Difference between revisions of "Interval"

(Symbols: sometimes infinity and -infinity can be used as endpoints)
(Symbols)
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== Symbols ==
 
== Symbols ==
  
If an interval has either ( or ) on it, the values at the end are NOT included.
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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. 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 ] on it, the values at the end ARE included.
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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: <math>-\infty</math> and <math>\infty</math> are generally not included as endpoints.
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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.'''
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''Note'': The symbols <math>(</math> and <math>)</math> are used with <math>-\infty</math> and <math>\infty.</math>
  
 
== Examples ==
 
== Examples ==

Revision as of 23:10, 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 $x \in (3,5)$ refers to the inequality $3 < x < 5.$

If an interval has either $[$ or $]$ in it, the values at the end ARE included. For example, the interval $x \in [2.5,7]$ refers to the inequality $2.5 \le x \le 7.$

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 $\infty.$

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