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Interval: Difference between revisions

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== Definition ==
== Definition ==


An '''interval''' is a range of values. The most common uses of an interval are for [[domain]] and [[range]].
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 ==


If an interval has either ( or ) on it, the values at the end are NOT included.
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 [ or ] on 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.


Note: <math>-\infty</math> and <math>\infty</math> are never included as endpoints
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> by convention.


== Examples ==
== Examples ==


*  (2,3) means all real values between 2 and 3, but not including 2 and 3
*  <math>(2,3)</math> means all real numbers between <math>2</math> and <math>3,</math> but not including <math>2</math> or <math>3.</math>
 
* <math>[-2,0)</math> means all real numbers between <math>-2</math> and <math>0,</math> including <math>-2,</math> but not including <math>0.</math>
 
* <math>[5, \infty)</math> means all real numbers greater than or equal to <math>5.</math>
 
* <math>[6,98]</math> means all real numbers between <math>6</math> and <math>98</math>, including <math>6</math> and <math>98.</math>
 


*  [-2,0) means all real values between -2 and 0, but does not include 0
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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