1. Algebra Review
Intervals
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Intervals

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:
Finite:
Open - does not include the endpoints
Closed - does include the endpoints
Semi-Infinite - includes one endpoint
Infinite: one or both endpoints are infinity
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Intervals

3. 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 <
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Intervals

4. 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, )
A union U combines sets
Example:
Sets A + B + C + D is written as (1,3) U [6,10) U [20,25] U (28, )
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Intervals

5. 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 ------
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Intervals

6. Inequality, Interval Notation, and Corresponding Graph
An interval may include:
Neither endpoint - open set
Example: all numbers between six and ten, but not 6 nor 10
6 < x < 10 or (6,10) or 6------10
One endpoint
Example: all numbers between six and ten, but not 6
6 < x or (6,10] or 6-----10
Both endpoints - closed set
Example: all numbers between six and ten, including 6 and 10
6 x or [6,10] or 6------10
4/6/99
Intervals