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Give an example of a set E such that both E and its complement are dense in R^1. Then show that such a set E can not be closed.

1. Give an example of a set E such that both E and its complement are dense in R^1. Then show that such a set E can not be closed.

Note: we are using the "Methods of Real Analysis by Richard R Goldberg"
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A non-closure proof is provided.

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