Izvorni kod stranice Georg Cantor

{{Naučnik
| ime = Georg Kantor
| slika = Matematiker georg cantor.jpg
| opis_slike = Georg Kantor
| puno_ime = 
| datum_rođenja = [[3. mart]] [[1845]].
| mesto_rođenja = [[Sankt Peterburg|Petrograd]]
| država_rođenja = [[Rusija]]
| datum_smrti = [[6. januar]]a [[1918]].
| mesto_smrti = [[Halle (Saale)|Hale]]
| država_smrti = [[Nemačka]]
| polje = [[matematika]]
| škola = [[ETH Cirih]]<br /> [[Humboltov univerzitet u Berlinu|Univerzitet u Berlinu]]
| mentor = [[Ernst Kumer]] <br /> [[Karl Vajerštras]]
| institucija = Univerzitet u Haleu
| akademija = 
| studenti = 
| poznat_po = [[teorija skupova]]
| nagrade  = 
| napomene = 
}}
'''Georg Kantor''' ({{Jez-nem|Georg Cantor}}, [[Sankt Peterburg|Petrovgrad]], Rusija, [[3. mart]]a [[1845]]— [[Halle (Saale)|Hale]], [[Nemačka]], [[6. januar]]a [[1918]]), nemački matematičar, utemeljivač [[Teorija skupova|teorije 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 [[racionalan broj|racionalnih brojeva]] ima isto koliko i prirodnih brojeva, to jest da ova dva skupa (<math>\mathbb{Q}</math> i <math>\mathbb{N}</math>) 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 [[iracionalan broj|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 [[beskonačnost]]i, i označavaju se simbolima <math>\aleph_0</math>, <math>\aleph_1</math>, ... ([[alef broj|alef nula]], alef jedan, ...).

