Note that, generally, books (such as Keisler's Elementary Calculus: An Infinitesimal Approach) that approach Calculus from the perspective of infinitesimals also discuss epsilon-delta limits the concept is so standard that it's hard to learn calculus without encountering it. The primary reason epsilon-delta limits were introduced and standardized was that infinitesimals were unable to be made rigorous. nonzero real) number is infinitesimal, and that the quotient of two infinitesimals is an indeterminate form. 50-51, Goldblatt includes among his hyperreal axioms that the sum of two infinitesimals is infinitesimal, that the product of an infinitesimal and an appreciable (i.e.

However, they are generally much more rarely encountered today. In Lectures on the hyperreals: an introduction to nonstandard analysis, pp. The publication first ponders on Greek mathematics, transition to Western Europe, and some. The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. Both Leibniz and Newton thought in terms of them. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus. Infinitesimals seem more intuitive to me - although I have not looked into them extensively, I often think of things as infinitesimals first and then translate my thoughts to limits. There is rarely a simple 'better' for this sort of thing.Įpsilon-delta limits are by far the most popular approach and are how the subject is most often taught.

Calculus of infinitesimals