Zero in Mathematics and Statistics
摘要
This chapter reaches the point where zero has finally been discovered, the demons surrounding it have somewhat been placated, and we can explore the mathematics that make it such a unique number. It deals with the mathematical properties that make zero such a central part of many disciplines and defines the rules of using zero in arithmetic and mathematics, as well as where misuse can cause issues in the real world. Zero is both a non-negative and non-positive integer that is the center point of the number line. Attempts to estimate its value in various mathematical functions led to the development of limits and calculus. The concept of the null hypothesis in statistics, and how this basically Taoist concept affects modern safety regulations in the guise of the precautionary principle, is discussed. This chapter illustrates the different contexts that zero finds itself in and introduces specific definitions and rules for its appropriate use. It also identifies situations in modern automated technology, computations, and Big Data analyses where a zero can inadvertently appear and cause havoc when it is used in a different context, a situation common in machine learning and AI scraping of the web.