Georg Cantor: whakaturia ariā, haurongo, me te pāngarau te utuafare

Georg Cantor (whakaatu whakaahua i muri i roto i te tuhinga) - mathematician Tiamana nei whakawhanakehia te ariā o huinga, ka whakaurua te ariā o tau transfinite, ta'efakangatangata nui, engari rerekē i ia atu. hoatu hoki e ia he whakamāramatanga o ngā tau raupapa me te faariro i a whakapumautia ratou tauhanga.

Georg Cantor: he haurongo poto

Fanauhia i roto i te St Petersburg 03.03.1845. ko he Danish porotetani Georg Waldemar Cantor tona papa, i mahi i roto i te hokohoko, i te Vol. H. A i runga i te utu kararehe. Tona whaea, ko Meri, ko Bem he Katorika, a ka haere mai i te hapu o kaiwaiata rongonui. A, no te i roto i te 1856 ka tona papa George kino, ko te hapu i roto i te rapu o te āhuarangi mähaki oho tuatahi ki Wiesbaden ka ki Frankfurt. taranata Mathematical, puta te tamaiti i mua i tona ra whanautanga 15 i te ako i roto i ngā kura tūmataiti me ngā kura tūmatanui i roto i Darmstadt me Wiesbaden. I roto i te mutunga, i whakakikitia Georg Cantor tona papa i roto i tona faaotiraa ki te riro i te mathematician, nui atu i te kaipūkaha.

I muri i te whakangungu poto i te University o Zurich i te tau 1863. Cantor i whakawhitia ki a University Berlin ki ako ahupūngao, rapunga whakaaro me te pāngarau. i whakaako ia i reira:

• Karl Theodor Weitarahāute, nei whāiti i te tātari, pea i te mana rahi i runga i George;
• Ernst Kummer, e whakaako te tauhanga teitei;
• Leopold Kronecker, i runga i te tau ariā mātanga, e ātete i muri Cantor.

Ka pau tetahi wāhanga i te University o Göttingen i 1866, i tuhituhi te tau i muri mai George tona tuhinga täkutatanga raro i te taitara "I roto i te pāngarau, he nui atu faufaa atu i whakaoti rapanga te toi o ui pātai" e pā ana ki te raruraru i mahue kāore anō i roto i tona Disquisitiones Arithmeticae Carl Friedrich Gauss (1801) . I muri whakaako poto i te kura Berlin mō ngā kōtiro tīmata Kantor mahi i te University o Halle, te wahi noho ia tae noa ki te mutunga o tona ora, te tuatahi i rite te pükenga, mai 1872 rite te tauturu orometua, a mai i 1879 i te tuatahi i rite te orometua.

rangahau

I te timatanga o te raupapa o te 10 mahi i te tau 1869 ki te 1873, whakaaro Georg Cantor te ariā o ngā tau. whakaata te mahi te weriweri mo te kaupapa o tona ako me te pānga o Gauss Kronecker. I te mana'o tauturu o Heinrich Eduard Heine, hoa a Cantor i Halle, e mohio ana taranata pāngarau, ka tahuri ia ki te ariā o te raupapa pākoki, i whakawhānui te ariā o tau tūturu.

I runga i te mahi mahi o te tāupe matatini o te mathematician German Bernhard Rēimāna i 1854, i roto i te 1870 whakaaturia Cantor kua e taea te māngai he taumahi taua i roto i te kotahi anake te ara - i te raupapa pākoki. Whakaaro o te huinga o ngā tau (ngā), e kore e pehi i tenei tirohanga, arahina ia, i roto i te wahi tuatahi, i roto i 1872, ki te whakamāramatanga o noatia tau i roto i ngā o raupapa convergent o tau kouma (hautau o tau tōpū) me ka ki te timatanga o te mahi i runga i te mahi a tona ora, whakaritea ariā me te ariā o te tau transfinite.

