OBJECTIVES
2 CHAPTER 1 Review of the Real Number System
OBJECTIVE 1 Write sets using set notation.A setis a collection of objects
called the elementsor membersof the set. In algebra, the elements of a set are usu-
ally numbers. Set braces, {}, are used to enclose the elements.
For example, 2 is an element of the set Since we can count the number
of elements in the set it is a finite set.
In our study of algebra, we refer to certain sets of numbers by name. The set
Natural (counting) numbersis called the natural numbers,or the counting numbers.The three dots (ellipsis
points) show that the list continues in the same pattern indefinitely. We cannot list all
of the elements of the set of natural numbers, so it is an infinite set.
Including 0 with the set of natural numbers gives the set of whole numbers.
Whole numbersThe set containing no elements, such as the set of whole numbers less than 0, is called
the empty set,or null set,usually written or 0 {}.
W 5 0, 1, 2, 3, 4, 5, 6, Á 6
N 5 1, 2, 3, 4, 5, 6, Á 6
5 1, 2, 3 6 ,
5 1, 2, 3 6.
Basic Concepts
1.1
1 Write sets using set
notation.
2 Use number lines.
3 Know the common
sets of numbers.
4 Find additive
inverses.
5 Use absolute value.
6 Use inequality
symbols.
7 Graph sets of real
numbers.CAUTION Do not write for the empty set. is a set with one element:.
Use the notation or { 0 } for the empty set.
506 506 0
To write the fact that 2 is an element of the set we use the symbol
(read “is an element of ”).
The number 2 is also an element of the set of natural numbers N.
To show that 0 is notan element of set N, we draw a slash through the symbol
Two sets are equal if they contain exactly the same elements. For example,
(Order doesn’t matter.) However, ( means “is
not equal to”), since one set contains the element 0 while the other does not.
In algebra, letters called variablesare often used to represent numbers or to de-
fine sets of numbers. For example,
(read “the set of all elements xsuch that xis a natural number between 3 and 15”)
defines the set
The notation is an example of set-
builder notation.
the set of all elements x such that xhas a given property P