1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Question about isolated points.

  1. Mar 18, 2012 #1
    1. The problem statement, all variables and given/known data
    If I just had the set containing [itex] \pi [/itex] on the real line.
    So this is an isolated point. Is this set closed?
    3. The attempt at a solution
    I think this set is closed because it contains its limit points, because it only has one point.
    Am i thinking about this correctly?
  2. jcsd
  3. Mar 18, 2012 #2
    Hmm, that's an interesting question. I guess it would be closed because that's the only point in the set, and there's no option for an e-neighbourhood around it.
  4. Mar 18, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper

    I think you are thinking about it correctly but that you are even asking this question makes me wonder. Can you explain your doubts further? What's the exact definition of a limit point?
  5. Mar 18, 2012 #4
    thats what I thought too
  6. Mar 18, 2012 #5
    If we wanted to put things on more definite footing, we could assume that it isn't closed. Then there is some point x1 such that for all E > 0 there is some x in our set such that d(x,x1) < E. However, since x = π in all cases, then the only such point is π, a contradiction.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook