ABSTRACT
Convinced of the importance of understanding the groundwork before dealing with the more advanced topics of probability, the authors have chosen to pave the way by beginning this chapter with a couple of simple narratives involving game theory in its early days. Pascal and Fermat entered the fray to assist with the explanation or rationalization of some surprisingly negative gambling results. This chapter swiftly but necessarily shifts its focus to certain set-theoretic concepts, counting techniques, and axioms, including those of Zermelo, Fraenkel, and the axiom of choice (Z, F, and C). This chapter also discusses the essentials of measure theory, σ-algebra, and the Lebesgue integral before ultimately concluding with a presentation of fuzzy logic.
