Difference between revisions of "Intervals"

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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 [[Inequlaities]].  
+
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.
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