Difference between revisions of "Absolute value"

Revision as of 16:08, 7 March 2015 (view source) Alec (Talk | contribs) (Created page with "The absolute value is sometimes called "abs" ==Definition== The absolute value is a function <math>|\cdot|:\mathbb{R}\rightarrow\mathbb{R}</math> given by: <mat...")		Revision as of 17:56, 18 March 2016 (view source) Boris (Talk | contribs) (→‎Examples: and notably, |0|=0) Newer edit →
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	# <math>|-2|=2</math>		# <math>|-2|=2</math>
	# <math>|2|=2</math>		# <math>|2|=2</math>
−		+	# <math>|0|=0</math>
	{{Definition|Real Analysis}}		{{Definition|Real Analysis}}

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Revision as of 17:56, 18 March 2016

The absolute value is sometimes called "abs"

Definition

The absolute value is a function

$$|\cdot|:\mathbb{R}\rightarrow\mathbb{R}$$ given by:

$$|x|=\left\{\begin{array}{lr} x & x\ge 0\\ -x & \text{otherwise} \end{array}\right.$$

It simply returns the positive value of a number.

Note

More strictly the function should be given as:

$$|\cdot|:\mathbb{R}\rightarrow\mathbb{R}_{\ge 0}$$

Examples

1. $$|-2|=2$$
2. $$|2|=2$$
3. $$|0|=0$$