Talk:Cantor's first set theory article/Archive 1

message: I am very happy to see a Wikipedia article about Cantor's first uncountability proof. Since I have studied Cantor's 1874 article and some of his correspondence, I started adding material and making some changes. The result of this work can be found at: Talk:Cantor's first uncountability proof/Temp. I hope you find my revisions interesting and relevant. I'm looking forward to your suggestions, modifications, and feedback. Here's a section-by-section summary of my revisions:
Introduction: Made some changes and mentioned two controversies that have developed around Cantor's article.  The "emphasis" controversy ("Why does Cantor's article emphasize the countability of the set of real algebraic numbers?") is already discussed in the current article. The "constructive/non-constructive" controversy concerns Cantor's proof of the existence of transcendental numbers.
Development and Publication: Expanded the current "Publication" section by adding material that comes mostly from Cantor's correspondence. Like the current section, this new section discusses the "emphasis" controversy, but I did add some material here.
The Article: Replaces the current "The theorem" section. Contains statements of the theorems that Cantor proves in his article. Also, uses Cantor's description of his article to bring out the article's structure. This structure is the key to handling the "constructive/non-constructive" controversy.
The Proofs: Contains proofs of Cantor's theorems. 
Cantor’s Method of Constructing Transcendental Numbers: Replaces the current "Real algebraic numbers and real transcendental numbers" section. Also, discusses the "constructive/non-constructive" controversy.
I have also added a "Notes" section, and I have added references to the current "References" section.
I highly recommend reading Cantor's original article, which is at: "Über eine Eigenschaft des Ingebriffes aller reelen algebraischen Zahlen". A French translation (which was reviewed and corrected by Cantor) is at: "Sur une propriété du système de tous les nombres algébriques réels". Unfortunately, I have not found an English translation on-line. However, an English translation is in: Volume 2 of Ewald's From Immanuel Kant to David Hilbert: A Source Book in the Foundations of Mathematics ().
Most of the material I added to this Wikipedia article comes from Cantor's article, Cantor's correspondence, Dauben's biography of Cantor (), and the article "Georg Cantor and Transcendental Numbers". 
Finally, I wish to thank all the people who have worked on this Wikipedia article. Without the excellent structuring of your article and the topics you chose to cover, I suspect that I would not have written anything. (This is the first time I've written for Wikipedia.) It's much easier to add and revise rather than develop from scratch. RJGray (talk) 23:30, 5 May 2009 (UTC)
replies: text: I've moved RJGray's draft to the article space and merged its edit history with that of the article as it appeared before. Michael Hardy (talk) 03:54, 23 January 2010 (UTC)
thread_title:  Proposed Changes to Article 

message: Cantor's 2nd theorem seems obvious at first glance to many people, as we usually are unable to imagine a sequence that could completely fill a whole interval. However, there are sequences (like that of all positive rational numbers) whose set of accumulation points equals a whole interval (or even whole ℝ+; cf. the picture there). Mentioning this in the article might prevent novice readers from thinking "Mathematicians make a big fuzz proving things that are obvious, anyway", and might generally help to sharpen one's intuition about what a sequence can do in relation to an interval and what it cannot. It would require, however, to explain the notion of an accumulation point (which is poorly represented in English Wikipedia in general). - Jochen Burghardt (talk) 11:52, 17 December 2013 (UTC)
thread_title:  Contrast 2nd theorem with sequence of rational numbers?