# Give an example of two closed sets $A, B \subseteq \mathbb{R}$ such that the set $A + B$ is not closed

Possible Duplicate:
Sum of two closed sets in $\mathbb R$ is closed?

Give an example of two closed sets $A, B \subseteq \mathbb{R}$ such that the set $A + B = \{a + b : a \in A, b \in B\}$ is not closed.

This question appears on an old analysis qual I am studying. I know that both $A, B$ must be unbounded sets, because in an earlier part of the problem I have proved that $A + B$ is closed if either of the two sets are compact. The simplest unbounded and closed subset of $\mathbb{R}$ that I know is $\mathbb{Z}$. So I was starting with $A = \mathbb{Z}$, but I’m not yet able to come up with an appropriate $B$.

Hints or solutions are greatly appreciated.