Question

The set of rational numbers is neither opened nor closed.

1. Find a point in the set which there is no e-neighborhood contained in the set.
2. Find a limit point not contained in the set

Answer 1

The e-neighborhood of a point, x is the open-interval (x-e, x+e) where e is any positive real number.

Answer 2

A set is closed if it contains its limit points.
A limit point is if every e-neighborhood of that point intersects the set at some point other than x