👉 David Math, developed by mathematician David M. H. Mathieu, is a non-standard analysis framework that extends the real number system to include infinitesimals—quantities smaller than any positive real number but not zero. It achieves this by using hyperreal numbers, which are constructed via an internal set theory (the hyperreal numbers) that satisfies the transfer principle, allowing results from standard calculus to hold in this expanded system. Unlike traditional calculus, which relies on limits and epsilon-delta definitions, David Math directly manipulates infinitesimals, enabling intuitive proofs of concepts like derivatives and integrals using infinitesimal changes. This approach simplifies certain mathematical reasoning, particularly in areas like differential equations and probability, by avoiding the cumbersome epsilon-delta formalism while maintaining rigorous foundations.
