Georg Cantor: setha ithiyori, biography kanye izibalo umndeni

Georg Cantor (isithombe sikhombisa kamuva esihlokweni) - sezibalo German abasungula le imfundiso yokuziphendukela amasethi futhi wethula umqondo izinombolo transfinite, ngokungenamkhawulo enkulu, kodwa ehlukene kusuka komunye nomunye. Ngakho-ke wabanikeza incazelo izinombolo odinali namakhadinali futhi osungulwe izibalo zabo.

Georg Cantor: Biography emfushane

Wazalelwa Petersburg 03.03.1845. Uyise wayengumGreki Danish YamaProthestani Georg Waldemar Cantor, eyingoduso kwezohwebo, e Umq. H. Futhi phezu exchange isitokwe. Unina, uMariya, Bem wayengumKatolika futhi wayevela emndenini ka abaculi abavelele. Lapho 1856 uyise George wagula, umndeni beyofuna sezulu onomoya omnene wathutha ngowokuqala Wiesbaden ke ukuze Frankfurt. ithalente Mathematical, umfundi uvele ngaphambi lokuzalwa kwakhe 15 ngenkathi ngisafunda nezikole ezizimele kanye ezikoleni zomphakathi e Darmstadt futhi Wiesbaden. Ekugcineni, Georg Cantor wathonyelwa uyise ekuzimiseleni kwakhe ukwenza ube sezibalo kunokuba wobunjiniyela.

Ngemva ukuqeqeshwa emfushane e-University of Zurich e 1863. Cantor wayiswa Berlin University ukufunda physics, ifilosofi kanye mathematics. Lapho, wafundiswa:

• Karl Theodor Weierstrass, lunye kabani ekucubunguleni, cishe zaba nethonya elikhulu kakhulu ku George;
• Ernst Kummer owafundisa arithmetic eliphakeme;
• Leopold Kronecker, ku inombolo theory onguchwepheshe, kamuva wamelana Cantor.

Ngachitha eyodwa semester e-University of Gottingen ngo-1866, ngonyaka ozayo George wabhala mqondo yakhe zobudokotela ngaphansi kwesihloko esithi "Esifundweni sezibalo, ikhono lokubuza imibuzo kuyigugu ngaphezu kwezimpahla ukuxazulula izinkinga" mayelana inkinga Carl Friedrich Gauss okushiywe kungalungiswanga e Disquisitiones yakhe Arithmeticae (1801) . Ngemva efundisa kafushane ngesikhathi Berlin School for girls Kantor waqala ukusebenza e-University of Halle, lapho wahlala kuze kube sekupheleni kokuphila kwakhe, kuqala njengendlela womfundisi, kusukela 1872 njengoba likaprofesa, futhi kusukela ngo-1879 wokuqala njengoba uprofesa.

ucwaningo

Ekuqaleni uchungechunge 10 imisebenzi kusuka 1869 kuya 1873, Georg Cantor kubhekwe imfundiso yokuziphendukela izinombolo. Umsebenzi ibonisa abanothando isihloko nokufunda futhi umphumela Gauss Kronecker. Ngokusikisela Heinrich Eduard Heine, nozakwethu Cantor nganoma Halle, owabheka ithalente lakhe zezibalo, waphendukela imfundiso yokuziphendukela uchungechunge Trigonometric, okuyinto wandisa umqondo izinombolo zangempela.

Ngokusekelwe umsebenzi umsebenzi kwenombolo eyinkimbinkimbi sezibalo German Bernhard Riemann ngo-1854, ngo-1870 Cantor selukhombisile ukuthi umsebenzi onjalo kungaba amelwe enye indlela kuphela - by uchungechunge Trigonometric. Ukucutshungulwa isethi izinombolo (amaphuzu), okwakuyoholela akuphikisani lo mbono, bamuka naye, okokuqala, ngo-1872, kuze kube definition izinombolo engenangqondo ngokuya convergent ukulandelana izinombolo okunengqondo (kukhishwa nezingxenyana ezithile integers) bese ekuqaleni umsebenzi umsebenzi wakhe wokuphila konke, isethi ithiyori nomqondo izinombolo transfinite.

