Talk:Cantor's first set theory article/Archive 2: Difference between revisions

Revision as of 14:13, 22 January 2010

Latest revision as of 06:48, 6 July 2023

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What an arrogant, foolish lot you are. [[Special:Contributions/91.105.179.213|91.105.179.213]] ([[User talk:91.105.179.213|talk]]) 14:01, 22 January 2010 (UTC)

==Assessment comment==

{{Substituted comment|length=251|lastedit=20160222213904|comment=The article could use expansion, but for its length it seems OK. The citations in the history section could be a little more specific. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 14:16, 22 January 2010 (UTC)}}

Substituted at 06:32, 7 May 2016 (UTC)

== 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). --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 03:38, 13 February 2016 (UTC)

:<small>Just an update on the italics issue &mdash; I went ahead and added {{tl|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. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 03:59, 13 February 2016 (UTC) </small>

== 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 (''a_N'', ''b_N'') besides ''x_n'' 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. --[[User:RJGray|RJGray]] ([[User talk: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. --[[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 15:37, 13 February 2016 (UTC)

:Ok, but in that case we needed to merge the histories to make it clearer that much of the content was rewritten from the older version. I have completed a history merge, so now the histories of both articles are in one place, and removed the merge tags. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 21:41, 13 February 2016 (UTC)

== Constructive? ==

The lede text on constructiveness seems a bit confused. There's not clear evidence for a controversy; the only "against" is "Stewart, 2015" but that's not enough to identify who Stewart is. Or who Sheppard 2014 might be. Fraenkel is a heavyweight though so you'd need a good reason to disagree with him [[User:William M. Connolley|William M. Connolley]] ([[User talk:William M. Connolley|talk]]) 22:46, 2 April 2016 (UTC)

:Those are standard Harvard citations and the sources are listed at the end, so it is clear enough to me what the references point to. There seems to be an entire section of the article related to this issue, with numerous sources. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 15:05, 3 April 2016 (UTC)