[SOLVED] example of closed set

[dwsmith]

Given an example of a set $S$ which is closed but not bounded and exhibit a countable open covering $F$ such that no finite subset of $F$ covers $S$.

The set of integers. Since it is a set of points, each point is closed. How would I show a countable covering.

 

[Ackbach]

Given an example of a set $S$ which is closed but not bounded and exhibit a countable open covering $F$ such that no finite subset of $F$ covers $S$.

The set of integers. Since it is a set of points, each point is closed. How would I show a countable covering.

How about a small $\epsilon$ interval about each integer, with $\epsilon<1/2$?