isethi theory

Georg Cantor ithiyori okuyinto lisinikeza eladabuka ukuxhumana ne Technical Institute of Braunschweig sezibalo Richard Dedekind, kwaba abangane naye kusukela ebuntwaneni. Baphetha ngokuthi amasethi, sivumelwano senhloko noma engaphelele, kukhona sebuningini izakhi (isib izinombolo {0, ± 1, ± 2 ...}) Yikuphi abe impahla ethile, kuyilapho esaziwa ubuntu babo. Kodwa lapho Georg Cantor, ngafaka isicelo sokufunda izici zabo eyodwa ukuxhumana (isib, {A, B, C} ukuze {1, 2, 3}), washeshe waqaphela ukuthi yabo ingafani degree kwabo ukubandakanya, ngisho uma bekungenjalo amasethi elingapheli , t. e. isethi ucezu noma isethi engezansi okuhlanganisa nenombolo yetintfo letilingana nayo njengoba ngokwaso. ngokushesha indlela yakhe wanika imiphumela emangalisayo.

Ngo-1873, Georg Cantor (sezibalo) yabonisa ukuthi izinombolo okunengqondo, nakuba obungapheli, kukhona letibalekako, ngoba kungenziwa abeke kwelinye-kokukodwa ukuxhumana ne yemvelo (isb. E. 1, 2, 3 ,. D.). Wabonisa ukuthi iqoqo izinombolo zangempela ehlanganisa elingapheli okunengqondo engenangqondo naletingabaleki. Yini indida, Cantor wafakazela ukuthi iqoqo zonke izinombolo algebraic iqukethe izinto eziningi njengoba isethi zonke integers, nokuthi izinombolo obabazekayo ezingesiyo algebraic, okuyizinto isethi engezansi izinombolo engenangqondo kuba naletingabaleki futhi ngalesosizathu inombolo yabo mkhulu integers futhi kufanele sithathwe njengehlelo elingapheli.

Abaphikisi nabasekeli

Kodwa lo msebenzi Cantor, lapho waqale wababuza phambili imiphumela, alishicilelwanga ku "Krell" umagazini njengoba omunye ababuyekezi, Kronecker wayephikisa. Kodwa ngemva kokungenela we Dedekind yanyatheliswa 1874 ngaphansi kwesihloko esithi "The izici zonke izinombolo zangempela we-Aljibhra."

Isayensi empilweni yakho

Ngawo lowo nyaka, phakathi kukankosikazi nomkakhe, Valli Gutman e Interlaken, Switzerland, Cantor wahlangana Dedekind ngomusa ubeke amazwana bayihlaba kakhulu inkolelo yakhe entsha. George iholo lalilincane, kodwa imadlana uyise, owashona ngo-1863, ayeyakhele umkakhe nezingane zakhe ezinhlanu ekhaya. Abaningi imisebenzi yakhe eziye zanyatheliswa komagazini Sweden ephephabhukwini elisha Acta Mathematica, umhleli kanye umsunguli wawo wawuvame Gösta Mittag-Leffler, kwabokuqala ukubona ithalenta sezibalo German.

Ukuxhumana ne Metaphysics

Theory Cantor wayeyizwa entsha ngokuphelele zocwaningo eziphathelene izibalo kwaphakade okunganqamukiyo (isb, ukulandelana 1, 2, 3 ,. D., Futhi amasethi eziyinkimbinkimbi), okuyinto incike okukodwa-eyodwa ngeposi. Cantor Kutfutfukiswa izindlela ezintsha zokuthola izinsuku kusethwa imibuto mayelana embili kanye infinity lent izifundo zakhe elixutshwe.

Lapho wagomela ngokuthi izinombolo okungenamkhawulo khona ngempela, waphendukela nefilosofi lasendulo futhi medieval ngokuphathelene infinity sangempela abangaba, kanye siwukuthi wafundiswa zenkolo, lawo abazali abangama wamnika. Ngo-1883, encwadini yakhe ethi "Kubaluleka inkolelo-mbono yokuziphendukela jikelele amasethi" Kantor kuhlangene umqondo wakhe we Metaphysics kaPlato.

Kronecker futhi, ngubani wagomela ngokuthi "kukhona" integers kuphela ( "UNkulunkulu wadala integers, lonke - umsebenzi indoda"), kwaphela iminyaka eminingi sinqatshiwe kakhulu amaphuzu akhe futhi kwavimbela nokuqokwa kwakhe e-University of Berlin.

izinombolo transfinite

Ngo 1895-97 GG. Georg Cantor owakheke ngokugcwele umqondo wakhe lenqubekela phambili kanye nokusebenza infinity, kuhlanganise i engapheli ukulandelana kanye ezinombolweni ezibalula inani, emsebenzini yakhe edume kunazo zonke, eshicilelwe ngaphansi kwesihloko esithi "Umnikelo kuyinkolelo-mbono yokuziphendukela izinombolo transfinite" (1915). Lo msebenzi uhilela uMariya, lapho wahola ukuboniswa ukuthi isethi okungenamkhawulo kungenziwa eshiwo omunye nobuso ukuxhumana nomunye subsets yayo.

