 Like the Continuity axiom of vNM, Non-Atomicity implies that no matter how bad an outcome \(X\) is, if \(g\) is already preferred to \(f\), then if we add \(X\) as one of the possible outcomes of \(f\)—thereby constructing a new alternative \(f'\)—\(g\) will still be preferred to the modified alternative as long as the probability of \(X\) is sufficiently small. In effect, Non-Atomicity implies that \(\bS\) contains events of arbitrarily small probability. It is not too difficult to imagine how that could be satisfied. For instance, any event \(F\) can be partitioned into two equiprobable sub-events according to whether some coin would come up heads or tails if it were tossed. Each sub-event could be similarly partitioned according to the outcome of the second toss of the same coin, and so on.