Sets
Advanced Level Pure Mathematics
2.1
Introduction
1.
A
set
is a collection of definite, distinguishable objects.
e.g.
{ chairs , desks , tables } is a set of furniture.
{ a , e , i , o , u } is a set of vowels.
{ 0 , 1 ,

1 , 2 ,

2 , 3 ,

3 , ... } is a set of integers.
2.
The objects of a set is called the
elements
or
members
of the set.
e.g.
a , e , i , o
and
u
are the elements of the set of vowels.
3.
Expressing a set in two ways:
(a)
Tabular form
:
e.g.
{ a , e , i , o , u } is the set of vowels.
e.g.
{0 , 2 ,

2 , 4 ,

4 , ...} is a set containing all the even numbers.
(b)
SetBuilder form
:
e.g.
{
x
:
x
is a vowels } is the set of vowels.
e.g.
{
x
:
x
is an even number } is a set containing all the even numbers.
4.
If
x
is a member of a set
A , we write
x
∈
A.
If
x
is not belong to a set
A , we write
x
∉
A.
e.g.
If
A = {
x
:
x
is a vowel } , then
a
∈
A ,
u
∈
A , but
g
∉
A.
e.g.
If
B = {
x
:
x
is an integer greater than 11 } , then
20
∈
B
, 999
∈
B ,
but
11
∉
B.
5.
Sets containing finite number of objects are called
finite sets
. Otherwise, it is
called an
infinite set
.
e.g.
{
x
:
x
is a vowel } is a finite set.
e.g.
{
x
:
x
is an integer greater than 11 } is a infinite set.
6.
Some symbols are frequently adopted:
Prepared by
K. F. Ngai
Page
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