Editing Georg Cantor (section)

==External links==
* {{Wikiquote-inline}}
* {{Commons category-inline}}
* {{Internet Archive author |sname=Georg Cantor}}
* {{MacTutor|id=Cantor}}
* {{MacTutor|class=HistTopics|id = Beginnings_of_set_theory|title = A history of set theory}} Mainly devoted to Cantor's accomplishment.
* [https://www.britannica.com/biography/Georg-Ferdinand-Ludwig-Philipp-Cantor Georg Cantor], britannica.com
* ''Stanford Encyclopedia of Philosophy'': [http://plato.stanford.edu/entries/set-theory/ Set theory] by [[Thomas Jech]]. [https://plato.stanford.edu/entries/settheory-early/ The Early Development of Set Theory] by José Ferreirós.
* "Cantor infinities", analysis of Cantor's 1874 article, ''[http://www.bibnum.education.fr/mathematiques/theorie-des-nombres/cantor-et-les-infinis BibNum]'' <small>(for English version, click 'à télécharger')</small>. There is an error in this analysis. It states Cantor's Theorem 1 correctly: Algebraic numbers can be counted. However, it states his Theorem 2 incorrectly: Real numbers cannot be counted. It then says: "Cantor notes that, taken together, Theorems 1 and 2 allow for the redemonstration of the existence of non-algebraic real numbers …" This existence demonstration is [[non-constructive]]. Theorem 2 stated correctly is: Given a sequence of real numbers, one can determine a real number that is not in the sequence. Taken together, Theorem 1 and this Theorem 2 produce a non-algebraic number. Cantor also used Theorem 2 to prove that the real numbers cannot be counted. See [[Cantor's first set theory article]] or [http://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Gray819-832.pdf Georg Cantor and Transcendental Numbers] {{Webarchive|url=https://web.archive.org/web/20220121155859/https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Gray819-832.pdf |date=21 January 2022 }}.

{{Classical logic}}
{{Fractals}}
{{Set theory}}
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