Difference between revisions of "Prove Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|logical}}{{betamanual|version=5.0}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|logical}}{{betamanual|version=5.0}} | ||
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;Prove[ <Boolean Expression> ]: Returns whether the given boolean expression is true or false in general. | ;Prove[ <Boolean Expression> ]: Returns whether the given boolean expression is true or false in general. | ||
Normally, GeoGebra decides whether a [[Boolean_values|boolean expression]] is true or not by using numerical computations. However, the Prove command uses [[w:Symbolic_computation|symbolic methods]] to determine whether a statement is ''true'' or ''false'' in general. If GeoGebra cannot determine the answer, the result is ''undefined''. | Normally, GeoGebra decides whether a [[Boolean_values|boolean expression]] is true or not by using numerical computations. However, the Prove command uses [[w:Symbolic_computation|symbolic methods]] to determine whether a statement is ''true'' or ''false'' in general. If GeoGebra cannot determine the answer, the result is ''undefined''. | ||
Revision as of 10:48, 5 September 2014
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This page is about a feature that is supported only in GeoGebra 5.0. |
- Prove[ <Boolean Expression> ]
- Returns whether the given boolean expression is true or false in general.
Normally, GeoGebra decides whether a boolean expression is true or not by using numerical computations. However, the Prove command uses symbolic methods to determine whether a statement is true or false in general. If GeoGebra cannot determine the answer, the result is undefined.
Example:
We define three free points,
A=(1,2), B=(3,4), C=(5,6). The command AreCollinear[A,B,C] yields true, since a numerical check is used on the current coordinates of the points. Using Prove[AreCollinear[A,B,C]] you will get false as an answer, since the three points are not collinear in general, i.e. when we change the points.Example:
Let us define a triangle with vertices A, B and C, and define
D=MidPoint[B,C], E=MidPoint[A,C], p=Line[A,B], q=Line[D,E]. Now both p∥q and Prove[p∥q] yield true, since a midline of a triangle will always be parallel to the appropriate side.
Note: See also ProveDetails command, Boolean values and technical details of the algorithms.
