I'm currently taking a college level probability course and I am stuck on a couple questions involving algebras and sigma-algebras. Let S be a fixed set. 1. What is the difference between an algebra on S and a sigma-algebra on S? 2. Why do we require an event space to be a sigma algebra instead of an algebra? 3. Find a set S and an algebra A on S such that A is not a sigma-algebra on S. Also, I have a proof that I could use some hints on how to start and the general form in which I should go about it. Prove that every sigma-algebra on S is an algebra on S. Thanks.