I have a question that I am trying to answer:
Suppose $C$ is a subset of the real numbers and $C$ is closed. If $\{x_n\}$ is a sequence of points in $C$ and $\lim x_n =x$, is $x$ an element of $C$? Why or why not?
I am thinking I should use either def. of open: $O$ is a subset of $\Bbb R$ is open if $x$ is an element of $O$, then there exists $\epsilon_x > 0$ such that $(x-\epsilon_x, x+\epsilon_x)$ is a subset of $O$
$C$ is a subset of $\Bbb R$ is closed if $C^C$ is open