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    Closed set proof

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    A set F is closed iff for all x_n in F for all n in the naturals (x_n) converges to l, then l is in F. (x_n) is a sequence

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    Solution Preview

    A closed set can have lots of equivalent definitions. This problem is one definition of a closed set. Now I use the other two equivalent definition of closed set to prove this problem.
    1. The complement of a closed set is an open set.
    2. Each point outside of a closed set has a disjoint neighborhood from this closed ...

    Solution Summary

    This provides an example of proving a set is closed.