Georg Cantor: anapereka chiphunzitso, mbiri ndi masamu banja

Georg Cantor (chithunzi limasonyeza kenako m'nkhani) - German masamu amene anayambitsa chiphunzitso kukukhala ndi kufotokozera mfundo manambala transfinite, wamphamvu zazikulu, koma osiyana Chrixitu. Iye anapereka tanthauzo la manambala ordinal ndi kadinala ndi kukhazikika masamu awo.

Georg Cantor: yochepa yonena

Anabadwira ku St. Petersburg 03.03.1845. Bambo ake anali Chidanishi Protestant Georg Waldemar Cantor, anali kuchita malonda, mu Vol. H. Ndipo pa katundu kuwombola. amake, Mariya, Bem anali Mkatolika ndipo kubanja la oimba ena otchuka. Pamene 1856 bambo wake George akadwala m'banja kufunafuna nyengo bata anasamukira oyamba Wiesbaden ndiye kuti Frankfurt. Masamu talente, mnyamata anakaonekera kubadwa kwake 15 pamene kuphunzira m'sukulu payekha ndi masukulu mu Darmstadt ndi Wiesbaden. Pomaliza, Georg Cantor anakopa bambo ake maganizo ake kukhala masamu osati injiniya.

Titamaliza maphunziro mwachidule pa University of Zurich mu 1863. Cantor kunditumiza ku University Berlin kuphunzira sayansi, nzeru ndi masamu. Pali iye anaphunzitsidwa:

• Karl Theodor Weierstrass, amene specialization pomaliza, mwina anali ndi chikoka chachikulu pa George;
• Ernst Kummer, amene ankaphunzitsa masamu apamwamba;
• Leopold Kronecker, pa nambala katswiri chiphunzitso, amene pambuyo anatsutsa Cantor.

Ndatha teremu chimodzi pa yunivesite ya Göttingen mu 1866, chaka chamawa George analemba nkhani yolembedwa wake digirii pansi udindo "Mu masamu luso kufunsa mafunso ndi ofunika kwambiri kuposa kuthetsa mavuto" ponena za vuto limene Carl Friedrich Gauss silinayankhidwe wake Disquisitiones Arithmeticae (1801) . Pambuyo mwachidule kuphunzitsa pa Sukulu Berlin atsikana Kantor anayamba kugwira ntchito pa yunivesite ya Halle, kumene mpaka mapeto a moyo wake, woyamba monga lecturer, popeza 1872 monga Pulofesa wina wokuthandizani, ndipo kuyambira 1879 woyamba monga Pulofesa wina.

kafukufuku

Pa chiyambi cha mndandanda wa ntchito 10 kuchokera 1869 mpaka 1873, Georg Cantor ankaona chiphunzitso cha manambala. ntchito umalimbikitsa chilakolako cha phunziro la lake ndi zotsatira za Gauss Kronecker. Malingaliro a Heinrich Eduard Heine, anzake Cantor pa Halle, anazindikira talente yake masamu, adatembenukira kwa chiphunzitso cha mndandanda trigonometric, amene anawonjezera mfundo manambala enieni.

Yachokera pa ntchito ntchito ya variable zovuta za German masamu Bernhard Riemann mu 1854, mu 1870 Cantor zasonyeza kuti ntchito yake akhoza akuimira mu njira imodzi yokha - ndi mndandanda trigonometric. Kuphunzira achikhalire a manambala (mfundo), n'cholinga zikutsutsana ndi zimene amakhulupirirazi, natulukira naye, mu malo oyamba, mu 1872, ku tanthauzo la manambala zopanda nzeru mu mawu a convergent mbali ya manambala zomveka (tuzigawo twa a integers) kenako chiyambi cha ntchito pa ntchito moyo wake, akonzedwa chiphunzitso ndi mfundo manambala transfinite.

