Georg Cantor: i kumumanaʻo, Kawaihae a me ka ohana makemakika

Georg Cantor (Hawaii photo hōʻike hope i loko o ka 'atikala) - German mathematician i hoʻomohala i ka kumumanaʻo o ka hoʻopaʻa i ka', a hoʻolauna i ka manaʻo o transfinite nui, infinitely nui, akā, okoa mai kekahi i kekahi. He i haawi mai i ka wehewehena o ordinal a me ka cardinal loa, a hookupaa i ko lakou makemakika.

Georg Cantor: he pōkole Kawaihae

Hânau 'ia i loko o St. Petersburg 03.03.1845. Kona makua kāne i kekahi Denemaka Protestant Georg Walademā Cantor, i hoʻoili ai i loko o ke kalepa, ma ka Vol. H. A ma luna o ke kumukuai, e loaa hou. Kona makuwahine, o Maria, bem i kekahi Hui, a hele mai, mai ka ohana o koʻikoʻi mele. A hiki i ka 1856 o kona makua kāne George lilo maʻi, i ka ohana ma ka huli ana i ka milder aniau neʻe mua i Wiesbaden laila i Frankfurt. Makemakika talena, ke keikiʻikeʻia ma mua o kona 15th hoomakaukau ana këia i loko o nā kula a me nā kula aupuni ma Darmstadt a me Wiesbaden. Ma ka hopena, Georg Cantor hookonokono ae la i kona makua kāne i loko o kona manao paa ia e lilo i mathematician makemake ana ia mea ma mua o ka lunaʻenehana.

Ma hope o ka manawa pōkole aʻo ma ke Kulanui o Zurich i ka 1863. Cantor i hoolilo ai i Pelelina University, e hoʻopaʻa haʻawina ke kālaikūlohea, kālaiʻike a me ka makemakika. Aiaʻo ia i ao mai ai:

• Karl Theodor Weierstrass, kona specialization i loko o ke Ka Ikepili, paha i ke keiki nui ma luna o George;
• Ernst Kummer, ka mea i ao mai i ka lani kiekie loa makemakika;
• Leopold Kronecker, ma ka helu kumumanaʻo hoʻomalu, ka mea hope kū'ē Cantor.

Ua lilo kekahi kau ma ke Kulanui o Göttingen i ka 1866, e hiki mai ka makahiki George kakau iho la i kona doctoral ia hoʻi ma lalo o ka inoa "Ma makemakika, ka no o ka noi ana nīnau Ua oi waiwai ma mua o ka hoʻoponopono pilikia" e pili ana i ka pilikia e Carl Friedrich Gauss waiho unresolved i loko o kona Disquisitiones Arithmeticae (1801) . Ma hope iki e ao ana ma ka Pelelina School no ka kaikamahine Kantor ka hoʻomaka 'ana e hana ana ma ke Kulanui o Halle, kahi āna i koe ia a hiki i ka hopena o kona ola ana, mua me ka lecturer, mai ka makahiki 1872 me ka Hope Kumu, a mai 1879 i ka mua me ke Kumu.

noiʻi

I ka hoʻomaka o ka moʻo hana 10 mai ka 1869 a hiki i ka makahiki 1873 o, Georg Cantor noʻonoʻo i ka kumumanaʻo o ka helu. Ke hana Hōʻike 'i ke kuko no ke kumuhana o kona kuka nei lakou, a me ka hope o Gauss Kronecker. Ma ke kōkua 'ana o Heinrich Eduard Heine, Cantor mau nā hoapili ma Halle, ka mea i ike i kona makemakika talena, haliu aku la oia i ka kumumanaʻo o trigonometric puke, i hoʻonui i ka manaʻo o maoli helu.

Ma muli o ka papa hana o ka luna 'ee iaaanu aey o ka German mathematician Bernhard Riemann i ka makahiki 1854, i ka 1870 Cantor ua hoike ia ia i kekahi kuleana pili i hiki ke poe i wale kekahiʻaoʻao - ma trigonometric moʻo. Noonoo o ka ahaaina o ka huahelu (kumu), i makemake ole hoole aku paha i keia manao, kai aku la, ma ka wahi mua, i ka makahiki 1872, a hiki i ka wehewehena o irrational loa ma ka hua'ōlelo o ka nń kaʻina o ka naauao helu (hapa iki o integers), a laila, i ka hoʻomaka o ka hana ma luna o kona ola i ka hana, i kumumanaʻo, a me ka manaʻo o transfinite helu.

huapalapala kumumanaʻo

Georg Cantor, ke kumumanaʻo i nā pūʻulu originated ma ka palapala me ka noa ka Institute o Braunschweig mathematician Richard Dedekind, ua mau hoa me ia, mai ka wā kamaliʻi. Lakou manao i na e puhi ia, finite a mana loa, i ka ai iiiaanoaa o ka oihana mua (e laʻa me, helu, 0, ± 1, ± 2 ...}) Ka mea i ka kekahi waiwai, oiai hoʻokoe iho i kā lākou individuality. Akā, i ka wā Georg Cantor noi e noiʻi i ko lakou mau ano kekahi palapala (e like,, A, B, C} i, 1, 2, 3}), ka mea, hoʻomaopopo koke ihola nō ia mea, oko i loko o kā lākou degere o ka affiliation, a ina he mea mana loa e puhi ia , ole, e ka. huapalapala apana paha he subset o i ka loaʻa o ka mea helu o nā mea e like me ia mea wale. Kona hana koke i haawi mai, heʻe piʻoloke ihola nā hualoaʻa.

