Iverson Bracket

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

$$[S]\equiv\cases{ 0 & if $S$\ is false\cr 1 & if $S$\ is true.\cr}$$

This notation conflicts with the brackets sometimes used to denote the Floor Function. For this reason, and because of the elegant symmetry of the Floor Function and Ceiling Function symbols $\left\lfloor{x}\right\rfloor$ and $\left\lceil{x}\right\rceil$, the use of $[x]$ to denote the Floor Function should be deprecated.

See also Ceiling Function, Floor Function

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.