Introduction to Infinitesimal Analysis

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Excerpt from Introduction to Infinitesimal Analysis: Functions of One Real VariableThe general aim has been to obtain rigor of logic with a minimum of elaborate machinery. It is hoped that the system atic use of the heine-bore] theorem has helped materially toward this end, since by means of this theorem it is possible to avoid almost entirely the sequential division or pinching process so common in discussions of this kind. The definition of a limit by means of the notion value approached has simplified the proofs of theorems, such as those giving necessary and sufficient conditions for the (existence of limits, and in general has largely decreased the number Of a's and a's. The theory of limits is developed for multiple-valued functions, which gives certain advantages in the treatment of the definite integral.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.