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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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* <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 18:34, 5 January 2024

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 $5.$
  • $[6,98]$ means all real numbers between $6$ and $98$, including $6$ and $98.$


Use latex \infty for infinity symbol and use latex \cup for OR symbol.

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