Welcome guest
You're not logged in.
300 users online, thereof 0 logged in

## Definition: Absolute Value of Real Numbers (Modulus)

Let $$x,y\in \mathbb R$$. Based on the ordering relation for real numbers, we define a function $$|~|:\mathbb R\times \mathbb R\mapsto \mathbb R$$ by

$|x-y| := \begin{cases} x-y & \text{ if } x\ge y \\ y-x & \text{ if } x < y \end{cases}$

and call it the distance of $$x$$ and $$y$$.

The distance of any real number $$x$$ from $$0$$

$|x| := |x-0|= \begin{cases} x & \text{ if } x\ge 0 \\ -x & \text{ if } x < 0 \end{cases}$

is called the absolute value of $$x$$.

| | | | | created: 2014-04-26 22:17:29 | modified: 2020-07-04 15:53:01 | by: bookofproofs