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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Revision as of 16:29, 23 September 2006

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


See Also

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