Iverson Bracket

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

(1)

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  and , the use of  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].

REFERENCES:

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.