Non-standard Analysis

Non-standard analysis is a branch of mathematics that extends traditional calculus by introducing "infinitesimals," which are quantities that are smaller than any positive real number but greater than zero. In the context of model theory, it studies the properties of mathematical structures using these infinitesimals. This approach allows for a more intuitive understanding of concepts like continuity and limits. By using models that include these non-standard elements, mathematicians can explore new insights and methods, bridging the gap between rigorous formalism and intuitive reasoning in mathematical analysis.