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Metric space

  1. Aug 19, 2007 #1
    Can somebody give me an other metric space that is not dependent on the inner product i mean which is not derived from the inner product between two vectors.
  2. jcsd
  3. Aug 19, 2007 #2


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    The function d(x,y) = 0 if x=y and d(x,y)=1 if not. It's called the discrete metric.
  4. Aug 20, 2007 #3


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    I remember a particularly exotic one given as an example to me, that the details elude me right at the moment. But here's a good one:

    [tex]m, n \in \mathbb{N}[/tex]

    [tex]d(m,n) = \left| m^{-1} - n^{-1} \right|[/tex]

    [tex]d(n,\infty) = d(\infty,n) = \frac{1}{n}[/tex]

    [tex]d(\infty,\infty) = 0[/tex]
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