Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Publisher: London : G. Allen ... Read more

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The book has no illustrations or index. It may have numerous typos or missing text. However, purchasers can download a free scanned copy of the original rare book from the publisher's website (GeneralBooksClub.com). You can also preview excerpts of the book there. Purchasers are also entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Original Publisher: Chicago, London : The Open court publishing company; Publication date: 1914; Subjects: Biography ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Customer Reviews (1)

A brief and lively excursion into the history and philosophy of mathematics
The history of mathematics consists of a sequence of discoveries, some of which enhance what has come before, others that clarify and still others completely revolutionize how mathematics is practiced. In this book, one of the best philosophers of mathematics describes some of the primary events and their consequences. The style of presentation is more in a casual style rather than an academic one.
The topics are:

*) The earliest principles of mathematics as developed in ancient times.
*) The development of the abstract symbolism of algebra and the revolution in thought processes and notation needed to practice it.
*) The development of analytic geometry and how it enabled mathematics to be applied to motion and figures.
*) The application of mathematics to the natural sciences.
*) The development of infinitesimals and the expanding role of calculus.
*) The modern concept of limits and how it was applied to complete the real number line.
*) The philosophy of certainty in mathematics and what it means.

All too brief, this book is an excellent primer on the history of mathematics and the historical context within which each of the developments occurred. His life and work were short, but neither are lacking in mathematical quality.
... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Customer Reviews (6)

THIS IS A SUPPLEMENT NOT THE REAL BOOK!!!
At least three of the Amazon listings for this book, including this one, fail to mention that it is only a supplement or appendix.The "look-inside" feature shows the real book.Don't waste your time.You will find yourself filing for a refund.

Not the original document
This book is a set of adenda to the original and not the original book.

A great book, but an awful printing...
Five stars for the content, three stars for this particular edition...

As far as this particular edition by Merchant Books of the famous Mach's "The Science of Mechanics" goes, the only excuse for the *very low* typographical quality is the low price (< $30). I always wanted to own a copy of this book, because, I believe, it is first book where the now famous "Mach's principle" (the debates among scientists have beenongoing for almost a century now !) has been stated. It is also famous for being a major influence to the young Albert Einstein in formulating the basic principles of his theory of general relativity. The price of the other editions seemed to be too steep for me, so, when this one came out, I instantly purchased it. Well, the major downside of the book is that the most of the formulas are printed terribly (for instance, most of the horizontal bars in formulas like A/B are missing, and they are also missing in most of the square root symbols (so they look more like the letter "V"). Fortunately, it requires only a couple of hours with a pencil and ruler in hand to correct all of these, as they all are self evident. The overall look of the text is like that of a photocopy of a photocopy of the original typographic text, which doesn't always please the eye. On the other hand it's <$30 vs. >$50, so it up to you to decide which edition to buy (and the $54 book is not ideal either)...

Intellectual giant
One of the most influential books that led Einstein to become skeptical of concepts like absolute space and time. Einstein enjoyed Mach's no-nonsense attitude. I found it a bit difficult to read but enjoyed it very much.

Priceless
If i am not mistaken this is the very book that Einstein read and from which he developed his idead of special relativity. It was the critique of Mach of the ideas of Newton which exposed the flaus in Newton's thinking. Einstein built on Mach's ideas and brought his own questions to the subject which brough great results, not only in classical physics but made possible the developement of modern physics.

Descartes said: "Today, then, as i have suitably freed my mind from all cares, and have secured for myself an assured leisure in peaceful solitude, i shall at last apply myself earnestly and freely to the general overthrow of all my former opinions."

It is in this spirit that new physics, and sciences in general, are created. A million experiments will not bring about any progress. Pure rationalism is the true creator, which is at the very nature of a theoretical physicist. This book exposes the thinking of such a person. ... Read more

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Covers addition, multiplication and exponentiation of cardinal numbers, smallest transfinite cardinal numbers, ordinal types of simple ordered aggregates and operations on ordinal types. Develops theory of well-ordered aggregates; investigates ordinal numbers of well-ordered aggregates and more.
... Read more

Customer Reviews (2)

Detailed Axiomatic Development of Transfinite Numbers - Not Suitable as Introduction
Georg Cantor's final and logically purified memoir on transfinite numbers was published in the late 1890s.This Dover reprint is the 1915 English translation by the mathematician Philip E. B. Jourdain; it also includes a lengthy, technically diffcult introduction by Jourdain.

Contributions to the Founding of the Theory of Transfinite Numbers is not suitable as an introduction. I unwisely disregarded caution from an earlier reviewer that Cantor's work would not be appropriate for a beginner in set theory. (I thought that I was reasonably acquainted with set theory, but I do admit that I was not a math major.)

The 82-page introduction by Jourdain assumes that the reader is reasonably familiar with the work of key nineteenth century mathematicians.While it is possible to skip the introduction, Jourdain's context setting is quite helpful. Cantor's transfinite numbers are so innovative and so unexpected that it almost seems as though they spring forth in a vacuum, but Jourdain shows that the earlier work of Dirichlet, Cauchy, Riemann, and Weierstrass helped point the way for Cantor.

Cantor's memoir (that is, his two-part discussion of transfinite number theory) comprise the remaining 125 pages. The difficulty with Cantor's axiomatic presentation is two-fold. First, the material itself is not easy - despite Cantor's careful approach. I even bogged down for awhile on his early discussion of the exponentiation of powers and how this leads to aleph-zero. And second, much of his terminology is outdated and unfamiliar. For example, there is no mention of sets, just aggregates and parts. Another example is that Cantor speaks of reciprocal and univocal correspondence. I have yet to complete Cantor's work, but I am continuing to plod along.

A recommendation: A much better starting point for readers new to transfinite numbers is a fascinating book by Mary Tiles, titled The Philosophy of Set Theory - An Historical Introduction to Cantor's Paradise. This work targets mathematics and philosophy majors, but is accessible to others.

An interesting book
There's nothing like reading the original.Here is the abstract theory of transfinite ordinals described by its originator, Georg Cantor.

It's probably not the best introduction to set theory for a beginner.The bookfocuses more on ordinal numbers than on cardinals or general sets.It'snot a great reference, either, since so many important results in settheory have been proven in the 100 years since Cantor.But I like thisbook a lot nonetheless.The exposition is beautiful -- concise, clear, andlogical.It's one of the most nicely presented math books I've read. ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing’s Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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An Unabridged Printing, To Include Updated Typeface ... Read more