of B are: 

Ø, {1}, {2}, {1, 2} 

Proper subsets of B are: 

Ø, {1}, {2}

A subset is more general than a proper subset. 

Just like 'green' is more general than 'dark green'. 

Every proper subset is a subset. 

Set A can only be a Proper subset of set B if set B contains elements that set A doesn't 

(so when set A is not equal to set B)

Universal and complementary set

The complementary set (notation: A' or Ac) of a set A contains all elements that DO NOT belong to A.

The universal set (notation: U) is a set which contains ALL ELEMENTS of a problem. 

Example: 

If U = { 1, 2, 3, 4, 5} and 

A = { 2, 4, 5} then 

A' = {1, 3} 

Homework

Standard:

P. 22: Practice 1 ALL

P. 24: Practice 2 (1, 2)

(+)

Extended:

P. 24: Practice 2 (3)

Due Monday 11-9!