# Absolute value

From Maths

This page is a

*dire page*and is in desperate need of an update.The message is:

Need of update, standardisation of layout, link to triangle inequality, link to norm of reals, link to metric spaces

(Unknown grade)

This page requires references, it is on a to-do list for being expanded with them.

Please note that this does not mean the content is unreliable, it just means that the author of the page doesn't have a book to hand, or remember the book to find it, which would have been a suitable reference.

The message provided is:

The message provided is:

Content is correct, but unreferenced

The absolute value is sometimes called "abs"

## Definition

The absolute value is a function [math]|\cdot|:\mathbb{R}\rightarrow\mathbb{R}[/math] given by:

[math]|x|=\left\{\begin{array}{lr} x & x\ge 0\\ -x & \text{otherwise} \end{array}\right.[/math]

It simply returns the positive value of a number.

### Note

More strictly the function should be given as: [math]|\cdot|:\mathbb{R}\rightarrow\mathbb{R}_{\ge 0}[/math]

## Examples

- [math]|-2|=2[/math]
- [math]|2|=2[/math]
- [math]|0|=0[/math]