# Intervals

From GeoGebra Manual

Revision as of 19:07, 15 August 2011 by Mathmum (talk | contribs) (→Commands for intervals: fixed command names)

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 an 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.