3. WRITE SETS USING SET NOTATION
A set is a collection of objects called the
elements or members of the set. Set braces
{ } are usually used to enclose the
elements. In Algebra, the elements of a set
are usually numbers.
• Example 1: 3 is an element of the set {1,2,3} Note: This is referred
to as a Finite Set since we can count the elements of the set.
• Example 2: N= {1,2,3,4,…} is referred to as a Natural Numbers or
Counting Numbers Set.
• Example 3: W= {0,1,2,3,4,…} is referred to as a Whole Number
Set.
4. WRITE SETS USING SET NOTATION
A set is a collection of objects called the
elements or members of the set. Set braces
{ } are usually used to enclose the
elements.
• Example 4: A set containing no numbers is shown as { } Note: This
is referred to as the Null Set or Empty Set.
Caution: Do not write the {0} set as the null set. This set contains
one element, the number 0.
• Example 5: To show that 3 “is a element of” the set {1,2,3}, use the
notation: 3 {1,2,3}. Note: This is also true: 3 N
• Example 6: 0 N where is read as “is not an element of”
5. WRITE SETS USING SET NOTATION
Two sets are equal if they contain
exactly the same elements. (Order
doesn’t matter)
• Example 1: {1,12} = {12,1}
• Example 2: {0,1,3} {0,2,3}
6. In Algebra, letters called variables are
often used to represent numbers or to
define sets of numbers. (x or y). The
notation {x|x has property P}is an example of
“Set Builder Notation” and is read as:
{x x has property P}
the set of all elements x such that x has a property P
• Example 1: {x|x is a whole number less than 6}
Solution: {0,1,2,3,4,5}
• Example 2: {x|x is a natural number greater than 12}
Solution: {13,14,15,…}
7. 1-1 Using a number line
-2 -1 0 1 2 3 4 5
One way to visualize a set a numbers
is to use a “Number Line”.
• Example 1: The set of numbers shown above includes
positive numbers, negative numbers and 0. This set is part of
the set of “Integers” and is written:
I = {…, -2, -1, 0, 1, 2, …}
8. 1-1 Using a number line
Graph of -1
o
1
2
11
4
o o
-2 -1 0 1 2 3 4 5
coordinate
Each number on a number line is called the
coordinate of the point that it labels, while the
point is the graph of the number.
• Example 1: The fractions shown above are examples of rational numbers. A
rational number is one than can be expressed as the quotient of two integers,
with the denominator not 0.
9. 1-1 Using a number line
Graph of -1
4 16
2
o o o o o
-2 -1 0 1 2 3 4 5
coordinate
Decimal numbers that neither terminate nor
repeat are called “irrational numbers”.
• Example 1: Many square roots are irrational numbers, however some square
roots are rational.
• Irrational:
Rational:
2 7
4 16
o
1
2
11
4
o o
7
Circumference
diameter
20. REAL NUMBERS (R)
Definition:
REAL NUMBERS (R)
- Set of all rational and
irrational numbers.
21. SUBSETS of R
Definition:
RATIONAL NUMBERS (Q)
- numbers that can be expressed as
a quotient a/b, where a and b are
integers.
- terminating or repeating decimals
- Ex: {1/2, 55/230, -205/39}
22. SUBSETS of R
Definition:
INTEGERS (Z)
- numbers that consist of
positive integers, negative
integers, and zero,
- {…, -2, -1, 0, 1, 2 ,…}
23. SUBSETS of R
Definition:
NATURAL NUMBERS (N)
- counting numbers
- positive integers
- {1, 2, 3, 4, ….}