Georg Cantor

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Georg Cantor
Georg Cantor (Porträt).jpg
Cantor, s. 1910
Kelahiran
Georg Ferdinand Ludwig Philipp Cantor

(1845-03-03)3 Mac 1845
Meninggal dunia6 Januari 1918(1918-01-06) (umur 72)
WarganegaraKerman
Pusat pendidikan
Terkenal keranaTeori set
PasanganVally Guttmann (k. 1874)
AnugerahSylvester Medal (1904)
Kerjaya saintifik
BidangMatematik
InstitusiUniversiti Halle
TesisDe aequationibus secundi gradus indeterminatis (1867)
Penasihat kedoktoran

Georg Ferdinand Ludwig Philipp Cantor (/ˈkæntɔːr/ KAN-tor, bahasa Jerman: [ˈɡeːɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantɔʁ]; 3 Mac 1845  – 6 Januari 1918[1]) ialah seorang ahli matematik Jerman. Beliau mencipta teori set, yang telah menjadi teori asas dalam matematik. Cantor menetapkan kepentingan surat-menyurat satu dengan satu antara ahli dua set, menentukan set tak terhingga dan tersusun dengan baik, dan membuktikan bahawa nombor nyata ialah lebih banyak daripada nombor asli. Malah, kaedah pembuktian Cantor bagi teorem ini membayangkan kewujudan infiniti. Beliau mentakrifkan nombor kardinal dan ordinal serta aritmetiknya. Karya Cantor mempunyai kepentingan falsafah yang besar, fakta yang beliau sedari.[2]

Rujukan[sunting | sunting sumber]

  1. ^ Grattan-Guinness 2000, p. 351.
  2. ^ The biographical material in this article is mostly drawn from Dauben 1979. Grattan-Guinness 1971, and Purkert and Ilgauds 1985 are useful additional sources.

Pautan luar[sunting | sunting sumber]

  • Karya oleh atau tentang Georg Cantor di Internet Archive
  • O'Connor, John J.; Robertson, Edmund F., "Georg Cantor", arkib MacTutor History of Mathematics, Universiti St Andrews.
  • O'Connor, John J.; Robertson, Edmund F., "A history of set theory", arkib MacTutor History of Mathematics, Universiti St Andrews. Mainly devoted to Cantor's accomplishment.
  • Stanford Encyclopedia of Philosophy: Set theory by Thomas Jech. The Early Development of Set Theory by José Ferreirós.
  • "Cantor infinities", analysis of Cantor's 1874 article, BibNum (for English version, click 'à télécharger'). 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 Georg Cantor and Transcendental Numbers.