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In mathematics, value commonly refers to the 'output' of a function
Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
. In the most basic case, that of unary, single-valued functions, there is one input (the argument) 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.






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In mathematics, value commonly refers to the 'output' of a function
Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
. In the most basic case, that of unary, single-valued functions, there is one input (the argument) 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 number of domains in the corresponding Cartesian product....
 and/or several values
Multivalued function

In mathematics, a multivalued function is a total relation; i.e. every input is associated with one or more outputs. Strictly speaking, a "well-defined" function associates one, and only one, output to any particular input....
; also cf. the discussion in the article function
Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
. 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

A variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e....
.
Example: for two separate values of , namely, for and for .


See also

  • Absolute value
    Absolute value

    In mathematics, the absolute value of a real number is its numerical value without regard to its Negative and non-negative numbers. So, for example, 3 is the absolute value of both 3 and -3....
  • Valuation (mathematics)
    Valuation (mathematics)

    In algebra , a valuation is a Function on a Field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size inherent in consideration of the degree of a pole or Multiplicity of a zero in complex analysis, the degree divisibility of a number by a prime number in num...
  • Value distribution theory of holomorphic functions
    Value distribution theory of holomorphic functions

    In mathematics, the value distribution theory of holomorphic functions is a division of mathematical analysis. It tries to get quantitative measures of the number of times a function f assumes a value a, as z grows in size, refining the Picard theorem on behaviour close to an essential singularity....