Emincane kakhulu transfinite inombolo cardinal ayekhuluma yanoma yisiphi isethi, okungase ukubeka kwelinye-kokukodwa ukuxhumana ne izinombolo zemvelo. Kantor echazwe Aleph-zero yakhe. Elikhulu sebuningini transfinite alef egunyazwe kwelinye, ababili noma Aleph-t. D. It athuthukiswe ordinals izibalo, okuyinto wayefana izibalo ezilinganiselwe. Ngaleyo ndlela, yena kuye kwathuthukisa umqondo okufanekisa ingunaphakade.

Aphikisayo ayelengela, kanye nesikhathi kwakuthatha ukuqinisekisa ukuthi imibono yakhe ezazamukelwa ngokugcwele, wachaza kwezingqinamba revaluation we umbuzo lasendulo kuyini inombolo. Kantor wabonisa ukuthi iqoqo amaphuzu emgqeni sinesikhundla ephakeme kunaleyo Aleph-zero. Lokhu kwaholela ekutheni inkinga owaziwa umbono continuum - akukho okhadinali phakathi Aleph-zero futhi akukho amaphuzu amandla emgqeni. Le nkinga engxenyeni yokuqala kanye yesibili yekhulu lama-20 Sinesithakazelo esikhulu futhi iye ufundwa zezibalo eziningi, e Umq. H. Kurt Gödel noPawulu Cohen.

ukucindezeleka

Biography Georga Kantora 1884 sonakala ukugula kwengqondo yakhe incipient, kodwa waqhubeka bezikhandla. Ngo-1897 yena zasiza ngowokuqala International Congress of zezibalo eZurich. Ngokwengxenye ngoba wamelana Kronecker, wayevame besho nokusho ukuthi abasha zezibalo luthela futhi wazama ukuthola indlela amsindise ukuhlukunyezwa ngothisha ngubani basongelwe imibono emisha.

ukuqashelwa

Ngesikhathi kwekhulunyaka umsebenzi wakhe wayebhekwa ngokugcwele njengesisekelo imfundiso yokuziphendukela imisebenzi, ukuhlaziywa kanye yomphindwa. Ngaphezu kwalokho, Kantora Georga ncwadi wakhonza njengomdala Umfutho ukuqhubeka esikoleni formalist futhi intuitionist of izisekelo okunengqondo wezibalo. kakhulu Lokhu useshintshe uhlelo lokufundisa futhi uvame ukuhlotshaniswa ne "izibalo ezintsha."

Ngo-1911, Cantor wayephakathi kwalabo ababemenyelwe ukugubha iminyaka engu-500th wase-University of St Andrews eScotland. Waya lapho ethemba hlangabeza uBertrand Russell, ngubani emsebenzini wakhe esanda kunyatheliswa Principia Mathematica ngokuphindaphindiwe ngokuthi sezibalo isiJalimane, kodwa akwenzekanga lokho. University ukhishwa Cantor zokumhlonipha, kodwa ngenxa yokugula wayengasaboni ukwamukela umklomelo mathupha.

Cantor wathatha umhlalaphansi ngo-1913 futhi wayehlala ubumpofu kanye belamba ngesikhathi seMpi Yezwe Yokuqala. Imikhosi behlonipha lokuzalwa kwakhe 70 ngo-1915 base kukhanselwe ngenxa yempi, kodwa emkhosini encane owawuse ekhaya lakhe. Ushonele 06.01.1918, e Galle, esibhedlela sabagula ngengqondo, lapho afike achitha khona iminyaka yokugcina yokuphila kwakhe.

Georg Cantor: A Biography. umndeni

9 Agasti 1874, isazi sezibalo German washada Valli Gutman. Lo mbhangqwana kwadingeka amadodana namadodakazi 2 no-4. I last child wazalwa ngo-1886 e Cantor uthenge ikhaya elisha. Sekela umndeni wasiza ifa likayise. Impilo Cantor kwasithinta kakhulu kokushona kwendodana yakhe encane kunawo wonke waba 1899 - njengoba elapha ukucindezeleka.