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Math 2.0

General topology Example

Usual metric on the real line

Example

On the set $\mathbb{R}$ of real numbers, let $d(x, y) = |x - y|,$ where $|\cdot|$ is the absolute value. Then $d$ is a metric on $\mathbb{R}$ . The triangle inequality for real numbers gives the triangle inequality for $d$ .

Remarks

The number $|x - y|$ is the absolute difference of $x$ and $y$ . This metric is the case $n = 1$ of the Euclidean metric. The same formula with the modulus gives a metric on the complex numbers.

Further reading

Web https://en.wikipedia.org/wiki/Absolute_difference, lead section

About this page

Tag	`0KXJTZSW9B`
URI	`m2://0KXJTZSW9B`
Aliases	`absolute-difference`
Kind	example
Writing	W2 usable
MSC	54E35
Instance of	Metric space
Same as	Wikidata Q1773230 Wikipedia Absolute difference

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