chiphunzitso akonzedwa

Georg Cantor, chiphunzitso chimene lili unachokera mu makalata ndi Institute of Braunschweig masamu Richard Dedekind zina, kucheza naye kuyambira ali mwana. Iwo anati Amakhazikitsa, amalire kapena wopandamalire, ndi kuchuluka kwa zinthu (mwachitsanzo, manambala {0, ± 1, ± 2 ...}) Amene ali ndi katundu wina, pamene kusunga payekha awo. Koma pamene Georg Cantor ntchito kuphunzira chikhalidwe chawo makalata limodzi (mwachitsanzo, {A, B, C} {1, 2, 3}), iye anazindikira msanga kuti iwo amasiyana digiri awo ndi osiyana, ngakhale anali waika malire , T. e. akonzedwa chidutswa kapena kagawo zimaphatikizapo zochuluka mofana ndi zinthu monga izo ndi palokha. njira wake Mosakhalitsa zotsatira zodabwitsa.

Mu 1873, Georg Cantor (masamu) anasonyeza kuti manambala zomveka, ngakhale wopandamalire, ndi akuwerengedwerabe, chifukwa iwo akhoza kuyika mu makalata wina ndi wina ndi zachilengedwe (ie. E. 1, 2, 3 ,. D.). Iye anasonyeza kuti ya manambala weniweni wopangidwa mwa wopandamalire zomveka ndi zopanda nzeru, ndi uncountable. Kodi chododometsa, Cantor anatsimikizira kuti ya manambala onse algebraic lili zinthu ambiri monga ya integers onse, ndi kuti manambala transcendental omwe si algebraic, amene ali kagawo wa manambala zopanda nzeru ndi uncountable motero chiwerengero chawo ndi wamkulu kuposa integers ndi ndipo ayenera kutengedwa ngati wopandamalire.

Otsutsa ndi mbali

Koma ntchito Cantor, limene kaye patsogolo zotsatira, sanali lofalitsidwa mu "Krell" magazini monga mmodzi wa opereka ndemanga pa, Kronecker ankatsutsa. Koma pambuyo phukusi la Dedekind inasindikizidwa mu 1874 pansi udindo "Makhalidwe a manambala chonse chenicheni algebraic."

Science ndi moyo

Mu chaka chomwecho, pa kokasangalala ndi mkazi wake, Valli Gutman mu Interlaken, Switzerland, Cantor anakumana Dedekind amene mokoma ndemanga pa chiphunzitso chake chatsopano. George Malipiro ake anali ochepa, koma ndi ndalama atate wake yemwe anamwalira mu 1863, anamanga mkazi wake ndi ana asanu kunyumba. Ambiri mwa ntchito zake afalitsidwa Sweden mu magazini atsopano Acta Mathematica, mkonzi ndipo anayambitsa amene anali Gösta Mittag-Leffler, mwa oyambirira kudziwa talente wa masamu German.

Kulankhulana ndi metaphysics ndi

Chiphunzitso Cantor anali zatsopano nkhani za kafukufuku zokhudza masamu wopandamalire (mwachitsanzo, akuyambira 1, 2, 3 ,. D., Ndipo chivundi zovuta zambiri), chimene chiri kwakukulukulu amadalira makalata wina ndi wina. Cantor Development wa njira zatsopano atakhala mafunso okhudza kupitiriza ndi osawerengeka Lenti maphunziro ake osokonezeka.

Pamene iye anati manambala wopandamalire zilipodi, iye anatembenuka nzeru akale ndi akale ndi nkhani osawerengeka yeniyeni osiyanasiyana, komanso oyambirira maphunziro achipembedzo makolo anampatsa. Mu 1883, m'buku lake "chikhazikitso cha chiphunzitso ambiri kukukhala" Kantor amaphatikiza mfundo za metaphysics cha Plato.

Kronecker, amene ananena kuti "pali" integers yekha ( "Mulungu analenga integers, ena - ntchito ya munthu"), kwa zaka zambiri mwamphamvu anakana mfundo zake ndi kuteteza udindo wake ku University of Berlin.

manambala transfinite

Mu 1895-97 gg. Georg Cantor athanzi lingaliro lake la kupitiriza ndi osawerengeka, kuphatikizapo wosatha zinayendera ndi kadinala manambala, ntchito wotchuka kwambiri, lofalitsidwa pansi udindo "Athandiza ku chiphunzitso cha manambala transfinite" (1915). ntchito imeneyi ikuphatikizapo amayi ake, amene anatsogolera chionetsero kuti amaika malire angathe kuperekedwa mu umodzi ndi umodzi makalata ndi mmodzi wa subsets ake.

