1. Intervals and Interval Notation
Algebra II
Intervals and Interval Notation

2. Intervals
The set of all numbers between two endpoints is called an interval.
An interval may be described either by an inequality, by interval notation, or by a straight line graph.
An interval may be:
Bounded:
Open - does not include the endpoints
Closed - does include the endpoints
Half-Open - includes one endpoint
Unbounded: one or both endpoints are infinity

3. Graphing Intervals
Set A with endpoints 1 and 3, neither endpoint included
1------3
Set B with endpoints 6 and 10, not including 10
6  10
Set C with endpoints 20 and 25, including both endpoints
20------25
Set D with endpoints 28 and infinity, not including 28
28 ------
Set E with endpoints 28 and infinity, including 28
28 ------

4. Inequality
Examples:
Set A with endpoints 1 and 3, neither endpoint included
1 < x < 3
Set B with endpoints 6 and 10, not including 10
6 x < 10
Set C with endpoints 20 and 25, including both endpoints x
Set D with endpoints 28 and infinity, not including 28
28 < x <
Set E with endpoints 28 and infinity, including 28
x <

5. Interval Notation
A parenthesis ( ) shows an open (not included) endpoint
A bracket [ ] shows a closed [included] endpoint
Examples:
Set A with endpoints 1 and 3, neither endpoint included (1,3)
Set B with endpoints 6 and 10, not including [6,10)
Set C with endpoints 20 and 25, including both endpoints [20,25]
Set D with endpoints 28 and infinity, not including (28, )

6. Interval Notation A union U combines sets Example:
Sets A + B + C + D is written as (1,3) U [6,10) U [20,25] U (28, )

7. Inequality, Interval Notation, and Corresponding Graph
An interval may include:
Neither endpoint – Open Interval
Example: all numbers between six and ten, but not 6 nor 10
6 < x < 10 or (6,10) or 6------10
One endpoint – Half-open Interval
Example: all numbers between six and ten, but not 6
6 < x or (6,10] or 6-----10
Both endpoints – Closed Interval
Example: all numbers between six and ten, including 6 and 10
6 x or [6,10] or 6------10