# Infinite sigma-algebra

1. Apr 21, 2005

### Zaare

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?

2. Apr 21, 2005

### chingkui

3. Apr 21, 2005

### Hurkyl

Staff Emeritus
No you can't.

Now, if you instead said countably infinite...

(I edited it)