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Difference between revisions of "Interval"

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== Definition ==
 
== Definition ==
  
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An '''interval''' is a range of values. The most common uses of an interval are to specify the [http://www.artofproblemsolving.com/Wiki/index.php/Domain_(function) domain] and [[range]] of a [[function]].
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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 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.'''
  
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''Note'': The symbols <math>(</math> and <math>)</math> are used with <math>-\infty</math> and <math>\infty,</math> by convention
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''Note'': The symbols <math>(</math> and <math>)</math> are used with <math>-\infty</math> and <math>\infty,</math> by convention.
  
 
== Examples ==
 
== Examples ==

Revision as of 23:22, 16 August 2013

Definition

An interval is a continuous range of values, such as all of the real numbers between $-2$ and $0,$ 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 $]$ 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 $-\infty$ and $\infty,$ by convention.

Examples

  • $(2,3)$ means all real numbers between $2$ and $3,$ but not including $2$ or $3.$
  • $[-2,0)$ means all real numbers between $-2$ and $0,$ including $-2,$ but not including $0.$
  • $[5, \infty)$ means all real numbers greater than or equal to $5.$
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