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I see that you have rephrased the subheadings so that they are no longer questions and tinkered with the corresponding phrasing in the lead. I am afraid this is not really getting to the heart of the matter. I think some structural changes to the article need to be made to take the emphasis off this alleged dispute/disagreement. The disagreement does not seem to amount to a whole pile of beans. If it does, some sources saying so are needed. Even more, fundamentally from a GA perspective (criterion 3b), the discussion of this dispute is part of a tendency for the article to go off at a tangent to discuss Cantor's other proof(s). The non-constructive proof is the diagonal argument, no? which is not the subject of this article. I have already commented on how easily the reader can become confused over which proof is being discussed. The diagonal argument should be discussed only inasmuch as it is needed to describe ''this'' method, or in passing to say Cantor went on to use other methods. [[User:Spinningspark|<b style="background:#FAFAD2;color:#C08000">Spinning</b>]][[User talk:Spinningspark|<b style="color:#4840A0">Spark</b>]] 13:05, 20 December 2014 (UTC)
* To me to the article seems to fall short of GA quality for structural reasons. In some ways it reads more like an essay than an article, and as such is difficult to follow as WP articles aren't essays, i.e. posing questions and answering them. For a mathematical article it contains relatively little mathematics, with too much relegated to footnotes, which themselves are far too long; they should contain only references, with footnotes kept to a minimum and clearly separated. And it has far too many quotes; quotes should be integrated into the article so the article not sources make the point, other than a quote of the proof I can see none that are needed. A reader should be able to read the article and extract the content without referencing footnotes, without the flow being interrupted by quotations.
: Some more particular points. The proof is given very discursively, with 'Cantor' used throughout. It's his proof with his name but in a mathematical proof there's no need to describe it as if he's doing it, just give the mathematics. It would also be clearer with proper math, i.e. <nowiki><math></nowiki>, formatting. The two 'answering the questions' sections seem very unclear; 'Constructive or non-constructive nature of Cantor's proof of the existence of transcendentals' seems to be mixing the proof up with the diagonal method from the very first quote. 'Why Cantor's article emphasizes the countability of the algebraic numbers' never clearly answers that point. It also mentions a "controversy" but does not say where it's from; such a controversy definitely needs a source or sources.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 14:18, 20 December 2014 (UTC)
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