Infinitesimal

An infinitesimal number is a nonzero quantity closer to zero than any nonzero real number, a notion whose name comes from the seventeenth-century Modern Latin coinage infinitesimus, originally meaning the infinitieth item in a sequence. Infinitesimals do not exist within the standard real number system, but they do exist in other number systems such as the surreal numbers and the hyperreal numbers, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities. They were introduced during the development of calculus, when the derivative was first conceived as a ratio of two infinitesimal quantities, a definition that was not rigorously formalized until infinitesimals were largely replaced by limits defined on the ordinary real numbers; they regained standing in the twentieth century through Abraham Robinson's nonstandard analysis, which showed in the 1960s that reasoning with infinitesimals could be made logically consistent whenever the real numbers themselves are. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/