👉 Hawaii math, also known as non-standard analysis, is a branch of mathematics that extends the real numbers by introducing infinitesimals—numbers smaller than any positive real number but not zero. Developed by Abraham Robinson in the 1960s, it provides a rigorous foundation for intuitive concepts of calculus, such as limits and derivatives, using these infinitesimals. Unlike traditional analysis, which relies on epsilon-delta definitions, Hawaii math uses hyperreal numbers, extending the real number line to include infinitesimals and infinitely large numbers. This allows for a more intuitive understanding of calculus concepts, making it easier to visualize and prove results. For instance, the derivative of a function can be interpreted as the average rate of change over an infinitesimally small interval, bridging the gap between intuitive geometric insights and formal mathematical rigor.
