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In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by or , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be". [1] More precisely, given a function , the domain of f is X. In modern mathematical language, the domain is ...
e. In mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. [1][2] Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility. In an integral domain, every nonzero element a has the cancellation property, that is, if a ...
The tensor algebra of a vector space, or equivalently, the algebra of polynomials in noncommuting variables over a field, K x 1 , … , x n , {\displaystyle \mathbb {K} \langle x_ {1},\ldots ,x_ {n}\rangle ,} is a domain. This may be proved using an ordering on the noncommutative monomials. If R is a domain and S is an Ore extension of R then S ...
In mathematical analysis, a domain or region is a non-empty, connected, and open set in a topological space. In particular, it is any non-empty connected open subset of the real coordinate space Rn or the complex coordinate space Cn. A connected open subset of coordinate space is frequently used for the domain of a function.
In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL 's use of SELECT) is a unary operation written as or where: and are attribute names, is a binary operation in the set. is a value constant, is a relation. The selection selects all those tuples in for which holds between the and the attribute.
Range of a function. is a function from domain X to codomain Y. The yellow oval inside Y is the image of . Sometimes "range" refers to the image and sometimes to the codomain. In mathematics, the range of a function may refer to either of two closely related concepts: the codomain of the function, or. the image of the function.
t. e. In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that these operations must satisfy. An algebraic structure may be based ...
e. In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set X into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication.
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