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: Intersection of an infinite set

  1. May 29, 2010 #1
    Let [tex]G_{n}[/tex] = (-1/n,1/n) for all n in N

    let [tex] G= \bigcap^{\inft}_{n=1} [/tex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 29, 2010 #2
    So, what's the question/problem?? The intersection is simply 0 (zero, a single number). Hence the intersection of an infinite number of open sets is not necessarily open, whereas the union is always open, as is the finite intersectiion of them. With the closed sets, it's the other way round :).
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook