# Arithmetic Arithmetic deals the 4 basic operations: add, sub, mul, div. Add and sub on the one hand, and mul and div on the other are each other's opposite operations. However, sub and div are somewhat of the second-class operations not only because they are easily defined in terms of add/mul with appropriate invertability axioms: * sub: 9 - 5 = 9 + (-5) * div: 5 ÷ 3 = 5 *⅓ = 5* 3⁻¹ After all, add/mul could be defined in terms of sub/div as well, but the bigger reasons for their "lesser" treatment is because sub and div do not obey all the axioms that they inverses do; namely, unlike add and mul, sub and div do not uphold the axioms of associativity, commutativity and closure (totallity). --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://mandober.gitbook.io/math-debrief/100-fundamentals/terms/arithmetic.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.