In
mathematics,
infinitesimals are things so small that there is no way to measure them. The insight with exploiting infinitesimals was that entities could still retain certain specific properties, such as
angle or
slope, even though these entities were quantitatively small. The word
infinitesimal comes from a 17th-century
Modern Latin coinage
infinitesimus, which originally referred to the "
infinite-th" item in a sequence. It was originally introduced around 1670 by either
Nicolaus Mercator or
Gottfried Wilhelm Leibniz. Infinitesimals are a basic ingredient in the procedures of infinitesimal
calculus as developed by Leibniz, including the
law of continuity and the
transcendental law of homogeneity. In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective, "infinitesimal" means "extremely small". To give it a meaning, it usually must be compared to another infinitesimal object in the same context (as in a
derivative). Infinitely many infinitesimals are summed to produce an
integral.