Limit Points in Zariski Topology If we have the set $\mathbb{R}$ with the Zariski topology and we have the sequence $x_n = n$. 
Am I right in thinking that any number in $\mathbb{R}$ is a limit point? My reasoning is as follows:

$x\in\mathbb{R}$ is a limit point if and only if $x\in\overline{\{1,
> 2, 3,\dots\}\backslash\{x\}} = \mathbb{R}$ in our topology. This is
  clearly true for any $x$, so all points are limit points.


Here is a different way to think about it.
Hint: For $\mathbb{R}$, Zariski topology is nothing but co-finite topology. Therefore the open sets are those whose complements are finite. Consider any point in $x\in \mathbb{R}$. Then any open set around $x$ contains all but finitely many points in $\mathbb{R}.$
