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⭐ Core Definition: Argument of a function

In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable.

For example, the binary function $f(x,y)=x^{2}+y^{2}$ has two arguments, $x$ and $y$ , in an ordered pair $(x,y)$ . The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the arity of the function. A function that takes a single argument as input, such as $f(x)=x^{2}$ , is called a unary function. A function of two or more variables is considered to have a domain consisting of ordered pairs or tuples of argument values. The argument of a circular function is an angle. The argument of a hyperbolic function is a hyperbolic angle.

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👉 Argument of a function in the context of Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory.The limit inferior and limit superior provide generalizations of the concept of a limit which are particularly relevant when the limit at a point may not exist.

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⭐ Core Definition: Argument of a function
👉 Argument of a function in the context of Limit (mathematics)
Argument of a function in the context of Optimal
Argument of a function in the context of Continuous function
Argument of a function in the context of Adicity
Argument of a function in the context of Categorial grammar

Argument of a function in the context of Optimal

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics.

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Argument of a function in the context of Continuous function

Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the most general continuous functions, and their definition is the basis of topology.

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Argument of a function in the context of Adicity

In logic, mathematics, and computer science, arity (/ˈærɪti/ ) is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and philosophy, arity may also be called adicity and degree. In linguistics, it is usually named valency.

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Argument of a function in the context of Categorial grammar

Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and semantic composition, since it typically treats syntactic categories as corresponding to semantic types. Categorial grammars were developed in the 1930s by Kazimierz Ajdukiewicz and in the 1950s by Yehoshua Bar-Hillel and Joachim Lambek. It saw a surge of interest in the 1970s following the work of Richard Montague, whose Montague grammar assumed a similar view of syntax. It continues to be a major paradigm, particularly within formal semantics.

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Argument of a function in the context of "Limit (mathematics)"

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⭐ Core Definition: Argument of a function

👉 Argument of a function in the context of Limit (mathematics)

Argument of a function in the context of Optimal

Argument of a function in the context of Continuous function

Argument of a function in the context of Adicity

Argument of a function in the context of Categorial grammar