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Forming a sigma field from a countable infinite set

  1. Sep 4, 2011 #1
    The professor did this problem in class but I need help with understanding it a little more.

    For any countably infinite set, the collection of its finite subsets and their complements form a field F.

    Prove that this conjecture.
     
  2. jcsd
  3. Sep 4, 2011 #2

    mathman

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    A field is defined as a collection which includes all finite unions and intersections as well as complements. A finite union or intersection of finite sets is finite. To handle complements, use the fact that the complement of unions is the intersection of complements, etc.
     
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