 If the utility function is bounded, then the expected utility of the St. Petersburg game will of course be finite. But why do the axioms of expected utility theory guarantee that the utility function is bounded? The crucial assumption is that rationally permissible preferences over lotteries are continuous. To explain the significance of this axiom it is helpful to introduce some symbols. Let \(\{pA, (1-p)B\}\) be the lottery that results in A with probability p and B with probability \(1-p\). The expression \(A\preceq B\) means that the agent considers B to be at least as good as A, i.e., weakly prefers B to A. Moreover, \(A\sim B\) means that A and B are equi-preferred, and \(A\prec B\) means that B is preferred to A. Consider: