# Number-Output Function

A Number-Output Function is a measure function whose function range is a numeric interval.

**AKA:**Scalar Output Function.**Context:**- It can range from being a Positive Function to being a Non-Negative Function to being a Non-Positive Function to being a Negative Function.
- It can range from being an Integer-Output Function, to being a Rational-Output Function, to being an Irrational-Output Function, to being a Real-Output Function, to being an Imaginary-Output Function.
- It can range, based on its function domain type, from being a Number-Input Numeric-Output Function, to being a Set-Input Numeric-Output Function, to being a Tuple-Input Numeric-Output Function, to being a Vector-Input Numeric-Output Function.

**Example(s):**- A Continuous Random Variable, such as
*f()*=>302.7, from a Lightbulb Lifetime Experiment. - An Arithmetic Function, such as
*addition*(3.3,4.1,0.1) =>7.5 - A Unit Function, such as a Probability Function
*P*(*X*=Heads) =>0.5 - a Distance Function, such as a Vector Distance Function [math]f[/math]((1,5),(4,1)) =>5.0
- a Polynomial Function.
- …

- A Continuous Random Variable, such as
**Counter-Example(s):****See:**Number-Input Function, Categorical Function, Differentiable Function, Tuple-Output Function.

## References

### 2013

- http://en.wikipedia.org/wiki/Scalar_function
- In mathematics and physics, a
**scalar field**associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same point in space (or spacetime). Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory

- In mathematics and physics, a

- http://en.wikipedia.org/wiki/Scalar_function#Definition
- Mathematically, a scalar field on a region
*U*is a real or complex-valued function or distribution on*U*.^{[1]}^{[2]}The region*U*may be a set in some Euclidean space, Minkowski space, or more generally a subset of a manifold, and it is typical in mathematics to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order. A scalar field is a tensor field of order zero,^{[3]}and the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form.Physically, a scalar field is additionally distinguished by having units of measurement associated with it. In this context, a scalar field should also be independent of the coordinate system used to describe the physical system—that is, any two observers using the same units must agree on the numerical value of a scalar field at any given point of physical space. Scalar fields are contrasted with other physical quantities such as vector fields, which associate a vector to every point of a region, as well as tensor fields and spinor fields.

^{[citation needed]}More subtly, scalar fields are often contrasted with pseudoscalar fields.

- Mathematically, a scalar field on a region

- ↑ Template:Citation
- ↑ Template:Springer
- ↑ {springer|id=s/s083260|title=Scalar field}}

### 2009

- http://en.wiktionary.org/wiki/scalar_function
- Noun" 1. (mathematics) Any function whose domain is a vector space and whose value is its scalar field

- Eric W. Weisstein. "Scalar Function." From MathWorld -- A Wolfram Web Resource.
- Scalar Function: A function [math]f(x_1,...,x_n)[/math] of one or more variables whose range is one-dimensional, as compared to a vector function, whose range is three-dimensional (or, in general, n-dimensional).