Download Set & Interval Notation

Set & Interval
Notation
Sets and Elements
A set is a collection of objects. To denote a
set we often enclose a list of its elements with
braces. This is called the Roster Method.
Natural Numbers {1, 2, 3, 4, 5, …}
Whole Numbers {0, 1, 2, 3, 4, …}
Integers {…, -3, -2, -1, 0, 1, 2, 3, …}
Since every natural number is also a whole
number, we say that the set of natural numbers
is a subset of the set of whole numbers.
Set Builder Notation
A set can also be written in set builder
notation. In this method, we write a rule that
describes what elements are in a set. For
example:
{x | x is greater than 2.}
The set
of all x
Such
that
A rule that describes
membership in the set
The graph would look like either of the
following:
OR
0
0
Example 1: Writing & Graphing Set
Notation
A)
x>0
B)
x≤2
C)
-2 < x ≤ 1
Interval Notation
Graphs of sets of real numbers are often
portions of a number line called intervals. The
interval can be written in interval notation.
For example, for -2 < x ≤ 1 we write the
interval notation as (-2, 1]. Parentheses are
used to show it does not contain that number,
where brackets show it does contain that value.
Example 2: Graph & Write in Interval
Notation
A)
{x|x is less than 9.}
B)
{x|x is greater than or equal to 6.}
C)
{x|x is greater than or equal to -5 and less than or equal
to 6.}
D)
{x|x is great than 2 and less than or equal to 8.}
OR Compound Inequalities and Union
The graph of the set {x|x is less than -2 or
greater than 3} is shown below. This graph is
called the union of two intervals and can
be written in interval notation as seen
below.
0
(-∞, -2) U (3, ∞)
Example 3: Unions
A)
{x|x is greater than 5 or less than 4.}
B)
{x|x is less than or equal or -1 or greater than 2.}