Let
be a mathematical statement, then the Iverson bracket is defined by

(1)

and corresponds to the socalled characteristic function. This notation conflicts with the brackets sometimes used to denote
the floor function. (However, because of the elegant
symmetry of the floor function and ceiling
function symbols
and ,
the use of
to denote the floor function should be deprecated.)
The Iverson bracket is implemented as a builtin function in the Wolfram
Language as Boole[S].
See also
Ceiling Function,
Characteristic
Function,
Floor Function
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References
Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete
Mathematics: A Foundation for Computer Science. Reading, MA: AddisonWesley,
p. 24, 1990.Iverson, K. E. A
Programming Language. New York: Wiley, p. 11, 1962.Referenced
on WolframAlpha
Iverson Bracket
Cite this as:
Weisstein, Eric W. "Iverson Bracket."
From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/IversonBracket.html
Subject classifications