# Difference between revisions of "Intervals"

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− | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}} |

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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|Min]], [[Max Command|Max]], [[Midpoint Command|Midpoint]] for an interval with lower bound ''a'' and upper bound ''b'' return numbers ''a'', ''b'' and <math>\frac{a+b}2</math> 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. |

## Latest revision as of 13:18, 5 August 2015

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 for an interval with lower bound
*a*and upper bound*b*return numbers*a*,*b*and \frac{a+b}2 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.