No, the number of events is necessarily also finite or uncountable. Indeed, it is a nice exercise that there are no countably infinite sigma algebras (extra cre

No, the number of events is necessarily also finite or uncountable. Indeed, it is a nice exercise that there are no countably infinite sigma algebras (extra credit for a solution!). It's just can't take uncountably many events, take their union, and assume that the result is also an event.