object and
A
is a set, then
a
∈
A
means a is a member of A or ‘a is an element
of
A
’. Then
a /
∈
A
means a is not a member of A or ‘a is not an element of
A
’
2.1.1
Listing of elements
There are two methods of representing a set which are:
1.
Listing the elements in a roster:
Here we list elements between the
two curly brackets (braces).
e.g.
The notation
{
a,
1
, e,
7
}
represents the set with four elements
a,
1
, e,
and 7. We call this a
roster method
.
Sometimes the roster method can be used to describe a set without listing
all the members. This is done by listing some of the members, and then
ellipses (
. . .
) are used when the general pattern of the elements is obvious.
e.g.
D
=
{
1
,
4
,
9
,
16
, . . . ,
81
,
100
}
which is clearly a set of all perfect square
numbers from 1 to 100. One can easily make note of obvious elements not
listed, for example, 36
∈
D
and 40
/
∈
D
.
2.
Set builder notation:
We characterized the elements of that set by a
specific property or properties they must have in order to be a member of
such set.
e.g.
A
=
{
x
:
x
is a prime number between 6 and 15
}
.
We often use this method when it is impossible to list such elements,
though in some instances it can be easy to list such element. From our ex-
ample it easy to list elements in set
A
, i.e.
A
=
{
7
,
11
,
13
}
; but it is not pos-
sible to list elements of set
B
=
{
x
:
x
=
a
b
,
where a and b are negative integers
}
,
since there are infinite such number in set
B
.
2.1.2
Important sets of numbers:
1.
Natural numbers:
Natural numbers are also known as counting num-
bers, beginning at 1. The set of natural numbers is denoted by
N
; i.e.
N
=
{
1
,
2
,
3
,
4
, . . .
}
.
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