# Difference between revisions of "Discrete metric"

m |
|||

Line 1: | Line 1: | ||

The '''discrete metric''' is a [[metric]] <math>d</math> which can be defined on any [[set]] <math>S</math>, <math>d: S\times S \to \{0, 1\}</math> as follows: if <math>x = y, d(x, y) = 0</math> and if <math>x \neq y, d(x, y) = 1</math>. All three conditions on a metric (symmetry, positivity and the validity of the [[triangle inequality]]) are immediately clear from the definition. | The '''discrete metric''' is a [[metric]] <math>d</math> which can be defined on any [[set]] <math>S</math>, <math>d: S\times S \to \{0, 1\}</math> as follows: if <math>x = y, d(x, y) = 0</math> and if <math>x \neq y, d(x, y) = 1</math>. All three conditions on a metric (symmetry, positivity and the validity of the [[triangle inequality]]) are immediately clear from the definition. | ||

+ | |||

+ | ==See Also== | ||

+ | |||

+ | * [[Metric space]] | ||

{{stub}} | {{stub}} |

## Revision as of 16:29, 23 September 2006

The **discrete metric** is a metric which can be defined on any set , as follows: if and if . All three conditions on a metric (symmetry, positivity and the validity of the triangle inequality) are immediately clear from the definition.

## See Also

*This article is a stub. Help us out by expanding it.*