Value (mathematics)

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 $\pi$ 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.

For example, if the function $f$ is defined by $f$($x$) = 2$x$2 – 3$x$ + 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.