Difference between revisions of "Discrete metric"
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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. | ||
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| + | ==See Also== | ||
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| + | * [[Metric space]] | ||
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| + | [[Category:Analysis]] | ||
{{stub}} | {{stub}} | ||
Latest revision as of 16:48, 28 March 2009
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.
