Infinitesimal

Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. Students easily relate to the intuitive notion of an infinitesimal difference 1-"0.999...", where "0.999..." needs to be interpreted differently from its standard meaning as a real number. The insight with exploiting infinitesimals was that objects could still retain certain specific properties, such as angle or slope, even though these objects 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 series. It was originally introduced around 1670 by either Nicolaus Mercator or Gottfried Wilhelm Leibniz.