An algebra is a collection of subsets closed under finite unions and intersections.
A sigma algebra is a collection closed under countable unions and intersections.
Whats the difference between finite and countable unions and intersections? Does "countable" mean it implies there can be infinitely many unions and intersections?
Secondly, I was reading a definition
For an algebra on a set: By De Morgan's law, $A \cap B = (A^c \cup B^c)^c$, thus an algebra is a collection of subsets closed under finite unions and intersections.
What law are they using here to get $A \cap B = (A^c \cup B^c)^c$? I thought de morgan's law was $(A\cap B)^c = A^c \cup B^c$?
Finally, what exactly do they mean by "closed under finite unions and intersections?