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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 ...
t. e. In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.
In mathematics, for a function , the image of an input value is the single output value produced by when passed . The preimage of an output value is the set of input values that produce . More generally, evaluating at each element of a given subset of its domain produces a set, called the " image of under (or through) ".
Piecewise function. In mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned into several intervals ("subdomains") on which the function may be defined differently. [1][2][3] Piecewise definition is actually a way of specifying ...
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.
A theory about a topic, such as set theory, a theory for groups, [3] or a formal theory of arithmetic, is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of axioms ...
A binomial coefficient gives the number of ways to choose k elements from a set of n elements; if k > n, there are of course no ways. If k > n , ( n − k )! is the factorial of a negative integer and hence infinite if we use the gamma function definition of factorials—dividing by infinity gives the expected value of 0.
In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. [1][2][3] Contour integration is closely related to the calculus of residues, [4] a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that are ...