If $A_\alpha$ are subsets of a set $S$ then $\bigcup_{\alpha \in I}A_\alpha$ = "all $x \in S$ so that $x$ is in at least one $A_\alpha$" $\bigcap_{\alpha \in I} A_\alpha$ = "all $x \in S$ so that $x$ is in all $A_\alpha$" It is the convention that $\bigcup_{\alpha \in \emptyset}A_\alpha = \em...