Georg Cantor: kuisa pfungwa, Biography uye mhuri masvomhu

Georg Cantor (Photo inoratidza gare gare munyaya) - yemasvomhu German dziridza Dzidziso seti uye akazivisa pfungwa transfinite nhamba, anoramba guru, asi zvakasiyana mumwe. Naiyewo akapa tsanangudzo ordinal uye mufundisi nhamba uye yakasimbiswa svomhu yavo.

Georg Cantor: pfupi Biography

Akaberekwa muna St. Petersburg 03.03.1845. baba vake aiva Danish Protestant Georg Waldemar Cantor, akanga achiparidza zvokutengeserana, muna Vol. H. Zvino Stock Exchange. mai vake, Mariya, Bem aiva muKaturike uye akauya kubva mhuri musicians vakakurumbira. Apo muna 1856 baba vake George akarwara, kwakabva mhuri vachitsvaka munhu munyoro okunze vakatamira kutanga Wiesbaden ipapo kuna muFrankfurt. Kwemasvomhu tarenda, mukomana pamberi ake rechi15 rokuzvarwa apo kudzidza mudzimba zvikoro uye voruzhinji zvikoro Darmstadt uye Wiesbaden. Pakupedzisira, Georg Cantor vakanyengetedza baba vake pakutsunga kwake kuva yemasvomhu pane imwe injiniya.

Mushure kurovedza pfupi payunivhesiti Zurich muna 1863. Cantor akachinjirwa Berlin University kudzidza wefizikisi, uzivi uye masvomhu. Ikoko akadzidziswa:

• Karl Theodor Weierstrass, ane specialization ari pachisara kunge aiva mukuru kuchinja George;
• Ernst Kummer, uyo akadzidzisa chepamusoro svomhu;
• Leopold Kronecker, iri nhamba dzidziso nyanzvi, uyo gare gare vaishora Cantor.

Apedzera mumwe kwetemu paUniversity Göttingen muna 1866, gore rinouya George akanyora ake doctorate chinyorwa pasi rokuti "In masvomhu, unyanzvi kubvunza mibvunzo chinokosha kupfuura matambudziko" pamusoro dambudziko kuti Carl Friedrich Gauss kusina kugadziriswa yake Disquisitiones Arithmeticae (1801) . Mushure muchidimbu kudzidzisa paChikoro Berlin School kuti vasikana Kantor akatanga kushanda paYunivhesiti Halle, apo akagara kusvikira pakuguma hwake, kutanga kuva mudzidzisi, kubva 1872 sechinhu purofesa mubatsiri, uye kubvira muna 1879 wokutanga kuva muzvinadzidzo.

tsvakurudzo

Pakutanga munhevedzano 10 mabasa kubva 1869 kusvika 1873, Georg Cantor vaiona dzidziso nhamba. Basa inoratidza chido nyaya yake kudzidza uye migumisiro Gauss Kronecker. Panguva pfungwa Heinrich Eduard Heine, Cantor kuti vatinoshanda navo Halle, uyo aiziva tarenda rake akarongeka, akatendeukira dzidziso trigonometric series, izvo akawedzera pfungwa chaiyo nhamba.

Inobva basa kushanda kunzwisisa shanduka kubva yemasvomhu German Bernhard Riemann muna 1854, muna 1870 Cantor yaratidza kuti basa rakadaro rinogona kuratidzirwa munzira imwe chete - ne trigonometric dzakatevedzana. Nokuongorora yakatarwa nenhamba (pfungwa), izvo haana kupikisana maonero ichi, akamutungamirira, pakutanga, muna 1872, kusvika tsanangudzo ine musoro nhamba maererano convergent sequences ose kufunga nhamba (zvikamu zviduku integers) uye zvadaro pakutanga basa iri basa rake muupenyu, yakatarwa yokuti uye pfungwa transfinite nhamba.

