how weary one gets of trying to explain the complex and fiddling theory of limits to wave after wave of uncomprehending freshmen.

(Rucker. [*Infinity and the Mind*]{}, Birkhäuser, Boston 1982, p. 87).\
Newton and Leibniz, Leibniz especially, seem to have conceived of very small quantities, “infinitesimals”, that lay outside of the ordinary number system. Leibniz spoke of the derivative of a function as being the ratio of two such infinitesimals. By the beginning of the twentieth century, however, the notion of “infinitesimal quantity” had disappeared from mathematics textbooks (although it persists in some physics and engineering texts as, for example, in the ”principle of virtual work”.). Then, in 1966, Abraham Robinson showed that the real number system can be extended to incorporate the notion of infinitesimal in approximately the sense of Leibniz (Robinson, [*Non-standard Analysis*]{}, North-Holland, Amsterdam 1966). While the foundations and rules developed by Robinson involve advanced mathematics (a readable account may be found in Stroyan and Luxembourg, [*Introduction to the Theory of Infinitesimals*]{}, Academic Press, New York 1976) the results can be used to simplify greatly the solutions of many long-standing mathematical problems.

There are existing texts that incorporate non-standard analysis [^1] These have failed, I believe, to 