In wikipedia I've read that
the discrete topology on X is defined by letting every subset of X be open (and hence also closed), and X is a discrete topological space if it is equipped with its discrete topology
"hence also closed"? I couldn't get that part. If you let every subset of $X$ to be open, how come that makes them closed? I know that $\emptyset$ and $X$ are open (hence closed), called "clopen". But for a point $x \in X$ if I let it to be open in the topological space (I also didn't understand what "letting" procedure is, $x \in X$ is clearly closed, since it is a point), how come it becomes closed?