Value (mathematics) - AbsoluteAstronomy.com

In mathematics, value commonly refers to the 'output' 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...

. In the most basic case, that of unary

Unary 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....

, single-valued functions, there is one input (the argument

Argument of a function

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....

) and one output (the value of the function).

Example: If the function

is defined by prescribing that

for each real number

, then the input 3 will yield the function value 10 (since indeed ).

The function

of the example is real-valued, since each and every possible function value is real. On the other hand, it is not injective, since different inputs may yield the same value; e.g.,

, too.

In some contexts, for convenience, functions may be considered to have several arguments

Arity

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...

and/or several values

Multivalued function

In mathematics, a multivalued function is a left-total relation; i.e. every input is associated with one or more outputs...

; also cf. the discussion in the article function. However, strictly seen, this is not an extension, since such functions may be considered as having single families and/or sets as input or output.

Value is also used in other senses, e.g., to specify a certain instance of a variable

Variable (mathematics)

In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...

Example:

for two separate values of

, namely, for

and for

See also