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

Set symbols

1. Copy this table and complete it. 

2. Use google to find the meaning of these symbols

Set symbols

1. Copy this table and complete it. 

2. Use google to find the meaning of these symbols

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}

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"

Sets and set notation

Translate these and write them in list form

You call this "Set builder notation"

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 

Homework

Standard:

P. 22: Practice 1 ALL

P. 24: Practice 2 (1, 2)

Extended:

P. 24: Practice 2 (3)

Homework

Standard:

P. 22: Practice 1 ALL

P. 24: Practice 2 (1, 2)

(+)

Extended:

P. 24: Practice 2 (3)

Due Monday 11-9!