Given that there are N events, and the probability of each event is equal to the other and each probability is equal to 1 (ex. P(B1)=P(B2)=P(B3)...=P(BN)=1, we can show by induction that P(B1B2B3...BN)=1. If the collection of these N events are countably infinite or uncountably infinite, how would each affect the fact that P(B1B2...BN)=1? My initial thoughts are that countably infinite collections can add up to 1, but with uncountably infinite the probabilities will be 0. But in this instance, we are given that P(B1)=P(B2)...=P(BN)=1. Does it make a difference if the set is countably infinite? How about if it is uncountably infinite?