It was this that led Newton's contemporary, Bishop Berkeley, to describe the idea of infinitesimals as “obscure, repugnant and precarious.” Consequently, a new calculus was devised that avoided recourse to infinitesimals.ĭr. Yet the use of infinitesimals in calculus implied that any number of them would still be infinitely small. This concept led to seemingly inescapable paradoxes.įor example, if infinitesimal distances were larger than zero, it would appear that a number of them (no matter how small) would still have significant length. The latter, while “infinitely” small, would be larger than zero. Keisler - and other mathematicians-consider approaching calculus in terms of inifinitesimals to be more intuitive than the modern method (using the concept of a so‐called limit) he wrote the new text, due to appear later this year.Īs the name implies, the infinitesimal calculus depended on such concepts as a line being formed of an infinite number of points separated by infinitesimal distances. Robinson's approach to calculus, using nonstandard analysis, is to some extent a return to the original form, devised by Newton and Leibnitz in the 17th cenutry, which came to be known as the “infinitesimal calculus.”īecause Dr.
Robinson's approach.ĭespite the latter's novelty, its roots, in particular as they deal with the concepts of the infinite and the infinitesimal, extend back to the speculations of the ancient Greeks and to the paradoxes of Zeno, who lived in the fifth century B.C.ĭr. leroma Keisler of the University of Wisconsin, who has written a new textbook on calculas, using Dr. Symptomatic of interest in the subject was its featured status, in the form of four special lectures, at last month's meeting of the American Mathematical Society in Washington.
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