Editing Functional (mathematics) (section)

===Duality===
The mapping
<math display=block>x_0 \mapsto f(x_0)</math>
is a function, where <math>x_0</math> is an [[argument of a function]] <math>f.</math> 
At the same time, the mapping of a function to the value of the function at a point
<math display=block>f \mapsto f(x_0)</math>
is a ''functional''; here, <math>x_0</math> is a [[parameter]].

Provided that <math>f</math> is a linear function from a vector space to the underlying scalar field, the above linear maps are [[Duality (mathematics)|dual]] to each other, and in functional analysis both are called [[linear functional]]s.