Book Description

Customer Reviews (4)

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.

Destined for Fame
This book seems full of interesting ideas - I predict it could have a significant impact if its ideas were to become widely known. ... Read more

Book Description
"In it, Jourdain outlines the contributions of many of Cantors¿including Fourier, Dirichlet, Cauchy, Weierstrass, Riemann, Dedekind, and Hankel¿and then further contextualizes Cantorking theory by recounting and examining his earlier work. In this volume, Cantor addresses: ¿ the addition and multiplication of powers ¿ the exponentiation of powers ¿ the finite cardinal numbers ¿ the smallest transfinite cardinal number aleph-zero ¿ addition and multiplication of ordinal types ¿ well-ordered aggregates ¿ the ordinal numbers of well-ordered aggregates ¿ and much more.German mathematician GEORG CANTOR (1845-1918) is best remembered for formulating set theory. His work was considered controversial at the time, but today he is widely recognized for his important contributions to the field of mathematics." ... 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

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

Book Description
A Supplement To The Third English Edition, Containing The Author's Additions To The Seventh German Edition - Translated And Annotated By Philip E. B. Jourdain. A Critical And Historical Account Of Its Development, And Unabridged Printing: Publisher's Preface To The Supplementary Volume - Author's Preface To The Seventh German Edition - Appendix Of Additions And Alterations To The Seventh German Edition - Corrections To Be Made In The Science Of Mechanics - Notes On Mach, By Philip E. B. Jourdain - Index ... Read more