 A typical sequence should satisfy all of the various ‘properties of stochasticity’ (Martin-Löf 1966: 604).  What are these properties? They include the property of large numbers, the claim that the limit frequency of a digit in a random sequence should not be biased to any particular digit. The (strong) law of large numbers is the claim that, with probability 1, an infinite sequence of independent, identically distributed Bernoulli trials will have the property of large numbers. If we concentrate on the sequence of outcomes as independently given mathematical entities, rather than as the products of a large number of independent Bernoulli trials, we can follow Borel’s (1909) characterisation of the strong law. Let \(S_n (x)\) be the number of 1s occurring in the first \(n\) places of sequence \(x\) (this is just \(\sum^{n}_{k=1}x_{k}\)), and let \(B\) be the set of infinite sequences \(x\) such that the limit of \(S_n (x)/n\) as \(n\) tends to infinity is \(\frac{1}{2}\). Borel’s theorem is that \(B\) has measure one; almost all infinite sequences are, in the limit, unbiased with respect to digit frequency.