TITLE: Is $[0,\infty)$ a closed subset?
QUESTION [20 upvotes]: A closed set is one where it contains all it's limit points, even though the end is 'open' as in the traditional sense any sequence tending to infinity will never leave the subset; therefore it's closed. Is my logic sound? Thanks!

REPLY [6 votes]: Note that the complement of $[0, \infty)$ is $(-\infty, 0)$, which is open in the usual topology on $\mathbb{R}$.  Therefore $[0, \infty)$ is closed.  I often find looking at the complement easier than thinking of limit points.