- Boolean domain
In

mathematics andabstract algebra , a**Boolean domain**is a set consisting of exactly two elements whose interpretations include "false" and "true". In mathematics andtheoretical computer science , a Boolean domain is usually written as {0,1} or $\{ot,\; op\}$.The

algebraic structure that naturally builds on a Boolean domain is the Boolean algebra with two elements. Theinitial object in the category ofbounded lattice s is a Boolean domain. TheSierpiński space, a certaintopological space with two elements, resembles a Boolean domain.In

computer science , a**Boolean variable**is avariable that takes values in some Boolean domain. Someprogramming language s featurereserved word s or symbols for the elements of the Boolean domain, for example`false`

and`true`

. However, many programming languages do not have aBoolean datatype in the strict sense. In C orBASIC , for example, falsity is represented by the number 0 and truth is represented by the number 1 or -1, respectively, and all variables that can take these values can also take any other numerical values.**ee also***

Boolean-valued function

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Boolean algebras canonically defined**— Boolean algebras have been formally defined variously as a kind of lattice and as a kind of ring. This article presents them more neutrally but equally formally as simply the models of the equational theory of two values, and observes the… … Wikipedia**Boolean logic**— is a complete system for logical operations. It was named after George Boole, who first defined an algebraic system of logic in the mid 19th century. Boolean logic has many applications in electronics, computer hardware and software, and is the… … Wikipedia**Boolean algebra (logic)**— For other uses, see Boolean algebra (disambiguation). Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of… … Wikipedia**Boolean-valued function**— A boolean valued function, in some usages a predicate or a proposition, is a function of the type f : X → B, where X is an arbitrary set and where B is a boolean domain.A boolean domain B is a generic 2 element set, say, B = {0, 1}, whose… … Wikipedia**Boolean algebra**— This article discusses the subject referred to as Boolean algebra. For the mathematical objects, see Boolean algebra (structure). Boolean algebra, as developed in 1854 by George Boole in his book An Investigation of the Laws of Thought,[1] is a… … Wikipedia**Boolean function**— In mathematics, a (finitary) Boolean function is a function of the form f : B k rarr; B, where B = {0, 1} is a Boolean domain and k is a nonnegative integer called the arity of the function. In the case where k = 0, the function is essentially a… … Wikipedia**Boolean algebra (structure)**— For an introduction to the subject, see Boolean algebra#Boolean algebras. For the elementary syntax and axiomatics of the subject, see Boolean algebra (logic). For an alternative presentation, see Boolean algebras canonically defined. In abstract … Wikipedia**Boolean analysis**— was introduced by Flament (1976). The goal of a Boolean analysis is to detect deterministic dependencies between the items of a questionnaire in observed response patterns. These deterministic dependencies have the form of logical formulas… … Wikipedia**Boolean algebra (introduction)**— Boolean algebra, developed in 1854 by George Boole in his book An Investigation of the Laws of Thought , is a variant of ordinary algebra as taught in high school. Boolean algebra differs from ordinary algebra in three ways: in the values that… … Wikipedia**Domain of a function**— Venn diagram showing f, a function from domain X to codomain Y. The smaller oval inside Y is the image of f, sometimes called the range of f. In mathematics, the domain of definition or simply the domain of a function is the set of input or… … Wikipedia