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## Homework Statement

A set E in ℝ is nowhere dense if and only if the closure of E's complement(E with a line over it) is dense in ℝ

## Homework Equations

I need help proving this lemma. I'm not entirely sure where to start.

## The Attempt at a Solution

I know we have to proof it two ways, backwards and forwards. For the forward, all I can think to use if the fact that the closure of E complement contains no nonempty open intervals, but I don't know where to go with that.

Any help would be appreciated.