 This syllogism can be combined with an observation about the behavior of increasingly large samples. From calculations of the sampling distribution, it can be shown that as the sample size increases, the probability that the sample frequency is in a range which closely approximates the population frequency also increases. In fact, Bernoulli’s law of large numbers states that the probability that the sample frequency approximates the population frequency tends to one as the sample size goes to infinity. Williams argues that such results support a “general over-all premise, common to all inductions, that samples ‘match’ their populations” (Williams 1947: 78).