An "infinitesimal" is a quantity that is so small that it is almost zero, but not quite. In mathematics, it is used to describe values that approach zero in limit processes, particularly in calculus. Infinitesimals help in understanding concepts like derivatives and integrals, which are fundamental in analyzing change and area under curves. The concept of infinitesimals was notably advanced by mathematicians such as Gottfried Wilhelm Leibniz and Augustin-Louis Cauchy. While traditional mathematics often deals with finite numbers, infinitesimals provide a way to rigorously handle very small quantities, leading to the development of non-standard analysis, a branch of mathematics that formalizes their use.