Iverson Bracket

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

 [S]={0   if S is false; 1   if S is true,

and corresponds to the so-called 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 |_x_| and [x], the use of [x] to denote the floor function should be deprecated.)

The Iverson bracket is implemented as a built-in function in the Wolfram Language as Boole[S].

See also

Ceiling Function, Characteristic Function, Floor Function

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Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science. Reading, MA: Addison-Wesley, p. 24, 1990.Iverson, K. E. A Programming Language. New York: Wiley, p. 11, 1962.

Referenced on Wolfram|Alpha

Iverson Bracket

Cite this as:

Weisstein, Eric W. "Iverson Bracket." From MathWorld--A Wolfram Web Resource.

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