Argument of a function
Encyclopedia
In mathematics
, an argument of a function
is a specific input in the function, also known as an independent variable
. When it is clear from the context which argument is meant, the argument is often denoted by arg.
A mathematical function has one or more arguments in the form of independent variables
designated in the function's definition, which can also contain parameter
s. The independent variables are mentioned in the list of arguments that the function takes, whereas the parameters are not. For example, in the logarithmic function
, the base b is considered a parameter.
A function that takes a single argument as input (such as
) is called a unary function
. A function of two or more variables is considered to have a domain
consisting of ordered pair
s or tuple
s of argument values. For example, the binary function
has two arguments, x and y, in an ordered pair 
. 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.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, an argument of a function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
is a specific input in the function, also known as an independent variable
Dependent and independent variables
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
. When it is clear from the context which argument is meant, the argument is often denoted by arg.
A mathematical function has one or more arguments in the form of independent variables
Dependent and independent variables
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
designated in the function's definition, which can also contain parameter
Parameter
Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....
s. The independent variables are mentioned in the list of arguments that the function takes, whereas the parameters are not. For example, in the logarithmic function
, the base b is considered a parameter.A function that takes a single argument as input (such as
) is called a unary functionUnary function
A unary function is a function that takes one argument. In computer science, a unary operator is a subset of unary function.Many of the elementary functions are unary functions, in particular the trigonometric functions and hyperbolic function are unary....
. A function of two or more variables is considered to have a domain
Domain (mathematics)
In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined...
consisting of ordered pair
Ordered pair
In mathematics, an ordered pair is a pair of mathematical objects. In the ordered pair , the object a is called the first entry, and the object b the second entry of the pair...
s or tuple
Tuple
In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair...
s of argument values. For example, the binary function
Binary function
In mathematics, a binary function, or function of two variables, is a function which takes two inputs.Precisely stated, a function f is binary if there exists sets X, Y, Z such that\,f \colon X \times Y \rightarrow Z...
has two arguments, x and y, in an ordered pair . The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the arityArity
In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes. The arity of a relation is the dimension of the domain in the corresponding Cartesian product...
of the function.