Abstract
In the course of a search for criteria which would assist in deciding whether a particular series of numbers was randomly arranged, it was found necessary to investigate some of the more obvious characters of a random series of numbers. If the series is an infinite one and all the numbers are unequal (the series of decimals between o and 1 selected in some random fashion may be considered) certain of the numbers will be maximal, that is greater than their immediate neighbours, whilst others will be minimal, that is less than their immediate neighbours. Every maximal number is succeeded by a run down, that is by a series of descending numbers ending in the succeeding minimal number. The length of a run down is the number of numbers it contains, including the maximal number which begins it and the minimal number which ends it. The length of a run up is similarly defined. Clearly the minimum length of a run is 2.
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