Emphasizing order relations rather than metric concepts in real analysis
by
Leonard Gillman

The family of all open intervals (A, B) about a point L assuredly constitutes a base for the neighborhood system at L. There is no need to restrict oneself to intervals (L - \epsilon, L + \epsilon), whose very notation suggests computation. Indeed the order relations A < L < B are usually sufficient, the distances of A and B to L being a distraction. One advantage is to simplify the notation and, in notable cases, to drastically simplify a proof. Another is to obtain a definition of limit that is less intimidating than epsilon-delta. Examples are given from elementary and semi-advanced calculus. Other, somewhat related topics are a characterization of limit that is very easy to understand, yet is completely rigorous; the composition of limits; the exceptional case in the proof of the chain rule; and a simple proof of L'Hôpital's rule.

Date received: May 31, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caag-10.