Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Open balls and limit points

  1. Nov 11, 2011 #1
    While learning about limit points the use of an open ball has been of high discussion. Why can you not use a closed ball to define a limit point?

    If someone could give me some intuition as to why I think I may get it.

    Thanks.
     
  2. jcsd
  3. Nov 11, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Are you working in metric space?? In that case, you can define limit points using open balls.

    Just define x to be a limit point of A if every ball around x intersects A\{x}.
     
  4. Nov 11, 2011 #3
    yes, I am working in a metric space.

    So can you use your definition for open and closed balls?
     
  5. Nov 11, 2011 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    No, only for open balls. Think about what could go wrong for closed balls.
     
  6. Nov 11, 2011 #5
    I've been trying to but I can't think of an example where having boundaries on the ball would cause a problem. That's really why I asked the original question.

    Can you give me one?
     
  7. Nov 11, 2011 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    What if the ball has radius 0?
     
  8. Nov 11, 2011 #7
    got it, thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Open balls and limit points
  1. Indentifying the ball (Replies: 2)

Loading...