👉 Aged math, also known as non-standard analysis, is a branch of mathematics that extends the real number system by introducing infinitesimals—numbers smaller than any positive real number but not zero. This approach, pioneered by Abraham Robinson in the 1960s, allows for a more intuitive understanding of calculus and analysis by avoiding the formalism of limits. Instead of rigorously defining limits through epsilon-delta proofs, aged math uses infinitesimals to directly manipulate expressions involving derivatives and integrals. For example, the derivative of a function f at a point x can be expressed as f'(x) = Δy/fΔx, where Δy and Δx are infinitesimal changes in y and x, respectively. This method simplifies proofs and provides a more geometric interpretation of calculus concepts, making it particularly useful for teaching and understanding foundational ideas in analysis.
