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1.2 Sets and set notation
Good morning!
Schedule:
Learning goals
Homework Padlet
Sets and set notation
Worksheet / Homework
1 / 16
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Slide 1:
Tekstslide
Wiskunde
HBO
Studiejaar 4
In deze les zitten
16 slides
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en
tekstslides
.
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Onderdelen in deze les
Good morning!
Schedule:
Learning goals
Homework Padlet
Sets and set notation
Worksheet / Homework
Slide 1 - Tekstslide
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
Slide 2 - Tekstslide
What is a set? (definition)
Slide 3 - Woordweb
Sets
Definition
A set (noun):
a number of things of the same kind that belong or are used together.
Slide 4 - Tekstslide
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
Slide 5 - Tekstslide
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
Slide 6 - Tekstslide
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
Slide 7 - Tekstslide
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
Slide 8 - Tekstslide
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
Slide 9 - Tekstslide
Types of numbers
Slide 10 - Tekstslide
Sets and set notation
if A = { -3, -2, 0, 1, 5}
Then
A
+
= {.... }
A
-
= { ....}
A
*
= { .... }
Find the elements of these 3 sets.
Slide 11 - Tekstslide
Sets and set notation
if A = { -3, -2, 0, 1, 5}
Then
A
+
= {1, 5}
A
-
= {-3, -2}
A
*
= {-3, -2, 1, 5}
Slide 12 - Tekstslide
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}
Slide 13 - Tekstslide
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)
Slide 14 - Tekstslide
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)
Slide 15 - Tekstslide
Universal and complementary set
The complementary set
(notation: A' or A
c
) 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}
Slide 16 - Tekstslide
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