Metric space and closed sets (book misprint?)

Question

I am not sure if there is a misprint in this corollary or if I am not getting the idea right.

Corollary. Let $X$ be a metric space and let $A\subset X$. Then A is closed in $X$ iff: $$ (x_n)_{n=1}^{\infty}\subset A \text{ and } x_n \rightarrow x \text{ implies } x_n \in A $$ Shouldn't it be $x \in A$ instead of $x_n \in A$? If not, why?

Answer 1

You are right, there is a misprint.