Georg Cantor

Georg Kantor (njemački: , Petrovgrad, Rusija, 3. marta 1845— Hale, Nemačka, 6. januara 1918), nemački matematičar, utemeljivač teorije skupova.

Georg Kantor
Rođenje	3. mart 1845. Petrograd
Smrt	6. januara 1918. Hale
Polje	matematika
Institucija	Univerzitet u Haleu
Alma mater	ETH Cirih Univerzitet u Berlinu
Akademski mentor	Ernst Kumer Karl Vajerštras
Poznat po	teorija skupova

Prvi je numeričke sisteme, poput racionalnih i stvarnih brojeva, istraživao sistematično, kao zaokružene entitete ili skupove. To pregnuće dovelo ga je do iznenaćujućeg otkrića da nisu svi beskrajni skupovi iste veličine. Dokaz za ovo je Kantorov dijagonalni postupak

Pokazao je da racionalnih brojeva ima isto koliko i prirodnih brojeva, to jest da ova dva skupa (${\displaystyle \mathbb {Q} }$ i ${\displaystyle \mathbb {N} }$) imaju istu kardinalnost (dokaz da racionalnih brojeva ima prebrojivo mnogo je Kantorovo prebrojavanje skupa Q). Dokazao je, takođe, da takve podudarnosti nema kod znatno većeg skupa iracionalnih brojeva, te su otuda oni poznati kao skup koji se ne može prebrojati.

Istraživanja je krunisao klasifikacijom transfinitnih brojeva koji, laički govoreći, predstavljaju stepene beskonačnosti, i označavaju se simbolima ${\displaystyle \aleph _{0}}$, ${\displaystyle \aleph _{1}}$, ... (alef nula, alef jedan, ...).

Literatura

Dedekind (p. 443-451) and Adolf Fraenkel Cantor biography (p. 452-483) in the appendix.

Aczel, Amir D. (2000), The Mystery of the Aleph: Mathematics, the Kabbala, and the Search for Infinity, New York: Four Walls Eight Windows Publishing. ISBN 0-7607-7778-0. A popular treatment of infinity, in which Cantor is frequently mentioned.

Dauben, Joseph W. (June 1983), „Georg Cantor and the Origins of Transfinite Set Theory”, Scientific American 248 (6): 122–131, DOI:10.1038/scientificamerican0683-122

Ferreirós, José (2007), Labyrinth of Thought: A History of Set Theory and Its Role in Mathematical Thought, Basel, Switzerland: Birkhäuser. ISBN 3-7643-8349-6 Contains a detailed treatment of both Cantor's and Dedekind's contributions to set theory.

Paul Halmos, Paul Halmos (1998) [1960], Naive Set Theory, New York & Berlin: Springer. ISBN 3-540-90092-6

Hilbert, David (1926). „Über das Unendliche”. Mathematische Annalen 95. DOI:10.1007/BF01206605.

Hill, C. O.; Rosado Haddock, G. E. (2000), Husserl or Frege? Meaning, Objectivity, and Mathematics, Chicago: Open Court. ISBN 0-8126-9538-0 Three chapters and 18 index entries on Cantor.

Meschkowski, Herbert (1983), Georg Cantor, Leben, Werk und Wirkung (Georg Cantor, Life, Work and Influence, in German), Vieweg, Braunschweig

Roger Penrose, Roger Penrose (2004), The Road to Reality, Alfred A. Knopf. ISBN 0-679-77631-1 Chapter 16 illustrates how Cantorian thinking intrigues a leading contemporary Theoretical physics.

Rudy Rucker, Rudy Rucker (2005) [1982], Infinity and the Mind, Princeton University Press. ISBN 0-553-25531-2 Deals with similar topics to Aczel, but in more depth.

Rodych, Victor (2007), „Wittgenstein's Philosophy of Mathematics”, Edward N. Zalta, The Stanford Encyclopedia of Philosophy.

Vanjske veze

Georg Cantor na Wikimedijinoj ostavi

• O'Connor, John J.; Robertson, Edmund F. „Georg Cantor – biografija”. MacTutor History of Mathematics archive. ()
• O'Connor, John J.; Robertson, Edmund F. „A history of set theory”. MacTutor History of Mathematics archive. ()
• Stanford Encyclopedia of Philosophy: Set theory by Thomas Jech.
• Grammar school Georg-Cantor Halle (Saale): Georg-Cantor-Gymnasium Halle
• Poem about Georg Cantor