This preview shows pages 1–9. Sign up to view the full content.
1
MA1100
Lecture 9
Sets
•
Set Notations
•
Set Relations
•
Set Operations
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document MA1100
Lecture 9
2
Sets
A
set
is a
well defined collection
of objects
The set of
all positive integers
Z
+
The set of all
rational numbers
Q
The set of all
integer
solutions of x
2
= 9
The set of all
rational numbers
of the form 1/n
where n is a positive integer
The set of all
real numbers
R
The set of all
positive
real numbers
less than 10
Example
MA1100
Lecture 9
3
Elements of a Set
Let A denote a set.
if y is an object that
belongs
to this set A,
we say y is an
element
of A and write
y
œ
A
.
If y is
not an element
of A, we write
y
–
A
Example
1.5
œ
Q
◊
2
–
Q
A set with finitely many elements is called a
finite set
.
The
number of elements
in a
finite set
A
is called the
cardinality
of A and is denoted by
A.
Example
A = {a, b, c}
A = 3
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document MA1100
Lecture 9
4
A strange “set”
Let T be the “set”
containing every set A
such that
A does not belong to itself
We can use
set
to refer to almost any collection
of objects:
•Theseto
f
all animals
•Theseto
f
all NUS students
Let S be the “set” of
all sets.
Then
S
œ
MA1100
Lecture 9
5
Roster Method
Roster method
is a way to
specify elements
of a
set by
listing
.
This method works for
•
small finite sets
•
sets with elements having a fixed pattern
The set of
all integer solutions of x
2
= 9
The set of
all positive integers less than 10
{3, 3}
{1, 2, 3, 4, 5, 6, 7, 8, 9}
{1, 2, 3, …, 9}
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document MA1100
Lecture 9
6
Roster Method
The set of
all even integers
{…, 6, 4, 2, 0, 2, 4, 6, …}
Infinite set with “
pattern
”
Roster method
is a way to
specify elements
of a
set by
listing
.
⎭
⎬
⎫
⎩
⎨
⎧
L
4
1
3
1
2
1
1
1
,
,
,
,
The set of all
rational numbers
of the form
1/n
where n is a positive integer
MA1100
Lecture 9
7
Set Builder Notation
The set of
all positive real numbers less than 10
We can describe the set using
set builder notation
{ x
œ
R
 0 < x < 10 }
underlying set
underlying condition
If we denote the
set of positive real numbers
as
R
+
we can also write the set builder notation as
{ x
œ
R
+
 x < 10 }
Not all
sets can be described using roster method:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document MA1100
Lecture 9
8
Set Builder Notation
{ x
œ
U

P(x)
}
General form
U
:
underlying set
for the variable x
P(x):
underlying condition
in terms of x
that describe the elements
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 03/19/2012 for the course SCIENCE MA1100 taught by Professor Forgot during the Fall '08 term at National University of Singapore.
 Fall '08
 Forgot

Click to edit the document details