Closed property of nonempty finite set I came across this text in Rudin's book where it has been mentioned that a non-empty finite set is closed. 
But a closed set is a set which contains all of it's limit points in the set itself but none of the elements of a non-empty finite set can possibly have a limit point because a neighborhood of a limit point has infinite points . So how come a non-empty finite set be a closed set ??

"$A$ contains all of its limit points" is short for "for all $x$ such that $x$ is a limit point of $A$, we have that $x \in A$".
This statement is voidly true if there are no limit points (as in this case).
Equivalently put, the condition can be written as $A' \subseteq A$ and the empty set is a subset of all sets.
