Download Number Sets

Number Set Notation
Reminder
Symbol
Natural Numbers: Counting numbers
Integers: Positive and negative counting numbers
Rational Numbers: a number that can be
expressed as an integer fraction
Irrational Numbers: a number that can
NOT be expressed as an integer
fraction
Real Numbers: The set of all rational
and irrational numbers
NONE
Set Notation
Not Included
The interval does NOT include the endpoint(s)
Interval Notation Inequality Notation Graph
Parentheses
( )
< Less than
> Greater than
Open Dot
Included
The interval does include the endpoint(s)
Interval Notation Inequality Notation Graph
Square Bracket
[ ]
≤ Less than or equal
≥ Greater than or equal
Closed Dot
Example 1
Graphically and algebraically represent the following:
All real numbers greater than 11
Graph:
10
Inequality:
Interval:
x  11
11, 
11
12
Infinity never ends. Thus
we always use
parentheses to indicate
there is no endpoint.
Example 2
Describe, graphically, and algebraically represent
the following:
1 x  5
Description: All real numbers greater than or
equal to 1 and less than 5
Graph:
Interval:
1
1,5
3
5
Example 3
Describe and algebraically represent the
following:
-2
1
4
All real numbers less than -2 or
Describe:
greater than 4
Inequality:
Interval:
x  2 or x  4
The union or combination
of the two sets.
 , 2  4, 