Let us consider the representation theorem in some more formal detail. For simplicity, say that the process generates time-indexed binary observations, i.e., 0's and 1's. The prediction rules take such bit strings of length \(t\), denoted \(S_{t}\), as input, and return a probability for the event that the next bit in the string is a 1, denoted \(Q^{1}_{t+1}\). So we write the prediction rules as partial probability assignments \(P(Q^{1}_{t+1} \mid S_{t})\). Exchangeable prediction rules are rules that deliver the same prediction independently of the order of the bits in the string \(S_{t}\). If we write the event that the string \(S_{t}\) has a total of \(n\) observations of 1's as \(S_{n/t}\), then exchangeable prediction rules are written as \(P(Q^{1}_{t+1} \mid S_{n/t})\). The crucial property is that the value of the prediction is not affected by the order in which the 0's and 1's show up in the string \(S_{t}\).