hyperreal numbers

Hyperreal numbers extend the real number system to include not only all familiar numbers but also infinitely large and infinitesimally small quantities. Imagine numbers that are so tiny they are smaller than any positive real number but not zero, or numbers so large they outrun any real number. This framework, used in nonstandard analysis, allows mathematicians to rigorously work with concepts like infinitesimals and infinite magnitudes, providing a powerful tool for calculus and analysis. In essence, hyperreals enrich the number system to better handle and formalize ideas involving quantities that are nearly zero or infinitely large.