==Literatura==
{{refbegin|2}}
* {{Citation |surname=Joseph Dauben |jstor=2708842|given= Joseph W.|year=1977|title=Georg Cantor and Pope Leo XIII: Mathematics, Theology, and the Infinite|journal=Journal of the History of Ideas|volume=38|number=1|pages=85–108|ref=Dauben1977}}.
* {{Citation |surname=Dauben|given= Joseph W.|year=1979|title=Georg Cantor: his mathematics and philosophy of the infinite|place=Boston|publisher=Harvard University Press|isbn=978-0-691-02447-9|ref=Dauben1979}}.
* {{Citation|surname=Dauben|given=Joseph|origyear=1993|year=2004|url=http://www.acmsonline.org/journal/2004/Dauben93.htm|chapter=Georg Cantor and the Battle for Transfinite Set Theory|title=Proceedings of the 9th ACMS Conference (Westmont College, Santa Barbara, CA)|pages=1–22|ref=Dauben2004|access-date=2015-05-09|archivedate=2015-01-08|archiveurl=https://web.archive.org/web/20150108022603/http://www.acmsonline.org/journal/2004/Dauben93.htm|deadurl=yes}}. Internet version published in Journal of the ACMS 2004.
* {{Citation |editor-last=Ewald|editor-first=William B.|year=1996|title=From Immanuel Kant to David Hilbert: A Source Book in the Foundations of Mathematics|place=New York|publisher=Oxford University Press|isbn=978-0-19-853271-2|ref=Ewald}}.
* {{Citation |surname= Ivor Grattan-Guinness |given=Ivor Grattan-Guinness |year=1971|title=Towards a Biography of Georg Cantor|doi=10.1080/00033797100203837|journal=Annals of Science|volume=27|pages=345–391|ref=Guinness1971}}.
* {{Citation |surname= Ivor Grattan-Guinness |given= Ivor Grattan-Guinness |year=2000|title=The Search for Mathematical Roots: 1870–1940|publisher=Princeton University Press|isbn=978-0-691-05858-0|ref=Guinness2000}}.
* {{Citation |surname=Hallett|given=Michael|title=Cantorian Set Theory and Limitation of Size|publisher=Oxford University Press|place=New York|year=1986|isbn=0-19-853283-0|ref=Hallett}}.
* {{Citation |surname=Purkert|given=Walter|surname2=Ilgauds|given2=Hans Joachim|year=1985|title=Georg Cantor: 1845–1918|publisher= Birkhäuser Verlag|Birkhäuser |isbn=0-8176-1770-1|ref=Purkert}}.
*{{Citation |surname=Suppes|given=Patrick|year=1972|origyear=1960|title=Axiomatic Set Theory|place=New York|publisher=Dover|isbn= 0-486-61630-4|ref=Suppes}}. Although the presentation is axiomatic rather than naive, Suppes proves and discusses many of Cantor's results, which demonstrates Cantor's continued importance for the edifice of foundational mathematics.
* {{Citation |surname=Cantor|given=Georg|year=1955|origyear=1915|url=http://www.archive.org/details/contributionstot003626mbp|title=Contributions to the Founding of the Theory of Transfinite Numbers|editor=Philip Jourdain |place=New York|publisher=Dover|isbn=978-0-486-60045-1|ref=Cantor1955}}.
* {{Citation|surname=Cantor|given=Georg|year=1874|url=http://bolyai.cs.elte.hu/~badam/matbsc/11o/cantor1874.pdf|title=Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen|journal=Journal für die Reine und Angewandte Mathematik|volume=77|pages=258–262|doi=10.1515/crll.1874.77.258|access-date=2015-05-09|archivedate=2012-02-07|archiveurl=https://web.archive.org/web/20120207190039/http://bolyai.cs.elte.hu/~badam/matbsc/11o/cantor1874.pdf|deadurl=yes}}.
* {{cite journal | author=Georg Cantor | title=Ueber unendliche, lineare Punktmannichfaltigkeiten (1) | journal=Mathematische Annalen | volume=15 | number=1 | pages=1–7 | url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235181684_0015&DMDID=DMDLOG_0004 | year=1879 | doi=10.1007/bf01444101}}
* {{cite journal | author=Georg Cantor | title=Ueber unendliche, lineare Punktmannichfaltigkeiten (2) | journal=Mathematische Annalen | volume=17 | number=3 | pages=355–358 | url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235181684_0017&DMDID=DMDLOG_0043 | year=1880 | doi=10.1007/bf01446232}}
* {{cite journal | author=Georg Cantor | title=Ueber unendliche, lineare Punktmannichfaltigkeiten (3) | journal=Mathematische Annalen | volume=20 | number=1 | pages=113–121 | url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235181684_0020&DMDID=DMDLOG_0015 | year=1882 | doi=10.1007/bf01443330}}
* {{cite journal | author=Georg Cantor | title=Ueber unendliche, lineare Punktmannichfaltigkeiten (4) | journal=Mathematische Annalen | volume=21 | number=1 | pages=51–58 | url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235181684_0021&DMDID=DMDLOG_0008 | year=1883 | doi=10.1007/bf01442612}}
* {{cite journal | author=Georg Cantor | title=Ueber unendliche, lineare Punktmannichfaltigkeiten (5) | journal=Mathematische Annalen | volume=21 | number=4 | pages=545–591 | url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235181684_0021&DMDID=DMDLOG_0051 | year=1883 | doi=10.1007/bf01446819 | ref={{harvid|Cantor|1883}} }}
* {{cite journal | author=Georg Cantor | title=Ueber eine elementare Frage der Mannigfaltigkeitslehre | journal=Jahresbericht der Deutsche Mathematiker-Vereinigung 1890-1891 | volume=1 | pages=75–78 | year=1892 |url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN37721857X_0001&DMDID=DMDLOG_0029&LOGID=LOG_0029&PHYSID=PHYS_0083}}
