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Incomplete and completion

  1. Nov 27, 2008 #1
    In the metric space [tex](\mathbb R, d)[/tex]

    1) [tex]d(x,y) = |{tan}^{ - 1}(x) - {tan}^{ - 1}(y)|[/tex] ,where x,y are real numbers .

    2) [tex]d(x,y) = |{tan}^{ - 1}(x) - {tan}^{ - 1}(y)|[/tex], where x,y are real numbers .

    Show that [tex](\mathbb R, d)[/tex] w.r.t (1) and (2) are incomplete metric space . Also, what is the completion space of both w.r.t. (1) and (2).

    I appreciate any help.
  2. jcsd
  3. Nov 27, 2008 #2


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    (1) and (2) are the same metric
  4. Nov 29, 2008 #3
    Show that (1, 2, 3, ...) is a Cauchy sequence under the given metric that does not converge.
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