TITLE: Example of $\sigma$-algebra
QUESTION [15 upvotes]: I understood the definition of a $\sigma$-algebra, that its elements are closed under complementation and countable union, but as I am not very good at maths, I could not visualize  or understand the intuition behind the meaning of "closed under complementation and countable union". 
If we consider the set X to be a finite set, then what would be a good real life example of a $\sigma$-algebra, for a noob to understand.

REPLY [2 votes]: steps to form the smallest sigma field 
step 1: break the whole space into sets that are mutually exclusive and exhaustive .
step 2: then form a new set using these sets(sets obtained in step 1) in this way{ take single sets ,take sum of two at a time ,take sum of three at a time ,..........,take sum of all } . the set so formed is sigma field you need