huinga ariā

Georg Cantor, te ariā e whakatakoto ahu i roto i te reta ki te Institute o Braunschweig mathematician Richard Dedekind Hangarau, i hoa ki a ia mai i te tamarikitanga. faaoti ratou e nga huinga, fakataimí mure ore ranei, ko te plurality o huānga (hei tauira, ngā tau {0, ± 1, ± 2 ...}) nei i te tetahi taonga, i te mau tonu to ratou tangatatanga. Otira ka tono Georg Cantor ki ako ratou āhuatanga kotahi reta (hei tauira, {A, B, C} ki {1, 2, 3}), ia hohoro mohio e rere ratou i roto i to ratou tohu o hononga, ara, ki te i te reira huinga mure ore , t. e. huinga wahi he huinga o e ngā te taua maha o ngā rite ko reira iho ranei. hohoro hoatu tona tikanga hua mīharo.

I roto i te 1873, Georg Cantor (mathematician) whakakitea e tau kouma, ahakoa mure ore, e Countable, no te mea e taea te hoatu e ratou i roto i te reta kotahi-ki-tetahi ki tūturu (ie. E. 1, 2, 3 ,. D.). whakakitea e ia e te huinga o ngā tau tūturu arā, o te mure ore kouma, me te noatia, me haro'aro'ai. He aha te lēsoni, Cantor whakamatauria e kei te huinga o nga tau taurangi katoa rite maha āhuatanga rite te huinga o ngā tau tōpū katoa, me e tau transcendental kore e taurangi i, i te hunga he haro'aro'ai te huinga o noatia tau, me te i konei he nui ake te tau tōpu ratou maha a kia whakaaro rite mure ore.

Hoariri me kaitautoko

Ko te mahi Cantor, i roto i nei te tuatahi hoatu e ia mua nga hua, e kore i whakaputaina i roto i "Krell" makasini rite tetahi o nga kaiarotake, i ātete Kronecker. Otiia i muri i te wawaotanga o te Dedekind i whakaputaina taua mea i roto i te tau 1874 i raro i te taitara "Te āhuatanga o tau taurangi tūturu katoa."

Pūtaiao me te ora whaiaro

I roto i te taua tau, i roto i te taime ki tana wahine, Valli Gutman i Interlaken, Switzerland, tutaki Cantor Dedekind e aroha kōrero i runga i tona ariā hou. i iti George utu, engari tona papa, e mate i roto i te tau 1863, i hanga e ia mo tana wahine, me rima tamariki te kāinga ki te moni. E rave rahi o ana mahi kua whakaputaina i roto i Sweden i te hautaka hou rangitaki Mathematica, te ētita, me te kaiwhakarewa o nei ko Gösta Mittag-Leffler, i roto i te tuatahi ki te mohio ki te taranata o te mathematician Tiamana.

Communication ki te metaphysics

ko Theory Cantor kaupapa tino hou o te rangahau e pā ana ki te pāngarau ta'efakangatangata (hei tauira, te raupapa 1, 2, 3 ,. D., ka huinga matatini atu), i te mea te nuinga o ti'aturi i runga reta kotahi-ki-kotahi. Cantor Whanaketanga o tikanga hou o te whakatakoto pātai mo tonu me te mutu- tukua ana akoranga i konatunatua.

A, no te tohe ia e te tīari tino tau mure ore, tahuri ia ki te kaupapa tawhito, me te wharekarakia ki te whakaaro ki te mutu- tūturu me pūmanawa, me te ki te tīmatanga te mātauranga fakalotú, i hoatu matua ia. I roto i 1883, i roto i tona pukapuka "Faá o te ariā whānui o ngā huinga" ngā Kantor tona ariā o te metaphysics o Plato.

Kronecker hoki, e kiia ana e "i reira e" tau tōpu anake ( "hanga e te Atua nga tau tōpu, te okiokinga - te mahi a te tangata"), no te tau maha kaha paopao ana tohenga, ka haukotia tona whakarite ki te University o Berlin.

tau transfinite

I te 1895-97 gg. Georg Cantor i hanga tino tona whakaaro o te tonu, me te mutu-, tae atu he raupapa me te faariro i mutunga tau, i roto i tona mahi tino rongonui, whakaputaina i raro i te taitara "Te Koha ki te ariā o ngā tau transfinite" (1915). Tenei mahi ngā tona hapu, ki i arahina e ia i te whakaaturanga e taea te tukua te huinga mure ore i roto i te reta kotahi-ki-tetahi ki tetahi o ona tautuhiroto.

