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===The legacy of Cantor's article===
*"In 1922, Thoralf Skolem proved that if the axioms of set theory are consistent" — Which axioms of set theory exactly? Is this referring to a specific collection of axioms (e.g. ZFC), or saying generally "given any set of consistent axioms ..."? (In the latter case, the definite article "'''the''' axioms of set theory" is misleading.)
*<s>"[[Skolem's paradox|this does not contradict Cantor's uncountability theorem]]" is an [[WP:EASTER|Easter egg]] link; mention the phrase "Skolem's paradox" in prose.</s>
===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>
*<s>"Cantor's article also contains a proof of the existence of transcendental numbers" — I would mention their infinitude as well.</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."
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: Rewrote sentence to eliminate Easter egg link to [[Skolem's paradox]]. —[[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 20:41, 5 August 2018 (UTC)
: Concerning "infinitude of transcendentals" in Lead. In [[WP:Lead]], it states: "The lead serves as an introduction to the article and a summary of its most important contents." The most important content is that Cantor devised a new method of proving the existence of transcendentals. Their infinitude follows easily from their existence in many different ways—one simple way is by adding rationals to a transcendental, which has nothing to do with Cantor's work. The fact that Cantor's method can also generate infinitely many transcendentals is just one of many ways to prove their infinitude and is a detail that I feel is best left to the later discussion of his method. —[[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 21:02, 5 August 2018 (UTC)
::Okay, fair enough. <span class="nowrap">— '''[[User:Bilorv|Bilorv]]'''<sub>[[Special:Contribs/Bilorv|(c)]][[User talk:Bilorv|('''talk''')]]</sub></span> 22:54, 5 August 2018 (UTC)
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