Irrational Numbers

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Excerpt from Irrational Numbers: And Their Representation by Sequences and Series This book is intended to explain the nature of irrational numbers, and those parts of Algebra which depend on what is usually called The Theory of Limits. Many of our text-books define irrational numbers by means of sequences, but to the author it has seemed more natural to define a number, or at. least to consider a number as determined, by the place which it occupies among rational numbers, and to assume that a separation of all rational numbers into two classes, those of one class less than those of the other, always determines a number which occupies the point of separation. Thus we have the definition of Dedekind, which is adopted by Weber in his Algebra. Without attempting to inquire too minutely into the significance of this definition, we have endeavored to show how the fundamental operations are to be performed in the case of irrational numbers and to define the irrational exponent and the logarithm. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This 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.