Ko te tau faufaa rahi transfinite iti rawa auraa e ia te mana o tetahi huinga, e taea te hoatu i roto i te reta kotahi-ki-tetahi ki te tau māori. fakamatala'i Kantor tona AREPE Ka-kore. Nui plurality transfinite Arewhe-whakaritea kotahi, e rua ranei AREPE-t. D. reira atu whakawhanakehia Tātaki tauhanga, i i rite ki te tauhanga fakataimí. Ko te kupu, kua taonga ia te ariā o te mutu-.

Te pato'iraa fehangahangai ia, me te wa ka mau te reira ki te whakarite i whakaaetia tino ona whakaaro, faataa nga hōhonutanga o te wāriutanga o te pātai i tahito ra o te mea ko te tau. whakakitea Kantor e te huinga o ngā i runga i te raina kua he kaha ki runga ake i AREPE-kore. arahina tenei ki te raruraru pai-mohiotia o te whakapae auroa - kahore katinara i waenganui i AREPE Ka-kore, me kore ngā mana i runga i te raina. Tenei raruraru i roto i te hawhe tuatahi, me te tuarua o te rau tau 20 he o te pānga nui, me te kua ako e numera maha, i roto i te Vol. H. Kurt Gödel ko Paora Cohen.

korekore

Haurongo Georga Kantora i 1884 i kino e tona mate hinengaro incipient, engari tonu ia ki te mahi kaha. I te 1897 i āwhina ia ki te mau i te tuatahi International Congress o Mathematicians i Zurich. Tetahi wahi no te mea te ātete ia te Kronecker, maha I mamae ia ki te kuao mathematicians hua ka tamata ki te kitea te ara ki te whakaora ia ratou i te inonotitanga e ngā kaiako e ite whakawehi e whakaaro hou.

āhukahuka

I te tahuri o te rau tau i tino mohio tona mahi rite he pūtake mo te ariā o ngā mahi, te tātari me te āhuawhatunga. I tua atu, i mahi Kantora Georga pukapuka hei whanaketanga mō te whanaketanga atu o te kura formalist me intuitionist o turanga arorau o pāngarau. Kua tino tenei ke te pūnaha o te whakaako, me te te maha e pā ana ki te "pāngarau hou."

I 1911, ko Cantor roto i te hunga karangatia ki te whakanui i o te tau 500th o te University o St Andrews i Scotland. haere ana ia ki reira tumanako ki te whakatau Bertrand Russell, e i roto i tona mahi tata whakaputaina Principia Mathematica toutou tuku ki te mathematician German, engari i kore e tupu. University whakawhiwhia Cantor he tohu hōnore, engari e tika ana ki te mate i taea ki te farii i te tohu tangata i roto ia.

mutu Cantor i roto i tau 1913, ka noho i roto i te rawakore, me te fiekaia i roto i te Pakanga Tuatahi o te Ao. i whakakorea Celebrations i te honore o tona huritau 70 i roto i te tau 1915 no te mea o te whawhai, engari i tū te hui iti i tona whare. mate ia i runga i 06.01.1918, i Galle, i roto i te hōhipera hinengaro, te wahi pau nga tau whakamutunga o tona ora ia.

Georg Cantor: A Biography. whānau

August 9, 1874, i moea e te mathematician German Valli Gutman. i 4 tama me 2 tamahine te tokorua. whanau te tamaiti whakamutunga i roto i 1886 i roto i hokona Cantor te kāinga hou. Tautoko i te whānau i āwhina ia taonga tuku o tona papa. uesia te hauora o Cantor nui te mate o tana tama whakaotinga i 1899 - mai i kore ai i mahue te whārua.