# Category:Functionals

Jump to navigation
Jump to search

This category contains results about **Functionals**.

Definitions specific to this category can be found in Definitions/Functionals.

## Definition

A **functional** is a mapping:

### 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.

## Examples

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**functional** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**functional**

*This category currently contains no pages or media.*