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===The article===
* "Cantor's article is short, not even four and a half pages" — Can we trim this to "Cantor's article is under five pages long" or "Cantor's article is roughly four and a half pages"?
*<s>"It begins with a discussion of the real algebraic numbers" — Would "definition" be better than "discussion"?</s>
*"Cantor restates this theorem in terms more familiar to mathematicians of his time" — This seems to be a stronger claim than is verified by the paper itself (or its English translation).
*<s>"The first part of this theorem implies the "Hence" part ..." — Agreed, but Cantor doesn't describe this in the article, right? Or am I missing the point/context of this paragraph?</s>
===The proofs===
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===Lead===
*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>"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>
*"Cantor's article also contains a proof of the existence of transcendental numbers" — I would mention their infinitude as well.
*"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."
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I'm putting the article formally {{on hold}} now, so you have seven days to begin addressing the points above. <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''<sub>[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]</sub></span> 01:50, 29 July 2018 (UTC)
=== Comments ===
* The review says this: <blockquote>"Cantor's article is short, not even four and a half pages" — Can we trim this to "Cantor's article is under five pages long" or "Cantor's article is roughly four and a half pages"?</blockquote> But I think it is better as it is. Informing the reader that that length is small by comparison to what was (and is) typical is relevant.
::But that's an unreferenced claim. The classic [[WP:SYNTH|Synthesis]] example is about "160" vs "only 160", and it's a similar thing here. Just say "four and a half pages", and the readers can easily work out for themselves that that's quite short. <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''<sub>[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]</sub></span> 18:40, 4 August 2018 (UTC)
: Then the review says <blockquote>"It begins with a discussion of the real algebraic numbers" — Would "definition" be better than "discussion"?</blockquote> There is indeed a terse definition at the beginning. Then there is a longer discussion that includes such things as the fact that every interval about a real algebraic number contains infinitely many others.
::Yes, that makes sense. <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''<sub>[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]</sub></span> 18:40, 4 August 2018 (UTC)
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: Next the review says <blockquote>"The first part of this theorem implies the "Hence" part ..." — Agreed, but Cantor doesn't describe this in the article, right? Or am I missing the point/context of this paragraph?</blockquote> But should we have no discussion of trivial consequences of what Cantor said?
::This initially confused me because I thought the section was solely about points made in the article, but I now see that "Cantor observes" and similar are used to distinguish points made by Cantor and secondary commentary. My mistake. I would prefer a source for the paragraph but I'm happy to let it go, on account of [[Wikipedia:Scientific citation guidelines#Uncontroversial knowledge|Uncontroversial knowledge]]. <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''<sub>[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]</sub></span> 18:40, 4 August 2018 (UTC)
: Then we see this: <blockquote>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</blockquote> {{ping|Bilorv}}What do you mean by "the closed interval simplification"?
::Sorry for the weird phrasing. I was referring to: "We simplify Cantor's proof by using open intervals." <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''<sub>[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]</sub></span> 18:40, 4 August 2018 (UTC)
: Next: <blockquote>"One of these theorems is "Cantor's revolutionary discovery" that ..." — It's not clear where this quote originates</blockquote> But a work of Joseph Dauben is cited.
::My mistake—I thought that citation covered the uncountability of the reals but not the quote. <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''<sub>[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]</sub></span> 18:40, 4 August 2018 (UTC)
: [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 18:11, 4 August 2018 (UTC)
::(So you're aware, I've changed this to a level 3 header per the "Please add all review comments..." hidden note at the top of the page. I'm also interspersing replies because I think that's simpler – feel free to move them if you prefer, or move your comments above to intersperse with my original review.) <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''<sub>[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]</sub></span> 18:40, 4 August 2018 (UTC)
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