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Intersection of sets with infinite number of elements

  1. Sep 10, 2011 #1
    I have to decide whether the following is true or false:

    If A1[itex]\supseteq[/itex]A2[itex]\supseteq[/itex]A3[itex]\supseteq[/itex]...are all sets containing an infinite number of elements, then the intersection of those sets is infinite as well.

    I think I found a counterexample but I'm not sure the correct notation. I to have sets {n, n+1, n+2,...} from n to infinity (so {1, 2, 3,...}[itex]\supseteq[/itex]{2,3,4,...}) and the intersection of those sets is obviously null. How do I write this out? Thanks!
     
  2. jcsd
  3. Sep 10, 2011 #2

    micromass

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    Just write it as

    [tex]A_n=\{n,n+1,n+2,...\}[/tex]

    then

    [tex]\bigcap_{n\in \mathbb{N}}{A_n}=\emptyset[/tex]
     
  4. Sep 10, 2011 #3

    disregardthat

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    The intersection of a set of sets is the set of elements contained in every of those sets. What number is contained in every such set? (Hint: assume n is in the intersection, and find a set which does not contain n)
     
  5. Sep 11, 2011 #4
    Thanks micromass, that's the notation I was looking for.
     
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