Infinitesimals
Although all these numbers above are very small, they are all still real numbers greater than zero. Some fields of mathematics define infinitesimal numbers. An infinitesimal is a number greater than zero yet smaller than any positive real number.
Infinitesimal numbers were originally developed to create the differential and integral calculus, but were replaced by systems using limits when they were shown to lack theoretical rigor. More recent work has restored rigor to infinitesimals, making them once more a legitimate mathematical topic (see non-standard analysis).
Systems of infinitesimals can be generated in the same way as systems of transfinite numbers can be generated. Some mathematical systems such as surreal numbers and hyperreal numbers generate elaborate systems of infinitesimals with amazing properties.
Read more about this topic: Small Number