Mathematics Algebra Number Theory 422960
Set of all finite and cofinite subsets of N
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A subset A of the set N of all natural numbers is defined to be cofinite if N - A (the complement of A in N) is finite. Show that the set of all finite and cofinite subsets of N is an algebra but not a sigma-algebra.

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A complete, detailed proof, including a clarification of what is meant by "the set of all finite and cofinite subsets of N," is provided.

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