# Math Help - Open/closed sets of Real Numbers

1. ## Open/closed sets of Real Numbers

For a set contained in the real numbers R, If R - S is open, then S is closed.

I have no idea where to start on this!

2. ## Re: Open/Closed sets of real numbers

Let $x$ be a real number. If $x\notin S,$ use the fact that $\mathbb R\setminus S$ is open to show that $x$ is not a limit point of $S.$ It will then follow that if $x$ is a limit point of $S$ then $x\in S,$ proving that $S$ contains all its limit points and so is closed.

3. ## Re: Open/closed sets of Real Numbers

Another way is to note that R-(R-S)=S, that is S is the complement of an open set. It helps to think better, sometimes, to write X-A as A^c. You will see the DeMorgan laws quicker as well as other stuff.