Talk:Cantor's first set theory article
Title containing "article"
This looks like a fascinating (Wikipedia) article, and I'm looking forward to reading it in detail.
I'm not too convinced by the title, though. I think it's more usual to refer to such contributions as "papers" rather than "articles". To me "article" sounds like something you find in a magazine, not a journal. Also, as I alluded to above, it's a bit problematic that "article" also is used to refer to Wikipedia articles, and there's possible interference from that, for editors discussing the Wikipedia article, but more importantly also for readers.
We could move it to Georg Cantor's first set theory paper, but to be honest I would rather move it to the actual title, On a Property of the Collection of All Real Algebraic Numbers, and put it in italics. I think in general we write articles on notable papers by their titles. See for example On Formally Undecidable Propositions of Principia Mathematica and Related Systems (not sure why it's not in italics; I think it should be). --Trovatore (talk) 03:38, 13 February 2016 (UTC)
- Just an update on the italics issue — I went ahead and added {{italic title}} to the other article. But now I'm having second thoughts; there may be an argument for preserving a distinction between book titles, which are italicized, and titles of papers, which are not. I don't know. I think it looks better with italics; it makes it clearer that it's a title of a published work. --Trovatore (talk) 03:59, 13 February 2016 (UTC)
The article rewrite and thanks to all those who helped me
It's been challenging rewriting the "Cantor's first uncountability proof" article because it's listed in the categories: History of mathematics, Set theory, Real analysis, Georg Cantor. So I had to consider both the math and the math history audiences. I did this by writing the article so all the math in Cantor's article appears in the first two sections, which is followed by a "Development" section that acts as a bridge from the math sections to the math history sections. I changed the title to "Cantor's first set theory article" to reflect its content better; actually, the old article could have used this title. It's a well-known, often-cited, and much-discussed article so I suspect the Wikipedia article will attract a number of readers.
I would like to thank SpinningSpark for his excellent critique of the old article. I really appreciate the time and thought he put into it. The new article owes a lot to SpinningSpark. His detailed section-by-section list of flaws was extremely helpful. I used this list and his suggestions to restructure and rewrite the article. I particularly liked his comment on whether the disagreement about Cantor's proof of the existence of transcendentals "has been a decades long dispute with neither side ever realising that they were not talking about the same proof." The lead now points out this disagreement has been around at least since 1930 and still seems to be unresolved. It was a major flaw of the old article that the longevity of the disagreement was never mentioned. I find it ironic that this disagreement is still around, while most mathematicians now accept transfinite (infinite) sets so the old dispute about the validity of these sets is mostly resolved.
I also thank JohnBlackburn for his comments. His comments that made me realize that I should think of the readers who just want to understand the math in Cantor's proof. This led to the restructuring mentioned above in the first paragraph. His comments also led me to put the long footnotes containing math proofs into the text. I also added some more math to the article.
I thank Jochen Burghardt for his help on the rewrite. He did the case diagrams for the proof of Cantor's second theorem, the subsectioning of "The Proof" section, the calculations in the table "Cantor's enumeration of the real algebraic numbers", and he pointed out places where my writing was unclear. The need for the case diagrams came from reading SpinningSpark's comment on what is now Case 1. I realized that a reader's possible confusion on whether there is point in the finite interval (aN, bN) besides xn could be handled with a diagram. I contacted Jochen with three simple ASCII diagrams. He took my simplistic diagrams and produced diagrams that capture the dynamics of the limiting process.
I thank my daughter Kristen who read a recent draft and made a number of suggestions that improved the writing. Especially important were her suggestions on improving the lead.
I also thank those who edited the old article. I started with a copy of the old article and have kept up with recent edits so that your edits would be preserved (except perhaps in the parts of the article where large changes were made).
Finally, I wish to thank Michael Hardy for his GA nomination for the old article, for giving me the go-ahead for the rewrite, and for his patience with the amount of time it has taken me to do the rewrite. I hope that this rewrite is much closer to GA standards than the old article. --RJGray (talk) 15:26, 13 February 2016 (UTC)
No need to merge article with Cantor's first uncountability proof -- already contains its content
There is no need to merge this article with Cantor's first uncountability proof because this is a rewrite of that article with guidance from the GA Review of that article. What is needed is a redirect from Cantor's first uncountability proof to this new article. Note that Cantor's first uncountability proof appears in boldface in first paragraph so readers will know that this article contains the content of that article. --RJGray (talk) 15:37, 13 February 2016 (UTC)
Requested move 13 February 2016
 | It has been proposed in this section that Cantor's first set theory article be renamed and moved to On a Property of the Collection of All Real Algebraic Numbers. A bot will list this discussion on the requested moves current discussions subpage within an hour of this tag being placed. The discussion may be closed 7 days after being opened, if consensus has been reached (see the closing instructions). Please base arguments on article title policy, and keep discussion succinct and civil. Please use {{subst:requested move}}. Do not use {{requested move/dated}} directly. |
Georg Cantor's first set theory article → On a Property of the Collection of All Real Algebraic Numbers – Article is about this paper, so name it after the paper. See more elaborate remarks at the section #Title_containing_.22article.22 above. Trovatore (talk) 20:20, 13 February 2016 (UTC)
A couple of points to think about:
- The title of Cantor's article "On a Property of the Collection of All Real Algebraic Numbers" does not capture what the article is famous for--namely, the uncountability of the set of real numbers. Gödel's article "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I" does capture what the article is famous for. The reason for Cantor's choice of name is covered in the Wikipedia article.
- If we drop the "Georg" in the Wikipedia article's title, a reader who is interested in Cantor can type "Cantor" into the Search box and see the Wikipedia article along with other articles about Cantor's work. Being a reader who uses this feature of the Search box when I'm curious about a mathematician's or scientist's work, I think "Cantor's first set theory article" would be more reader-friendly than "On a Property of the Collection of All Real Algebraic Numbers."
- As far as "article" vs. "paper". See Difference Between Research Article and Research Paper. Two items of interest: "• There is a trend to refer to term papers and academic papers written by students in colleges as research papers whereas articles submitted by scholars and scientists with their groundbreaking research are termed as research articles. • Research articles are published in renowned scientific journals whereas papers written by students do not go to journals."