yakatarwa dzidziso

Georg Cantor, dzidziso rinotaura dzakatangira kunyorerana Technical Institute of Braunschweig yemasvomhu Richard Dedekind, aiva shamwari naye kubva pauduku. Vakazongofunga kuti rinovira, finite kana magumo, muri muzvizhinji kuti zvinhu (semuenzaniso, nhamba {0, ± 1, ± 2 ...}) Izvo vane imwe pfuma, apo ukaramba kwavo munhu akazvimiririra. Asi kana Georg Cantor akashandisa kudzidza unhu hwavo chete matsamba (semuenzaniso, {A, B, C} kune {1, 2, 3}), iye akakurumidza kuona kuti zvisingapindirani kwavo mwero chavanopinda, kunyange dai risina mugumo unobatsira , t. e. yakatarwa chidimbu kana subset izvo zvinosanganisira chete nhamba zvinhu sezvazviri pacharo. nokukurumidza nzira yake akapa zvinoshamisa zvabuda.

Muna 1873, Georg Cantor (yemasvomhu) akaratidza kuti pfungwa nhamba, kunyange magumo, muri countable, nekuti vanogona kuiswa chete-kuti-imwe tsamba dzinongoitika (kureva. E. 1, 2, 3 ,. D.). Akaratidza kuti yakatarwa chaiyo nhamba zvinosanganisira ndaisagona uye musoro, uye zvazvisingaverengeki hazviperi. Zvechokwadi gangaidzo, Cantor akaratidza kuti yakatarwa vose algebraic nhamba rine zvinhu zvizhinji yakatarwa pakati integers zvose, uye kuti transcendental nhamba dzisiri algebraic, izvo subset ose safunga nhamba iri zvazvisingaverengeki saka nhamba yavo mukuru kupfuura integers uye dzinofanira kuzokurukurwa sezvo ziendanakuenda.

Vanopikisa uye vatsigiri

Asi basa Cantor, umo akatanga kuisa mberi migumisiro, haana yakabudiswa "Krell" magazini somumwe reviewers, Kronecker aishora. Asi pashure kupindira pakati Dedekind zvakanzi rakabudiswa muna 1874 pasi rokuti "The zvinoitwa zvose zvechokwadi algebraic nhamba."

Science uye upenyu pachako

Zvegore, panguva hanimunu nomudzimai wake, Valli Gutman muna Interlaken, Switzerland, Cantor akasangana Dedekind avo vakataura zvakanaka pamusoro pake matsva. George muhoro yaiva duku, asi mari baba vake vakafa muna 1863, akanga avakirwa wake nevana vashanu kumusha. Vakawanda mabasa ake dzakabudiswa muSweden muna magazini itsva Acta Mathematica, mupepeti uye akatanga raiva Gösta Mittag-Leffler, pakati kutanga kuona tarenda iri German yemasvomhu.

Kukurukurirana pamwe metaphysics

Pfungwa Cantor pasi zvitsva kutsvakurudza chokuita pamasvomhu parinogumira (semuenzaniso, kutevedzana 1, 2, 3 ,. D., uye kupfuura kunzwisisa nemhando), riri zvikurukuru novimba chimwe-kuti-imwe tsamba. Cantor Development nzira itsva kuisa mibvunzo pamusoro chamazuva uye kusaverengeka wamakapa zvidzidzo ake yakavhenganiswa.

Paakanga nharo kuti haaperi nhamba zvechokwadi kurarama, akatendeukira yekare uye Ages uzivi panyaya chaiwo uye zvinogona kusaverengeka, uyewo kune vokutanga rechitendero dzidzo, iyo vabereki akamupa. Muna 1883, mubhuku rake "kunyatsogona mukuru dzidziso seti" Kantor mubatanidzwa pfungwa yake metaphysics dzaPlato.

Kronecker zvakare, uyo akati kuti "kune" chete integers ( "Mwari akasika integers, vamwe - basa murume"), kwemakore akawanda vakaramba zvakasimba mashoko ake uye kudziviswa kugadzwa kwake University of Berlin.

transfinite nhamba

Muna 1895-97 gg. Georg Cantor zvakazara kuumbwa pfungwa yake chamazuva uye kusaverengeka, kusanganisira reupenyu kutevedzana uye mufundisi nhamba, basa rake dzakakurumbira, rakabudiswa pasi unoti "Mupiro kuti dzidziso transfinite nhamba" (1915). Basa iri rinosanganisira pamuviri wake, aakataura akatungamirira muenzaniso kuti isingaperi yakatarwa anogona nenzira imwe-to-imwe tsamba imwe subsets ayo.

