In order to translate the informal versions of Benford's law into more precise formal statements, it is necessary to specify exactly what the Benford property means in various mathematical contexts. For the purpose of this book, the objects of interest fall mainly into three categories: sequences of real numbers, real-valued functions defined on [0,+ ∞), and probability distributions and random variables. This chapter defines Benford sequences, functions, and random variables, with examples of each.