MATH0201 BASIC CALCULUS
MATH0201
BASIC CALCULUS
Set
Dr. WONG Chi Wing
Department of Mathematics, HKU
MATH0201 BASIC CALCULUS
What is a set?
Representation and Membership of a Set
Some Examples
Venn Diagram and Subset Relation
Set Operations
Union
Intersection
Complement
MATH0201 BASIC CALCULUS
What is a set?
Definition 1
A
set
is a well–defined collection of objects, i.e., we can
determine wether a given object belongs to that set or not
without any ambiguity.
Example 2
Which of the following is/are a set/sets?
1.
The collection of students who enroll in MATH0201.
2.
The collection of excellent students who enroll in
MATH0201.
3.
BOTH of them.
4.
NONE of them.
MATH0201 BASIC CALCULUS
What is a set?
Representation and Membership of a Set
We may represent a set by
1.
WORD DESCRIPTION
S is the set of the first five prime numbers.
2.
LISTING
S
:=
{
2
,
3
,
5
,
7
,
11
}
3.
SET–BUILDER NOTATION
{
x
:
x
is one of the first five primes
}
.
It is read as the set of all elements
x
such that
x
is one of
the first five primes.
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MATH0201 BASIC CALCULUS
What is a set?
Representation and Membership of a Set
Example 4
The following three sets are indeed the same:
1.
The set of solutions of
x
2

1
=
0.
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 Spring '11
 CHOW
 Calculus, Set Theory

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