may be expressed in terms of the Iverson bracket. The Kronecker delta notation is a specific case of Iverson notation when the condition is equality. That is, The indicator function, often denoted , or , is an Iverson bracket with set membership as its condition: The Heaviside step function, sign function, and absolute value function are also easily expressed in this notation: and The comparison functions max and min (returning the larger or smaller of two arguments) may be written as and The floor and ceiling functions can be expressed as and where the index of summation is understood to range over all the integers. The ramp function can be expressed The trichotomy of the reals is equivalent to the following identity: The Möbius function has the property (and can be defined by recurrence as) Formulation in terms of usual functions In the 1830s, Guglielmo dalla Sommaja used the expression to represent what now would be written ; he also used variants, such as for . Following one common convention, those quantities are equal where defined: is 1 if , is 0 if , and is undefined otherwise. Notational variations In addition to the now-standard square brackets and the original parentheses wiggly brackets have also been used, e.g. as well as other unusual forms of bracketing marks available in the publisher's typeface, accompanied by a marginal note. See also Boolean function Type conversion in computer programming: many languages allow numeric or pointer quantities to be used as boolean quantities Indicator function References Mathematical notation