- #1

- 54

- 0

## Main Question or Discussion Point

I'm supposed to answer the question "Can a sigma-algebra be infinite and countable?"

I think I can show that if it has a countable number of disjoint subsets, then it can't be countable considering the possible combinations of the subsets.

Now I need to show that if a sigma-algebra consists of an infinite number of subsets, then it has a countable number of disjoint subsets.

Any ideas on how I can do this?

I think I can show that if it has a countable number of disjoint subsets, then it can't be countable considering the possible combinations of the subsets.

Now I need to show that if a sigma-algebra consists of an infinite number of subsets, then it has a countable number of disjoint subsets.

Any ideas on how I can do this?