Hyperreal numbers are an extension of the real number system that includes infinitesimal and infinite quantities. They are used in non-standard analysis, a branch of mathematics developed by Abraham Robinson in the 1960s. Hyperreal numbers allow mathematicians to rigorously work with concepts that involve quantities smaller than any positive real number or larger than any real number. In the hyperreal number system, every real number has an associated infinitesimal and infinite counterpart. This framework provides a way to analyze limits, derivatives, and integrals in calculus, offering a different perspective compared to traditional methods. Hyperreal numbers enhance our understanding of continuity and change in mathematical analysis.