Introduction to Infinitesimal Analysis : Functions of One Real Variable (Classic Reprint)

Excerpt from Introduction to Infinitesimal Analysis: Functions of One Real Variable

The 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.

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