- Boole is also known as Iverson bracket, indicator function and characteristic function.
- Boole is typically used to express integrals and sums over regions given by logical combinations of predicates. It is also used as a dummy variable encoding for categorical variables in statistics.
- Boole[expr] remains unchanged if expr is neither True nor False.
- Boole[expr] is effectively equivalent to If[expr,1,0].
- Boole is Listable.
- Integrate[f Boole[pred],…] can be used to integrate f over the region in which pred is True.
Examplesopen allclose all
Basic Examples (3)
Properties & Relations (7)
The inverse of Boole:
Use PiecewiseExpand to convert Boole to Piecewise:
Correspondence between logic operations on conditions and arithmetic operations on Boole:
Use Refine, Simplify, and FullSimplify to transform expressions involving Boole:
Reduce equations and optimize functions involving Boole:
Use Boole as a characteristic function for integration problems:
Boole can be represented as a DifferenceRoot in certain cases:
Wolfram Research (2004), Boole, Wolfram Language function, https://reference.wolfram.com/language/ref/Boole.html (updated 2007).
Wolfram Language. 2004. "Boole." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/Boole.html.
Wolfram Language. (2004). Boole. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Boole.html