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In
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
, an argument of a
function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern comp ...
is a value that must be provided to obtain the function's result. It is also called an
independent variable Dependent and Independent variables are variables in mathematical modeling A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to f ...
. For example, the
binary function In mathematics, a binary function (also called bivariate function, or function of two variables) is a function (mathematics), function that takes two inputs. Precisely stated, a function f is binary if there exists Set (mathematics), sets X, Y, Z ...
$f\left(x,y\right) = x^2 + y^2$ has two arguments, $x$ and $y$, in an
ordered pair In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...

$\left(x, y\right)$. The
hypergeometric function In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
is an example of a four-argument function. The number of arguments that a function takes is called the
arity Arity () is the number of arguments In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also related to (''logo ...
of the function. A function that takes a single argument as input (such as $f\left(x\right) = x^2$) is called a
unary function A unary function is a function that takes one argument In logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, lit=possessed of reason, intellectual, dialectical, argumentative, translit=logikḗ)Also ...
. A function of two or more variables is considered to have a
domain 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 *Doma ...
consisting of ordered pairs or
tuple In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
s of argument values. The argument of a
circular function In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
is an
angle In Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematics , Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's method c ...

. The argument of a
hyperbolic function In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities an ...

is a
hyperbolic angle is in ''standard position'' if In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathe ...

. A mathematical function has one or more arguments in the form of independent variables designated in the definition, which can also contain
parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whol ...
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 In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
$f\left(x\right) = \log_b\left(x\right),$ the
base Base or BASE may refer to: Brands and enterprises * Base (mobile telephony provider), a Belgian mobile telecommunications operator *Base CRM Base CRM (originally Future Simple or PipeJump) is an enterprise software company based in Mountain Vie ...
$b$ is considered a parameter. Sometimes,
subscript A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the Baseline (typog ...

s can be used to denote arguments. For example, we can use subscripts to denote the arguments with respect to which
partial derivative In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

s are taken. The use of the term "argument" in this sense developed from
astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...
, which historically used tables to determine the spatial positions of planets from their positions in the sky. These tables were organized according to measured angles called arguments, literally "that which elucidates something else."

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Domain of a function In mathematics, the domain of a Function (mathematics), function is the Set (mathematics), set of inputs accepted by the function. It is sometimes denoted by \operatorname(f), where is the function. More precisely, given a function f\colon X\t ...
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Value (mathematics) In mathematics, value may refer to several, strongly related notions. In general, a mathematical value may be any definite mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematic ...
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Propositional function In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of logical truth, true or false (logic), false, except that within the sentence there is a Variable (mathematics), variab ...
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Parameter (computer programming)In computer programming Computer programming is the process of designing and building an executable computer program to accomplish a specific computing result or to perform a specific task. Programming involves tasks such as: analysis, generatin ...