TITLE: Closed set on Euclidean space that is not compact
QUESTION [21 upvotes]: I have read that a subset of Euclidean space may be called compact if it is both closed and bounded.  I was wondering what a good example of a closed but unbounded set would be?
Would a closed ball inside a sphere with an infinite radius do the trick?  If that example works are there any other examples people could think of?

REPLY [6 votes]: A simple example of a closed but unbounded set is $[0,\infty)$.