Results 1 to 3 of 3

Math Help - cluster points

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    US
    Posts
    5

    cluster points

    So I have to prove the following but I have NO idea about cluster points. Could anyone help explain cluster points and help me prove this?

    Show that 0 is a cluster point of S = {1/n: n is an elemnt of Z+}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2012
    From
    NY
    Posts
    62
    Thanks
    8

    Re: cluster points

    Cluster points are also known as accumulation points. In this case you need to show that every neighborhood of 0 contains atleast one point of S. Then 0 will be a cluster/accumulation point of S. The cluster point need not have to be in the set S
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1

    Re: cluster points

    Quote Originally Posted by duckyone View Post
    So I have to prove the following but I have NO idea about cluster points. Could anyone help explain cluster points and help me prove this?
    Show that 0 is a cluster point of S = {1/n: n is an elemnt of Z+}

    Do you know that if \delta>0 then (\exists n\in\mathbb{Z}^+)[1/n <\delta]~?

    If your class has not done that, then it is pointless to try this question.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. lim sup, lim inf and cluster points.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 13th 2011, 10:24 AM
  2. Quick Cluster Points Question
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: July 4th 2011, 10:54 AM
  3. Cluster Points in a Sequence
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: March 6th 2010, 06:09 AM
  4. Replies: 3
    Last Post: January 11th 2009, 11:49 AM
  5. Need Help with Cluster Points
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 11th 2008, 01:54 PM

Search Tags


/mathhelpforum @mathhelpforum