Nonstandard Analysis

Nonstandard Analysis is a mathematical framework that extends traditional calculus by rigorously including infinitesimally small and infinitely large quantities. It allows mathematicians to work with these "infinitesimals" as actual entities, making calculations and reasoning more intuitive—similar to how early calculus was originally conceived. This approach provides a powerful alternative to standard methods, often simplifying complex proofs and concepts by treating infinitesimals as genuine, manageable objects within an expanded number system.