Constructing and Generating Surreal Numbers Using the Day Structure
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The aim of this paper is to understand and interpret the work with constructing surreal numbers, and the consequences of the axioms that create them. This paper is written as an introduction to the topic and a dissection of the many intricacies baked into the surreal numbers. It is aimed to be understandable for those with a basic understanding of Set Theory, Group Theory and Number Theory, as well as some proof-writing skills. The structure of the paper involves analyzing a definition, asking if the definition makes sense, and applying the definition and understanding its consequences. Then, I analyze how the new definition can assist us in understanding the iterative process that creates the surreal numbers. Finally, I circle back around and analyze how the definitions can be narrowed down and understood more concretely.