Value (mathematics)

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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 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.^[1][2]

For example, if the function f is defined by f(x) = 2x² – 3x + 1, then assigning the value 3 to its argument x yields the function value 10, since 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.