Cantor's diagonal argument (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Cantor's diagonal argument" in English language version.

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Bell, John L. (2004), "Russell's paradox and diagonalization in a constructive context" (PDF), in Link, Godehard (ed.), One hundred years of Russell's paradox, De Gruyter Series in Logic and its Applications, vol. 6, de Gruyter, Berlin, pp. 221–225, MR 2104745

andrej.com

math.andrej.com

Bauer, A. "An injection from N^N to N Archived 27 November 2021 at the Wayback Machine", 2011

archive.org

Rudin, Walter (1976). Principles of Mathematical Analysis (3rd ed.). New York: McGraw-Hill. p. 30. ISBN 0070856133.
Bloch, Ethan D. (2011). The Real Numbers and Real Analysis. New York: Springer. p. 429. ISBN 978-0-387-72176-7.

arxiv.org

Pradic, Cécilia; Brown, Chad E. (2019). "Cantor-Bernstein implies Excluded Middle". arXiv:1904.09193 [math.LO].
Bauer; Hanson (2024). "The Countable Reals". arXiv:2404.01256 [math.LO].
Robert S. Lubarsky, On the Cauchy Completeness of the Constructive Cauchy Reals, July 2015

books.google.com

Keith Simmons (30 July 1993). Universality and the Liar: An Essay on Truth and the Diagonal Argument. Cambridge University Press. ISBN 978-0-521-43069-2.
Sheppard, Barnaby (2014). The Logic of Infinity (illustrated ed.). Cambridge University Press. p. 73. ISBN 978-1-107-05831-6. Extract of page 73

digizeitschriften.de

Georg Cantor (1891). "Ueber eine elementare Frage der Mannigfaltigkeitslehre". Jahresbericht der Deutschen Mathematiker-Vereinigung. 1: 75–78. Archived from the original on 3 January 2023. Retrieved 11 June 2018. English translation: Ewald, William B., ed. (1996). From Immanuel Kant to David Hilbert: A Source Book in the Foundations of Mathematics, Volume 2. Oxford University Press. pp. 920–922. ISBN 0-19-850536-1.
See page 254 of Georg Cantor (1878), "Ein Beitrag zur Mannigfaltigkeitslehre", Journal für die Reine und Angewandte Mathematik, 84: 242–258, archived from the original on 6 November 2018, retrieved 17 August 2017. This proof is discussed in Joseph Dauben (1979), Georg Cantor: His Mathematics and Philosophy of the Infinite, Harvard University Press, ISBN 0-674-34871-0, pp. 61–62, 65. On page 65, Dauben proves a result that is stronger than Cantor's. He lets "φ_ν denote any sequence of rationals in [0, 1]." Cantor lets φ_ν denote a sequence enumerating the rationals in [0, 1], which is the kind of sequence needed for his construction of a bijection between [0, 1] and the irrationals in (0, 1).

doi.org

Gray, Robert (1994), "Georg Cantor and Transcendental Numbers" (PDF), American Mathematical Monthly, 101 (9): 819–832, doi:10.2307/2975129, JSTOR 2975129, archived from the original (PDF) on 21 January 2022, retrieved 6 December 2013

jstor.org

Gray, Robert (1994), "Georg Cantor and Transcendental Numbers" (PDF), American Mathematical Monthly, 101 (9): 819–832, doi:10.2307/2975129, JSTOR 2975129, archived from the original (PDF) on 21 January 2022, retrieved 6 December 2013

leeds.ac.uk

www1.maths.leeds.ac.uk

Rathjen, M. "Choice principles in constructive and classical set theories", Proceedings of the Logic Colloquium, 2002

maa.org

Gray, Robert (1994), "Georg Cantor and Transcendental Numbers" (PDF), American Mathematical Monthly, 101 (9): 819–832, doi:10.2307/2975129, JSTOR 2975129, archived from the original (PDF) on 21 January 2022, retrieved 6 December 2013

stanford.edu

plato.stanford.edu

Russell's paradox. Stanford encyclopedia of philosophy. 2021. Archived from the original on 30 August 2022. Retrieved 12 July 2016.

uwo.ca

publish.uwo.ca

Bell, John L. (2004), "Russell's paradox and diagonalization in a constructive context" (PDF), in Link, Godehard (ed.), One hundred years of Russell's paradox, De Gruyter Series in Logic and its Applications, vol. 6, de Gruyter, Berlin, pp. 221–225, MR 2104745

web.archive.org

Georg Cantor (1891). "Ueber eine elementare Frage der Mannigfaltigkeitslehre". Jahresbericht der Deutschen Mathematiker-Vereinigung. 1: 75–78. Archived from the original on 3 January 2023. Retrieved 11 June 2018. English translation: Ewald, William B., ed. (1996). From Immanuel Kant to David Hilbert: A Source Book in the Foundations of Mathematics, Volume 2. Oxford University Press. pp. 920–922. ISBN 0-19-850536-1.
Gray, Robert (1994), "Georg Cantor and Transcendental Numbers" (PDF), American Mathematical Monthly, 101 (9): 819–832, doi:10.2307/2975129, JSTOR 2975129, archived from the original (PDF) on 21 January 2022, retrieved 6 December 2013
Russell's paradox. Stanford encyclopedia of philosophy. 2021. Archived from the original on 30 August 2022. Retrieved 12 July 2016.
See page 254 of Georg Cantor (1878), "Ein Beitrag zur Mannigfaltigkeitslehre", Journal für die Reine und Angewandte Mathematik, 84: 242–258, archived from the original on 6 November 2018, retrieved 17 August 2017. This proof is discussed in Joseph Dauben (1979), Georg Cantor: His Mathematics and Philosophy of the Infinite, Harvard University Press, ISBN 0-674-34871-0, pp. 61–62, 65. On page 65, Dauben proves a result that is stronger than Cantor's. He lets "φ_ν denote any sequence of rationals in [0, 1]." Cantor lets φ_ν denote a sequence enumerating the rationals in [0, 1], which is the kind of sequence needed for his construction of a bijection between [0, 1] and the irrationals in (0, 1).
Bauer, A. "An injection from N^N to N Archived 27 November 2021 at the Wayback Machine", 2011