If we want to firmly understand the behavior of Hopfield nets and many quantum computing algorithms, we first need to understand quite a few properties of vectors whose entries can only assume one of two values. In this chapter, we therefore look at sets of bivalent numbers and vectors and study their characteristics from various different angles. These include Boolean logic, (multi-)liner algebra, probability theory and statistics, geometry, and graph theory. The content of this chapter is therefore dense and technical but its seemingly unrelated topics turn out to be interlinked and fundamental to many of the upcoming chapters. In short, this chapter equips us with a very broad perspective on the apparently innocuous ideas of bivalent numbers and vectors and introduces important terminology and concepts which we will need later on.