Results 1 to 5 of 5

Math Help - Incomplete Metric Space

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    160

    Incomplete Metric Space

    Dear Colleagues,

    Could you please help me in solving the following problem:

    show that the set of all real number constitutes an incomplete metric space if we choose
    d(x,y)=|arc tan(x) - arc tan(y)|

    Best Regards
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by raed View Post
    Dear Colleagues,

    Could you please help me in solving the following problem:

    show that the set of all real number constitutes an incomplete metric space if we choose
    d(x,y)=|arc tan(x) - arc tan(y)|

    Best Regards
    What can you say about the sequence (x_n), where x_n = n ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    160
    Thank you very much for your reply. But is this Cauchy.

    Regards,

    Raed.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by raed View Post
    Thank you very much for your reply. But is this Cauchy.
    That is what you have to decide, using the given metric.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,390
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by raed View Post
    But is this Cauchy.
    Here is a large hint: \displaystyle\lim _{n \to \infty } \arctan (n) = \frac{\pi }{2}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 8th 2011, 02:16 PM
  2. Metric space
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 29th 2011, 08:18 PM
  3. Limit of function from one metric space to another metric space
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: September 17th 2010, 02:04 PM
  4. Sets > Metric Space > Euclidean Space
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 25th 2010, 10:17 PM
  5. metric space
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 28th 2008, 08:34 AM

Search Tags


/mathhelpforum @mathhelpforum