 To state some of the thornier puzzles generated by the mathematics of probability, we need a more formal presentation. Kolmogorov’s (1933/1950) axiomatization begins with a finite set \(\Omega\) and an algebra \(F\) of subsets of \(\Omega\): a set closed under complementation and union. The members of \(\Omega\) are known as states while the members of \(F\) are known as events. A probability function is a function from \(F\) to the real numbers. It is non-negative, assigns 1 to \(\Omega\), and it is (finitely) additive—the probability that one of two mutually exclusive events occurs is the sum of their individual probabilities: