Difference between revisions of "Interval"
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== Definition == | == Definition == | ||
| − | An '''interval''' is a range of values. | + | An '''interval''' is a continuous range of values, such as all of the real numbers between <math>-2</math> and <math>0,</math> inclusive. The most common uses of an interval are to specify the [[Domain_(function) | domain]] and [[range]] of a [[function]]. |
== Symbols == | == Symbols == | ||
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If an interval has either <math>(</math> or <math>)</math> in it, the values at the end are '''NOT''' included in the interval. | If an interval has either <math>(</math> or <math>)</math> in it, the values at the end are '''NOT''' included in the interval. | ||
| − | If an interval has either <math>[</math> or <math>]</math> in it, the values at the end '''ARE''' included. | + | If an interval has either <math>[</math> or <math>]</math> in it, the values at the end '''ARE''' included. |
If both endpoints are not included, then the interval is '''open.''' If both endpoints are included, then the interval is '''closed.''' | 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 | + | ''Note'': The symbols <math>(</math> and <math>)</math> are used with <math>-\infty</math> and <math>\infty,</math> by convention. |
== Examples == | == Examples == | ||
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* <math>[5, \infty)</math> means all real numbers greater than or equal to <math>5.</math> | * <math>[5, \infty)</math> means all real numbers greater than or equal to <math>5.</math> | ||
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| + | * <math>[6,98]</math> means all real numbers between <math>6</math> and <math>98</math>, including <math>6</math> and <math>98.</math> | ||
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| + | Use latex \infty for infinity symbol and use latex \cup for OR symbol. | ||
Latest revision as of 19:34, 5 January 2024
Definition
An interval is a continuous range of values, such as all of the real numbers between 
and 
inclusive. The most common uses of an interval are to specify the domain and range of a function.
Symbols
If an interval has either 
or 
in it, the values at the end are NOT included in the interval.
If an interval has either 
or ![$]$](http://latex.artofproblemsolving.com/0/7/1/07174a92e49be0bb0db1beef2bb6c245a8b212f9.png)
in it, the values at the end ARE included.
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 
by convention.
Examples
means all real numbers between 
and 
but not including or 
means all real numbers between 
and 
but not including 
means all real numbers between 
and 
including 
but not including 
means all real numbers between 
but not including 
means all real numbers greater than or equal to 
means all real numbers greater than or equal to 
![$[6,98]$](//latex.artofproblemsolving.com/2/b/a/2ba2c872140660f745f26928def43d38aad8dffb.png)
means all real numbers between 
and 
, including and 
![$[6,98]$](http://latex.artofproblemsolving.com/2/b/a/2ba2c872140660f745f26928def43d38aad8dffb.png)
means all real numbers between 
and 
, including 
Use latex \infty for infinity symbol and use latex \cup for OR symbol.
