In a lecture today, a professor of mine described an event as being "in" the sample space. When writing on the board, for a sample space $S$ and event $E$, it was denoted: $$E \in S $$ This confused me, as I have always thought that events were subsets of the sample space, in which I case I would write: $$E \subset S$$
When I asked after class, I was told that events are not subsets of the sample space. If they are not subsets of the sample space, then how are they defined?
For example, let $S$ be the 6 possible outcomes of rolling a 6-sided die. If we were interested in event $E$, where the number of pips is even, would $E$ not be a subset of all possible outcomes?