Zviduku mufundisi nhamba transfinite aireva simba upi yakatarwa, iyo inogona kuisa chimwe-kuti-imwe tsamba zvepanyama nhamba. Kantor akarondedzera aleph-razero ake. Large transfinite muzvizhinji ZEKARIA-akasarudzwa chete, vaviri kana Aleph-t. D. It mberi yakatanga svomhu ordinals, rakanga rakafanana finite svomhu. Saka, iye zvabatsira pfungwa kusaverengeka.

The kushorwa akatarisana, uye nguva zvakatora rekuona kuti pfungwa dzake dzakanga zvizere kugamuchirwa, akatsanangura akaoma chaizvo revaluation pamusoro mubvunzo hwekare chii nhamba. Kantor akaratidza kuti chine pfungwa pamusoro mutsetse ane wakakwirira kukwanisa kupfuura Aleph-razero. Izvi zvakazoita kuti inonyatsozivikanwa dambudziko continuum pfungwa - hapana vafundisi pakati aleph-razero uye hapana simba pfungwa mumutsetse. dambudziko iri pakutanga uye yechipiri yezana remakore rechi20 riri zvikuru uye kwave vakadzidza ne mathematicians zhinji, muna Vol. H. Kurt Gödel uye Paul Cohen.

kusuruvara

Biography Georga Kantora 1884 hwakanganiswa ake incipient chirwere chepfungwa, asi akaramba kushanda nokushingaira. Muna 1897 akabatsira kubata wokutanga International Congress of Mathematicians muna Zurich. Neimwe nokuti vaishora Kronecker, aiwanzoenda tsitsi pamwe muduku yotunga mathematicians uye vakaedza kuwana nzira kuponesa pakunetswa nevadzidzisi vanonzwa kutyisidzirwa pfungwa itsva.

ndangariro

At kwezana remakore basa rake rakanga zvakakwana kuzivikanwa sepokutangira dzidziso mashandiro, ongororo uye topology. Uyezve, Kantora Georga bhuku aiva nhangaruvanze kuti pakuzadzisa pachikoro formalist uye intuitionist nheyo wemasvomhu musoro. Izvi zvinooneka kwakachinja maitiro rokudzidzisa uye rinowanzoshandiswa chokuita "masvomhu itsva."

Muna 1911, Cantor aiva pakati vaya vakakokwa mhemberero yacho 500th gore paYunivhesiti St Andrews kuScotland. Akaenda ikoko vachitarisira kusangana Bertrand Russell, uyo yake basa richangobva kubudiswa Principia Mathematica akataura kakawanda German yemasvomhu, asi izvi hazvina kuitika. University paakavapa Cantor ane honorary dhigirii, asi nokuda chirwere akanga asingakwanisi kugamuchira mubayiro mune munhu.

Cantor pamudyandigere muna 1913 uye vaigara urombo uye nenzara panguva World War First. Mhemberero vachikudza 70 okuberekwa muna 1915 vakanga akadzima nemhaka yehondo, asi mutambo duku wakaitwa kumba kwake. Akafa musi 06.01.1918, muna Galle, muchipatara chepfungwa, uko akapedza makore okupedzisira oupenyu hwake.

Georg Cantor: A Biography. mhuri

August 9, 1874, nyanzvi yemasvomhu German akaroorwa Valli Gutman. Vaviri ava vakava 4 vanakomana 2 nevanasikana. Mwana wokupedzisira akaberekwa muna 1886 muna Cantor akatenga musha mutsva. Tsigirai mhuri akabatsira nhaka yababa vake. Utano Cantor zvikuru sei rufu mwanakomana wake wegotwe muna 1899 - sezvo kumbobva mwoyo.