Laling'ono transfinite kadinala chiwerengero iye amatanthauza mphamvu ya akonzedwa uliwonse, amene angathe kuikidwa makalata wina ndi wina ndi manambala zachilengedwe. Kantor anafotokoza aleph-ziro wake. Large transfinite kuchuluka Alef-anasankha wina, awiri kapena Aleph-T. D. Iwo inakulitsidwa ordinals masamu, amene anali wofanana ndi masamu amalire. Motero, iye wandikhutiritsa mfundo osawerengeka.

Chitsutso anakumana ndi nthawi imene munataya kuonetsetsa kuti maganizo ake anavomereza kotheratu, anafotokoza zovuta za revaluation funso wakale wa kodi chiwerengero. Kantor anasonyeza kuti mndandanda wa mfundo pa mzere ali ndi mphamvu kuposa Aleph-ziro. Zimenezi zinachititsa kuti vuto odziwika wa popitilira kungoganizira - palibe makadinala pakati aleph-ziro ndi mfundo alibe mphamvu pa mzere. Vutoli mu zoyambirira ndi wachiwiri kwa zaka za m'ma 20 ndi yofunika kwambiri ndipo wakhala kuphunzira ndi masamu ambiri, Vol. H. Kurt Gödel ndi Paulo Cohen.

maganizo

Wambiri Georga Kantora kuchokera 1884 anali chodetsedwa ndi matenda ake incipient maganizo, koma iye anapitiliza kugwira ntchito mwakhama. Mu 1897 anathandizira kugwira woyamba Congress mayiko a masamu mu Zurich. Mwina chifukwa anatsutsa Kronecker, nthawi zambiri chifundo ndi achinyamata masamu budding ndipo anayesa kupeza njira yoti awapulumutse iwo ku kuvutitsidwa ndi aphunzitsi amene mantha ndi malingaliro atsopano.

Kuzindikila

Kumayambiriro kwa zaka za m'ma ntchito yake mokwanira anazindikira ngati maziko a chiphunzitso cha ntchito, kusanthula ndi mtunda. Komanso, Kantora Georga buku anali kutsogolera chitukuko winanso wa formalist ndi intuitionist sukulu ya maziko lomveka la masamu. Zimenezi zathandiza kwambiri anasintha dongosolo la kuphunzitsa ndipo amaganizira ndi "masamu latsopano."

Mu 1911, Cantor anali mwa anthu oitanidwa ku phwando la tsiku 500th wa pa yunivesite ya St Andrews ku Scotland. Iye anapita kumeneko akuyembekeza kuti akumane Bertrand Russell, amene ntchito yake posachedwapa lofalitsidwa Principia Mathematica mobwerezabwereza anatchula masamu German, koma zimenezo sizinachitike. University kupereka Cantor ndi digiri aulemu, koma chifukwa matenda anali kuvomereza za mphoto mwa munthu.

Cantor anapuma mu 1913 ndipo anakhala umphawi ndi njala pa First World nkhondo. Zikondwerero polemekeza kubadwa kwake 70 mu 1915 anali zimafika chifukwa cha nkhondo, koma mwambo yaing'ono unachitikira ku nyumba kwace. Iye anafa pa 06.01.1918, mu Galle, kuchipatala cha anthu amisala, komwe anakhala zaka zomalizira za moyo wake.

Georg Cantor: MBIRI. banja

August 9, 1874, katswiri wa masamu German anakwatira Valli Gutman. Banjalo ana 4 ndi aakazi 2. The mwana womaliza atabadwa mu 1886 mu Cantor anagula nyumba yatsopano. Kuthandiza banja anathandiza cholowa bambo ake. Thanzi la Cantor kwambiri bwanji imfa ya mwana wake wamng'ono mu 1899 - chifukwa sanasiye vuto.