# Category:Definitions/Functionals

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This category contains definitions related to Functionals.

Related results can be found in Category:Functionals.

## Definition

### Real Functional

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.