Talk:Union of Connected Sets with Non-Null Intersection is Connected

I don't understand the following statements in this proof:


 * If $s \in V$, then $S, V$ serve as separated sets whose union now covers $\left\{{A_\alpha}\right\}$.


 * $\exists x \in U \cap \left\{{A_\alpha}\right\}$.

My reasons are:


 * $\left\{{A_\alpha}\right\}$ is not a set that contains $S$ and $V$; thus it cannot be covered by them. Also by definition of $V$, $S$ and $V$ are not disjoint.


 * $U$ and $\left\{{A_\alpha}\right\}$ are sets that contain different kind of elements, hence their intersection is empty.

--Dan232 09:18, 27 July 2012 (UTC)