BranchesHistoryFPLHelpLogin
Welcome guest
You're not logged in.
354 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

1.Corollary: Properties of the Absolute Value

Edit or AddNotationAxiomatic Method

This work was contributed under CC BY-SA 4.0 by:

This work is a derivative of:

Bibliography (further reading)

(none)