* {{Cite journal|ref=harv|surname=Cantor|given=Georg|year=1895|url=http://gdz-lucene.tc.sub.uni-goettingen.de/gcs/gcs?&&action=pdf&metsFile=PPN235181684_0046&divID=LOG_0044&pagesize=original&pdfTitlePage=http%3A%2F%2Fgdz.sub.uni-goettingen.de%2Fdms%2Fload%2Fpdftitle%2F%3FmetsFile%3DPPN235181684_0046%7C&targetFileName=PPN235181684_0046_LOG_0044.pdf&|title=Beiträge zur Begründung der transfiniten Mengenlehre (1)|journal=Mathematische Annalen|volume=46|pages=481–512|doi=10.1007/bf02124929|access-date=2015-05-09|archive-date=2014-04-23|archive-url=https://web.archive.org/web/20140423224341/http://gdz-lucene.tc.sub.uni-goettingen.de/gcs/gcs?&&action=pdf&metsFile=PPN235181684_0046&divID=LOG_0044&pagesize=original&pdfTitlePage=http%3A%2F%2Fgdz.sub.uni-goettingen.de%2Fdms%2Fload%2Fpdftitle%2F%3FmetsFile%3DPPN235181684_0046%7C&targetFileName=PPN235181684_0046_LOG_0044.pdf&|dead-url=yes}}
* {{Cite journal|ref=harv|surname=Cantor|given=Georg|year=1897|title=Beiträge zur Begründung der transfiniten Mengenlehre (2)|journal=Mathematische Annalen|volume=49|pages=207–246|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0049&DMDID=DMDLOG_0024&L=1}}
* {{Citation |surname=Cantor |given=Georg |year=1932 <!---|url=http://web.archive.org/web/20070630234312/http://philosophons.free.fr/philosophes/cantor1932.pdf| format=PDF---> |url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN237853094&DMDID=DMDLOG_0001&L=1 |title=Gesammelte Abhandlungen mathematischen und philosophischen inhalts |editor=Ernst Zermelo |publisher=Springer |location=Berlin |access-date=2015-05-09 |archivedate=2014-02-03 |archiveurl=https://web.archive.org/web/20140203234213/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN237853094&DMDID=DMDLOG_0001&L=1 |deadurl=yes }}. Almost everything that Cantor wrote. Includes excerpts of his correspondence with Richard Dedekind|Dedekind (p.&nbsp;443-451) and Adolf Fraenkel Cantor biography (p.&nbsp;452-483) in the appendix.
* {{Citation |last1=Aczel|first1=Amir D.|author1-link=Amir Aczel|year=2000|title=The Mystery of the Aleph: Mathematics, the Kabbala, and the Search for Infinity|place=New York|publisher=Four Walls Eight Windows Publishing}}. {{ISBN|0-7607-7778-0}}. A popular treatment of infinity, in which Cantor is frequently mentioned.
* {{Citation |surname=Dauben|given= Joseph W.|date=June 1983|title=Georg Cantor and the Origins of Transfinite Set Theory|journal=Scientific American|volume=248|issue=6|pages=122–131|doi=10.1038/scientificamerican0683-122}}
* {{Citation |surname=Ferreirós|given=José |year=2007|title=Labyrinth of Thought: A History of Set Theory and Its Role in Mathematical Thought|place=Basel, Switzerland|publisher=Birkhäuser}}. {{ISBN|3-7643-8349-6}} Contains a detailed treatment of both Cantor's and Dedekind's contributions to set theory.
* {{Citation |surname= Paul Halmos |given= Paul Halmos |year=1998|origyear=1960|title=Naive Set Theory|place=New York & Berlin|publisher=Springer}}. {{ISBN|3-540-90092-6}}
* {{Cite journal|ref=harv|last1=Hilbert|first1=David|author1-link=David Hilbert|year=1926|url=http://www.digizeitschriften.de/main/dms/img/?PPN=GDZPPN002270641|title=Über das Unendliche|journal=Mathematische Annalen|volume=95|pp=161–190|doi=10.1007/BF01206605}}
* {{Citation |surname=Hill|given= C. O.|surname2=Rosado Haddock|given2=G. E.|year=2000|title=Husserl or Frege? Meaning, Objectivity, and Mathematics|place=Chicago|publisher=Open Court}}. {{ISBN|0-8126-9538-0}} Three chapters and 18 index entries on Cantor.
* {{Citation |surname=Meschkowski|given= Herbert|year=1983|title=Georg Cantor, Leben, Werk und Wirkung (Georg Cantor,  Life, Work and Influence, in German)|publisher= Vieweg, Braunschweig}}
* {{Citation |surname= Roger Penrose |given= Roger Penrose |year=2004|title=The Road to Reality|publisher=Alfred A. Knopf}}. {{ISBN|0-679-77631-1}} Chapter 16 illustrates how Cantorian thinking intrigues a leading contemporary Theoretical physics.
* {{Citation |surname= Rudy Rucker |given= Rudy Rucker |year=2005|origyear=1982|title=Infinity and the Mind|publisher=Princeton University Press}}. {{ISBN|0-553-25531-2}} Deals with similar topics to Aczel, but in more depth.
* {{Citation |surname=Rodych|given=Victor|year=2007|chapter=[http://plato.stanford.edu/entries/wittgenstein-mathematics/ Wittgenstein's Philosophy of Mathematics]|title=The Stanford Encyclopedia of Philosophy|editor=Edward N. Zalta|ref=harv}}.
{{refend}}

== Spoljašnje veze ==
{{Commonscat|Georg Cantor}}
* {{MacTutor|id=Cantor}}
* {{MacTutor|class=HistTopics|id = Beginnings_of_set_theory|title = A history of set theory}}
* Stanford Encyclopedia of Philosophy: [http://plato.stanford.edu/entries/set-theory/ Set theory] by Thomas Jech.
* Grammar school Georg-Cantor Halle (Saale): [http://www.cantor-gymnasium.de Georg-Cantor-Gymnasium Halle]
* [http://www.readmypoems.co.uk/2014/02/a-pentameter-of-questions-about-infinity.html Poem about Georg Cantor]

{{Lifetime|1845|1918|Cantor, Georg}}

[[Kategorija:Njemački matematičari]]