# Closed set proof

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.

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