Value (mathematics)

{{Short description|Notion in mathematics}}

{{more citations needed|date=January 2014}}

In mathematics, value may refer to several, strongly related notions.

In general, a mathematical value may be any definite mathematical object. In elementary mathematics, this is most often a number – for example, a real number such as {{mvar|π}} or an integer such as 42.

• The value of a variable or a constant is any number or other mathematical object assigned to it. Physical quantities have numerical values attached to units of measurement.
• The value of a mathematical expression is the object assigned to this expression when the variables and constants in it are assigned values.
• The value of a function, given the value(s) assigned to its argument(s), is the quantity assumed by the function for these argument values.{{Cite web|url=http://mathworld.wolfram.com/Value.html|title = Value}}

{{cite book

|last=Meschkowski

|first=Herbert

|title=Introduction to Modern Mathematics|date=1968|publisher=George G. Harrap & Co. Ltd.

|isbn=0245591095

|page=32

|url=https://archive.org/details/IntroductionToModernMathematics}}

For example, if the function {{mvar|f}} is defined by {{nowrap|1={{mvar|f}}({{mvar|x}}) = 2{{mvar|x}}² – 3{{mvar|x}} + 1}}, then assigning the value 3 to its argument {{mvar|x}} yields the function value 10, since {{nowrap|1={{mvar|f}}(3) = 2·3² – 3·3 + 1 = 10}}.

If the variable, expression or function only assumes real values, it is called real-valued. Likewise, a complex-valued variable, expression or function only assumes complex values.