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Perhaps my unfinished manuscript [http://www.geocities.com/bencawaling/cantor_anti-diagonal_argument.pdf "Cantor Anti-Diagonal Argument -- Clarifying Determinateness and Consistency in Knowledgeful Mathematical Discourse"] would be useful now to those interested in understanding Cantor anti-diagonal argument. I was hoping to submit it to the Bulletin of Symbolic Logic this year. Unfortunately, since 1 January 2008, I have been suffering from recurring extremely blurred vision due to frequent “exploding optical nerves” brought on by my diabetes (I can’t afford laser eye surgery) and I had only about 20 productive days in the last 8 months. At this rate, it would take me a long while to finish my paper or may not be able to complete it if I go permanently blind soon. I just hope my endeavors to clarify mathematical infinity and modern logic would reach the next (if not the present) generations of mathematicians, philosophers, and logicians. [BenCawaling@Yahoo.com] [[User:BenCawaling|BenCawaling]] ([[User talk:BenCawaling|talk]]) 08:08, 4 September 2008 (UTC)
== Proposed Changes to Article ==
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: [http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=266194 "Über eine Eigenschaft des Ingebriffes aller reelen algebraischen Zahlen"]. A French translation (which was reviewed and corrected by Cantor) is at: [http://www.springerlink.com/content/37030699752l2573/fulltext.pdf "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'' (ISBN 9780198532712).
Most of the material I added to this Wikipedia article comes from Cantor's article, Cantor's correspondence, Dauben's biography of Cantor (ISBN 0674348710), and the article [http://mathdl.maa.org/mathDL/22/?pa=content&sa=viewDocument&nodeId=2907 "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. [[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 23:30, 5 May 2009 (UTC)
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