Everything I Know About Nothing: A Mathematical Exploration of the Void and its Role in Constructing Mathematics

This article investigates the concept of "nothing" as the foundational entity in mathematical structures, starting with the concept of the void, as in the beginning (Genesis), there was emptiness (void). By considering the void as a primal entity in mathematics, we show how its existence is central to the construction of the number system/concept of infinity, set theory, and other mathematical concepts such as void's role in topology and logic. Through the careful examination of basic operations, sets, and structures, we demonstrate that "nothing" can give rise to something which, in turn, gives rise to everything. The article concludes with a discussion on the necessity of "nothing" in both mathematical abstraction and practical application.