Talk:Cantor's first set theory article/GA2: Difference between revisions

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#It is '''reasonably well written'''.

#:a ''(prose, spelling, and grammar)'': {{GAList/check|y}} b ''([[Wikipedia:Manual of Style|MoS]] for [[Wikipedia:Manual of Style/Lead section|lead]], [[Wikipedia:Manual of Style/Layout|layout]], [[Wikipedia:Manual of Style/Words to watch|word choice]], [[Wikipedia:Manual of Style/Writing about fiction|fiction]], and [[Wikipedia:Manual of Style/Embedded lists|lists]])'': {{GAList/check|y}}

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#It is '''factually accurate''' and '''[[Wikipedia:Verifiability|verifiable]]'''.

#:a ''([[Wikipedia:Manual of Style/Layout#Notes and references|reference section]])'': {{GAList/check|y}} b ''(citations to [[Wikipedia:Identifying reliable sources|reliable sources]])'': {{GAList/check|y}} c ''([[Wikipedia:No original research|OR]])'': {{GAList/check|y}} d ''([[Wikipedia:Copyrights|copyvio]] and [[Wikipedia:Plagiarism|plagiarism]])'': {{GAList/check|y}}

#::

#It is '''broad in its coverage'''.

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#'''Overall''':

#:''Pass/Fail'': {{GAList/check|y}}

#:: <!-- Template:GAList -->

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===The proofs===

*<s>I'm confused about the sourcing for these subsections, other than the parts which are direct rephrasing of Cantor's article. In particular, it seems like there should be inline citations somewhere for the table in the first proof, the closed interval simplification in the second proof and the entirety of the example of Cantor's construction.</s>

===The development of Cantor's ideas===

*<s>"[[Liouville_number#Liouville_numbers_and_transcendence|Liouville's theorem that there are transcendental numbers]]" — Is this the same theorem mentioned above that there exist infinitely many transcendental numbers in any closed interval? Or an earlier theorem of Liouville's? If it's the same theorem, the link probably belongs under its first mention (and rephrasing to connect the two mentions would be good); if not, ignore me.</s>

===The disagreement about Cantor's existence proof===

*<s>In the third paragraph, the "exact" asymptotics <math>O(2^{\sqrt[3]{n}})</math> and <math>O(n^2 \log^2 n \log \log n)</math> might as well be mentioned.</s>

*<s>"The proof of Cantor's second theorem does not state why some limits exist. The proof he was using does." — I don't quite understand either of these sentences. My understanding from reading the paper is that Cantor implicitly invokes what I would describe as the [[Monotone convergence theorem|Monotonic Sequence Theorem]] to deduce that <math>\alpha^\infty</math> and <math>\beta^\infty</math> exist. Does this bullet point mean that Cantor is using this without statement, but requires it for his claims? Or that Cantor didn't explain this bit but the editor added in an explanation? Or something completely different?</s>

*<s>Is the 1870 Heine article relevant to Cantor or his work (e.g. a close friend / publication on a similar topic)? Is the point here that Kronecker is delaying publication in the journal because of his finitist views? (If so, add a few words to spell this out.)</s>

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===Lead===

*<s>Add a link to [[Georg Cantor]] somewhere (but not in the bolded text). In fact, it's not really necessary to use the phrase "Georg Cantor's first set theory article" verbatim in the first sentence: I recommend "[[Georg Cantor]] published his first set theory article in 1874; it contains ..."</s>

*<s>"One of these theorems is "Cantor's revolutionary discovery" that ..." — It's not clear where this quote originates, and it's also not mentioned in the body of the article.</s>

*<s>"Cantor's article also contains a proof of the existence of transcendental numbers" — I would mention their infinitude as well.</s>

*<s>"In addition, they have looked at the article's legacy" — I think it would be better to actually describe the legacy e.g. "The uncountability theorem and the concept of countability have had a significant impact on mathematics, and Cantor's later work followed on from these ideas."</s>

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:The example of Cantor's construction is another "illustrative example" with the additional feature of being able to be verified by doing some calculations. — [[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 16:12, 10 August 2018 (UTC)

::I retract the comment about the table and the closed intervals.

::Can you describe to me how the [[Georg Cantor%27s first set theory article#Example of Cantor's construction|Example of Cantor's construction]] was written? If you mean to say that you claim the entire section falls under [[WP:SCG]], then I'll have to take a closer look and research into what the standard is in this area. I wouldn't describe it as a "simple derivation" or a "routine calculation", not due to complexity but due to the length of the section. The table is trivial, but not the proof of {{nowrap|''x_i'' ∉ (''a_n'', ''b_n'')}}. But then, surely there's a source which covers this step that Cantor omitted. <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''_{[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]}</span> 18:58, 10 August 2018 (UTC)

:I came up with a short proof that that for all&nbsp;''n'', (''a''_''n'',&nbsp;''b''_''n'') excludes ''x''₁,&nbsp;…&nbsp;,&nbsp;''x''_2''n''. This implies Cantor's statement ''x''_''n'' does not belong to the interval (''a''_''n'',&nbsp;''b''_''n''). Your comment on looking for a source helped me even though I couldn't find a source that had a proof. Discussions of Cantor's 1874 method seem to be fairly rare; nearly everyone seems to prefer discussing the diagonal method. However, seeing again that Cantor made the unproven observation ''x''_n&nbsp;&notin;&nbsp;(''a''_n,&nbsp;''b''_n) led me to think that he probably left out the proof because it was a simple proof. In his book, Dauben approaches the result differently. He points out, but doesn't prove, that if ''a''_∞&nbsp;=&nbsp;''x''_''k'', then for sufficiently large index ''n'', ''x''_k would be excluded from all intervals nested within (''a''_n,&nbsp;''b''_n). I believe that the new proof fits within the [[WP:SCG]] guidelines (it's a simple derivation that makes Cantor's proof more accessible to Wikipedia readers than Cantor's original proof, which was meant for research mathematicians). Also, the trimmed down Example section is now strictly an example.

:Your observations have led to this very significant improvement of the article. This together with your other suggestions prove that you've done an excellent job as a Good Article reviewer. In the next few days, I plan to finish working through your remaining suggestions. —[[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 23:14, 14 August 2018 (UTC)

::I'm very happy with the new version, and glad that you appreciate my comments. The article is in pretty good shape! Just a couple of small things left. <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''_{[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]}</span> 00:06, 15 August 2018 (UTC)

: Added asymptotic complexity of computer programs computing digits of a transcendental to a footnote. Changed wording of sentence on article's legacy in Lead. Kept it general and changed "namely" to "which includes" which is more accurate. I didn't follow suggestion to mention Cantor's later work because the legacy section mentions quite a few mathematicians. I have mixed feelings about "significant impact" vs. "impact". Either way is fine with me; I just used the more conservative "impact".

:It looks like all suggested improvements have been made. The first "Lead" item: The link to "Georg Cantor" has already been done, but wasn't crossed out. —[[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 18:53, 17 August 2018 (UTC)

::I've changed the complexity reference to a note (in [[Special:Diff/855385322|this edit]]), but feel free to revert me or make other changes if you wish. That is indeed everything, so thanks for all your hard work, I hope you think the article is at a higher standard than it was before the review and that's a '''pass for GA'''! <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''_{[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]}</span> 22:20, 17 August 2018 (UTC)

:I agree that the complexity reference should be a note, thanks for catching that. I especially wish to thank you for all your hard work on the review. It's been a pleasure working with you and I do think the article is at a higher standard than it was before the review. —[[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 00:23, 18 August 2018 (UTC)