Contributions to the Founding of the Theory of Transfinite Numbers (Dover Books on Mathematics) First Edition

Cantor probably contributed more to our modern theory than any other mathematician. In my opinion, a true genius who dedicated most of his life to getting a clearer and more in-depth understanding of the topic than almost any other human. However, reading this book is for those who might enjoy reading "Euclid's Elements." A wonderful co-joining of a truly powerful mind and allowing insights into how they approached the topic, but definitely not a modern textbook. For a historian, it is where modern foundations of numbers were first treated. I hope you enjoy it as much as I did.

I love number theory and my first argument with a mathematics teacher was when I was eight years old on the topic of inequalities, integers, and real numbers. Enjoy reading Mr. Cantor’s foundations.

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 And second, much of his terminology is outdated and unfamiliar.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.

Good book.

Bought this over the Dover edition because I wanted a hardcover, and had great experience with Fermat's Oeuvres in reproduction. Nope. This one is a repro of a Harvard library copy that is badly marked up. Underlines in the text, check marks and scribbling in the margins. Get the Dover paperback instead.

Dover has up 'till now done a flawless job in its Kindle transcriptions, but I had to return this particular book. The scans of Cantor's equations and theorems are low quality blow-ups from the print edition and, what's worse, when some are transcribed into actual text, they often get garbled into question marks. Perhaps it's a technological problem and the kindle software just cannot parse some of the more esoteric mathematical symbols used in this publication. In any case, I advise everyone to stick with their hardcopies until Dover issues an improved edition.

Arrived quickly and in perfect condition.