Domains And Domain Walls
Domain may refer to: Mathematics *Domain of a function, the set of input values for which the (total) function is defined **Domain of definition of a partial function **Natural domain of a partial function **Domain of holomorphy of a function *Domain (mathematical analysis), an open connected set *Domain of discourse, the set of entities over which logic variables may range *Algebraic structure, Domain of an algebraic structure, the set on which the algebraic structure is defined *Domain theory, the study of certain subsets of continuous lattices that provided the first denotational semantics of the lambda calculus *Domain (ring theory), a nontrivial ring without left or right zero divisors **Integral domain, a non-trivial commutative ring without zero divisors ***Atomic domain, an integral domain in which every non-zero non-unit is a finite product of irreducible elements ***Bézout domain, an integral domain in which the sum of two principal ideals is again a principal ideal ***Eu ...
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Domain Of A Function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by \operatorname(f) or \operatornamef, where is the function. More precisely, given a function f\colon X\to Y, the domain of is . Note that in modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that and are both subsets of \R, the function can be graphed in the Cartesian coordinate system. In this case, the domain is represented on the -axis of the graph, as the projection of the graph of the function onto the -axis. For a function f\colon X\to Y, the set is called the codomain, and the set of values attained by the function (which is a subset of ) is called its range or image. Any function can be restricted to a subset of its domain. The restriction of f \colon X \to Y to A, where A\subseteq X, is written as \left. f \_A \colon A \to Y. Natural domain If a real function is giv ...
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