I am having a bit of trouble understanding this definition. "A collection $\Sigma$ of subsets of S is called a $\sigma$-algebra on S if $\Sigma$ is an algebra on S such that whenever $F_n \in\Sigma (n \in N)$, then $\bigcup\limits_{n} F_{n} \in \Sigma$.
The part im not sure with is $\bigcup\limits_{n} F_{n} \in \Sigma$. Lets say n=3, then $F_3 \in\Sigma$, so then $\bigcup\limits_{3} F_{3} \in \Sigma$. Does $\bigcup\limits_{3} F_{3} \in \Sigma$ = $F_1+F_2+F_3$? With $F_1,F_2,F_3 \in \Sigma$?
Im just a bit confused with the union notation. What would $\bigcup\limits_{3} F_{3} \in \Sigma$ equals to? Thanks.