A set of real numbers whose interior is empty

[monkey372]

Homework Statement

Give an example of a set of real numbers whose interior is empty but whose closure is all of the real numbers if it exists. Otherwise, explain why such example cannot be true.

2. The attempt at a solution
For a set S ⊆ X, the closure of S is the intersection of all closed sets in X that contain A. I am having a lot of trouble thinking of an example and am beginning to think one does not exists but intuitively this does not make sense.

 

[rummgamon]

Try thinking of a set that's "everywhere" on the real line and compute the interiors of any such set you can think of. There is a more formal definition for this "everywhere"-ness that I'm alluding to. However, using that term directly would be handing you the answer.
e.g. [0,1] is certainly not "everywhere" on the real line.