Georg Cantor (Portuguese Wikipedia)

Analysis of information sources in references of the Wikipedia article "Georg Cantor" in Portuguese language version.

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archive.org

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dx.doi.org

  • Cantor's construction starts with the set of transcendentals T and removes a countable subset {tn} (for example, tn = e / n). Call this set T0. Then T = T0 ∪ {tn} = T0 ∪ {t2n-1} ∪ {t2n}. The set of reals R = T ∪ {an} = T0 ∪ {tn} ∪ {an} where an is the sequence of real algebraic numbers. So both T and R are the union of three pairwise disjoint sets: T0 and two countable sets. A one-to-one correspondence between T and R is given by the function: f(t) = t if t ∈ T0, f(t2n-1) = tn, and f(t2n) = an. Cantor actually applies his construction to the irrationals rather than the transcendentals, but he knew that it applies to any set formed by removing countably many numbers from the set of reals (Cantor 1879, p. 4). Georg Cantor (1879). «Ueber unendliche, lineare Punktmannichfaltigkeiten (1)». Mathematische Annalen. 15 (1): 1–7. doi:10.1007/bf01444101 
  • Cantor 1883. Georg Cantor (1883). «Ueber unendliche, lineare Punktmannichfaltigkeiten (5)». Mathematische Annalen. 21 (4): 545–591. doi:10.1007/bf01446819  Published separately as: Grundlagen einer allgemeinen Mannigfaltigkeitslehre.

education.fr

bibnum.education.fr

mathgenealogy.org

st-andrews.ac.uk

www-history.mcs.st-andrews.ac.uk

uni-goettingen.de

gdz.sub.uni-goettingen.de

  • Cantor's construction starts with the set of transcendentals T and removes a countable subset {tn} (for example, tn = e / n). Call this set T0. Then T = T0 ∪ {tn} = T0 ∪ {t2n-1} ∪ {t2n}. The set of reals R = T ∪ {an} = T0 ∪ {tn} ∪ {an} where an is the sequence of real algebraic numbers. So both T and R are the union of three pairwise disjoint sets: T0 and two countable sets. A one-to-one correspondence between T and R is given by the function: f(t) = t if t ∈ T0, f(t2n-1) = tn, and f(t2n) = an. Cantor actually applies his construction to the irrationals rather than the transcendentals, but he knew that it applies to any set formed by removing countably many numbers from the set of reals (Cantor 1879, p. 4). Georg Cantor (1879). «Ueber unendliche, lineare Punktmannichfaltigkeiten (1)». Mathematische Annalen. 15 (1): 1–7. doi:10.1007/bf01444101 
  • Cantor 1883. Georg Cantor (1883). «Ueber unendliche, lineare Punktmannichfaltigkeiten (5)». Mathematische Annalen. 21 (4): 545–591. doi:10.1007/bf01446819  Published separately as: Grundlagen einer allgemeinen Mannigfaltigkeitslehre.

worldcat.org

  • Bruno, Leonard C.; Baker, Lawrence W. (1999). Math and mathematicians: the history of math discoveries around the world. Detroit, Mich.: U X L. p. 54. ISBN 0787638137. OCLC 41497065