Editing Nonstandard analysis (section)

=== Historical ===
Much of the earliest development of the infinitesimal calculus by [[Isaac Newton|Newton]] and Leibniz was formulated using expressions such as ''infinitesimal number'' and ''vanishing quantity''.  These formulations were widely criticized by [[George Berkeley]] and others. The challenge of developing a consistent and satisfactory theory of analysis using infinitesimals was first met by Abraham Robinson.<ref name="NSA" />

In 1958 Curt Schmieden and [[Detlef Laugwitz]] published an article "Eine Erweiterung der Infinitesimalrechnung"<ref>Curt Schmieden and Detlef Laugwitz: ''Eine Erweiterung der Infinitesimalrechnung'', Mathematische Zeitschrift 69 (1958), 1-39</ref> ("An Extension of Infinitesimal Calculus") which proposed a construction of a ring containing infinitesimals. The ring was constructed from sequences of real numbers. Two sequences were considered equivalent if they differed only in a finite number of elements. Arithmetic operations were defined elementwise. However, the ring constructed in this way contains [[zero divisor]]s and thus cannot be a field.