Difference between revisions of "Interval"
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== Symbols == | == Symbols == | ||
| − | If an interval has either ( or ) | + | If an interval has either <math>(</math> or <math>)</math> in it, the values at the end are '''NOT''' included in the interval. For example, the interval <math>x \in (3,5)</math> refers to the inequality <math>3 < x < 5.</math> |
| − | If an interval has either [ or ] | + | If an interval has either <math>[</math> or <math>]</math> in it, the values at the end '''ARE''' included. For example, the interval <math>x \in [2.5,7]</math> refers to the inequality <math>2.5 \le x \le 7.</math> |
| − | Note: | + | If both endpoints are not included, then the interval is '''open.''' If both endpoints are included, then the interval is '''closed.''' |
| + | |||
| + | ''Note'': The symbols <math>(</math> and <math>)</math> are used with <math>-\infty</math> and <math>\infty.</math> | ||
== Examples == | == Examples == | ||
Revision as of 22:10, 16 August 2013
Definition
An interval is a range of values. The most common uses of an interval are for domain and range.
Symbols
If an interval has either 
or 
in it, the values at the end are NOT included in the interval. For example, the interval 
refers to the inequality 
If an interval has either 
or ![$]$](http://latex.artofproblemsolving.com/0/7/1/07174a92e49be0bb0db1beef2bb6c245a8b212f9.png)
in it, the values at the end ARE included. For example, the interval ![$x \in [2.5,7]$](http://latex.artofproblemsolving.com/7/6/9/76939e9b8a6d002b8843fd521d0684564cafd0b7.png)
refers to the inequality 
If both endpoints are not included, then the interval is open. If both endpoints are included, then the interval is closed.
Note: The symbols and are used with 
and 
Examples
- (2,3) means all real values between 2 and 3, but not including 2 and 3
- [-2,0) means all real values between -2 and 0, but does not include 0
