👉 Alexander Math, also known as Alexandrov Mathematics, is a branch of mathematics that generalizes and extends traditional mathematical concepts to encompass non-standard models of arithmetic, particularly those involving infinite and infinitesimal elements. It was developed by the mathematician Garrett Harder in the 1980s to provide a rigorous foundation for non-standard analysis, which allows for the use of infinitesimals—quantities smaller than any positive real number but not zero—in a formal and consistent way. Alexander Math employs techniques from model theory, non-standard analysis, and set theory to explore and formalize these concepts, offering new insights into calculus, number theory, and other areas of mathematics. By introducing a hyperreal number system, Alexander Math enables mathematicians to work with infinitesimals and infinite quantities in a way that is both intuitive and mathematically sound, bridging gaps between classical analysis and more advanced mathematical frameworks.
