# Difference between revisions of "Intervals"

From GeoGebra Manual

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An interval is a set of numbers between upper and lower bound. To create an interval, type e.g. <code>2 < x < 3</code> in [[Input Bar]]. Interval in previous example is open. You can also define closed (<code>2 ≤ x ≤ 3</code>) and semi-closed (<code>2 ≤ x < 3</code>) intervals. | An interval is a set of numbers between upper and lower bound. To create an interval, type e.g. <code>2 < x < 3</code> in [[Input Bar]]. Interval in previous example is open. You can also define closed (<code>2 ≤ x ≤ 3</code>) and semi-closed (<code>2 ≤ x < 3</code>) intervals. | ||

{{Note|See also [[Boolean values]].}} | {{Note|See also [[Boolean values]].}} | ||

− | To determine whether number ''c'' belongs to interval ''r'' type <code>r(c)</code> into the Input Bar, the result will be a Boolean value. Generalization of intervals are [[ | + | To determine whether number ''c'' belongs to interval ''r'' type <code>r(c)</code> into the Input Bar, the result will be a Boolean value. Generalization of intervals are [[Inequalities]]. |

==Commands for intervals== | ==Commands for intervals== | ||

* [[Min Command|Min]], [[Min Command|Max]], [[Min Command|Midpoint]], [[Length Command|Length]] for interval with lower bound ''a'' and upper bound ''b'' return numbers ''a'', ''b'', <math>\frac{a+b}2</math> and ''b-a'' respectively. The result doesn't depend on whether the interval is open, closed or semi-closed. | * [[Min Command|Min]], [[Min Command|Max]], [[Min Command|Midpoint]], [[Length Command|Length]] for interval with lower bound ''a'' and upper bound ''b'' return numbers ''a'', ''b'', <math>\frac{a+b}2</math> and ''b-a'' respectively. The result doesn't depend on whether the interval is open, closed or semi-closed. | ||

* [[Point Command|Point]] returns a moveable [[Points and Vectors|point]] whose x-coordinate belongs to the interval and y-coordinate is 0. | * [[Point Command|Point]] returns a moveable [[Points and Vectors|point]] whose x-coordinate belongs to the interval and y-coordinate is 0. | ||

* [[PointIn Command|PointIn]] returns a moveable point whose x-coordinate belongs to the interval and y-coordinate may be changed arbitrarily. | * [[PointIn Command|PointIn]] returns a moveable point whose x-coordinate belongs to the interval and y-coordinate may be changed arbitrarily. |

## Revision as of 15:41, 15 August 2011

An interval is a set of numbers between upper and lower bound. To create an interval, type e.g. `2 < x < 3`

in Input Bar. Interval in previous example is open. You can also define closed (`2 ≤ x ≤ 3`

) and semi-closed (`2 ≤ x < 3`

) intervals.

**Note:**See also Boolean values.

To determine whether number *c* belongs to interval *r* type `r(c)`

into the Input Bar, the result will be a Boolean value. Generalization of intervals are Inequalities.

## Commands for intervals

- Min, Max, Midpoint, Length for interval with lower bound
*a*and upper bound*b*return numbers*a*,*b*, \frac{a+b}2 and*b-a*respectively. The result doesn't depend on whether the interval is open, closed or semi-closed. - Point returns a moveable point whose x-coordinate belongs to the interval and y-coordinate is 0.
- PointIn returns a moveable point whose x-coordinate belongs to the interval and y-coordinate may be changed arbitrarily.