Let S be a mathematical statement, then the Iverson bracket is defined by [S] congruent {0 | if S is false 1 | if S is true, auto right match 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].

ceiling function | characteristic function | floor function

Boole