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Basic question about sets

  1. Mar 6, 2009 #1
    I'm starting a book on topology and I've come to this come to this confusing statement:

    Let A1, A2, ... be subsets of some universal set U.

    If the class {A1, A2, ...} is empty, then the intersection of all the Ai is U.


    I know that the intersection of empty sets is empty, but I don't quite see how to even think of the intersection of the Ai when {A1, A2, ...} is empty.

    Can anyone explain this?
     
  2. jcsd
  3. Mar 6, 2009 #2

    Hurkyl

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    What does it mean for a point not to be in the intersection of a class?

    Let P be a point. Can you find a set in your class that doesn't contain P?
     
  4. Mar 6, 2009 #3
    I think I get it now. If P is not in some Ai, then Ai must exist in {A1, A2, ...}, which is empty.

    Thanks.
     
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