Forming a sigma field from a countable infinite set

  • Thread starter johnG2011
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  • #1
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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.
 

Answers and Replies

  • #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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