# Category:Definitions/Functionals

This category contains definitions related to Functionals.
Related results can be found in Category:Functionals.

## Definition

A functional is a mapping:

whose domain is a set of mappings
whose codomain is another set of mappings.

### Real Functional

Let $S$ be a set of mappings.

Let $J: S \to \R$ be a mapping from $S$ to the real numbers $\R$:

$\forall y \in S: \exists x \in \R: J \sqbrk y = x$

Then $J: S \to \R$ is known as a (real) functional, denoted by $J \sqbrk y$.

That is, a (real) functional is a real-valued function whose arguments are themselves mappings.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Definitions/Functionals"

The following 3 pages are in this category, out of 3 total.