I am trying to show that the countable union of partitions A form a sigma algebra. I am able to prove every conditions(which is obvious) except that the empty set belongs to A.
I checked the definitions of partition and apparently empty set is not in the set of partitions. And union operation can only make a set bigger which means it is impossible to get empty set.
Is there anything wrong with this problem? Is it that people assume the empty set to be in the partition?
Apparently "countable" means "finite or countably infinite" in that context.