I ka makahiki 1873, Georg Cantor (mathematician) hoike mai i ka naauao nui, nae mana loa, e countable, no ka mea, hiki ke waiho i loko o hoʻokahi-i-kekahi palapala me maoli ( 'o ia hoʻi, E. 1, 2, 3 ,. D.). He hōʻike i ka huapalapala o maoli helu oia hoi o ka naauao a me ka irrational, a me uncountable mana loa. He aha ka paradox, Cantor hoao i ka lākou o nā mea a pau algebraic helu kekahi me na oihana mua i ka 'ia paha o nā integers, a ua transcendental huahelu i mea ole algebraic, a mea he subset o irrational huahelu mea uncountable, a ma keia hope aku i ko lakou helu, ua oi aku ma mua o ka integers a e e noʻonoʻo like mana loa.

Mau hoa paio a me kākoʻo

Akā, i ka hana Cantor, ma ka mea āna i waiho mua aku i nā hualoaʻa, ia i paʻiʻia ma ka "Krell" Magazine me kekahi o na nā mea hoʻoholo, Kronecker i kū'ē. Akā, ma hope o ka piʻiʻana o ka Dedekind mea i paʻiʻia ma 1874 ma lalo o ka inoa "nā 'ano o nā mea a pau maoli algebraic helu."

ʻEpekema a me ka ola

I ka hookahi makahiki, iloko o ka Honeymoon me kana wahine, Valli Gutman ma Interlaken, Kuikilana, Cantor halawai Dedekind ka mea launa aku ua'ōleloʻia ma luna o kona hou kumumanaʻo. George uku ua liʻiliʻi, akā, me ke kālā i kona makua kāne, ka mea i make i ka 1863, āna i kūkulu ai no kana wahine, a me elima mau keiki i ka hale. He nui o kana mau hana i ua paʻi ma Kuekene ma ka hou puke Acta Mathematica, i ka hoʻoponopono a me ka mea hoʻoheheʻe kālā a i ua Gösta Mittag-Leffler, i waena o ka mea mua, e ike i ke tālena o ka Kelemānia mathematician.

Palapala me ka metaphysics

Kumumanaʻo Cantor ua loa hou kumuhana o ka noiʻi e pili ana i ka makemakika aloha (e laʻa me, ke kaʻina, 1, 2, 3 ,. D., A oi eiiieaen e puhi ia), a mea pili kēia kalele iho ma kekahi-i-kekahi palapala. Cantor Development o hou ano o ka holo ana nīnau e pili ana i ka hoʻomauʻana a me ka infinity noi ai i kona mau haʻawina i hui pūʻia.

A hiki aku ka mea, ua kūkākūkāʻia i aloha pauʻole, nui maoli nei, haliu aku la oia i ke akeakamai kahiko a me ka medieval me ka pili ana i ka maoli a me ka Loaʻaʻia infinity, e like me ia i ka kakahiaka nui haipule hoʻonaʻauao, a na makua i haawi mai ai ia ia. I ka 1883, i loko o kona puke "paʻa o ka mau kumumanaʻo o ka hoʻopaʻa i ka '" Kantor hui i kona manaʻo o ka metaphysics o Plato.

Kronecker no hoi, ka poe i hoʻike ana "he mau" wale integers ( "ke Akua i hana mai i na integers, ke koena - o ka hana ana o ke kanaka"), no ka mea, he nui na makahiki ua hōʻole ikaika maila i kona mau manaʻo hoʻopiʻi kū'ē, a hooki i kona hookohu ia i ke Kulanui o Pelelina.

transfinite helu

Ma 1895-97 GG. Georg Cantor maopopo i hanaʻia i kona manaʻo o ka hoʻomauʻana a me ka infinity, a me ka pau ole, ke kaʻina, a me ka cardinal nui, ma o kona hana kaulana loa, paʻiʻia ma lalo o ka inoa "na makana i ka kumumanaʻo o ka transfinite huahelu" (1915). Kēia hana kikowaena o kona hapai ana, i ka i ana i alakai i ka h ÷ ike i ka mana loa kau hiki e haawiia i loko o ka hoʻokahi-i-kekahi palapala a me kekahi o kona subsets.

Ka mea uuku transfinite cardinal helu oia i ke ano o ka mana o kekahi huapalapala, i hiki ke waiho i loko o hoʻokahi-i-kekahi palapala i ka helu maoli. Kantor i ho'ākāka 'ia i kona aleph-Aʻohe. Nui transfinite iiiaanoaa Alef-hoʻohikiʻia kekahi, elua a Aleph-ole. D. It hou ulu makemakika ordinals, a ua like me ka finite makemakika. Pela, oia ua waiwai i ka manaʻo o ka infinity.

Ke kū'ēʻo iaʻalo, a me ka manawa ia i ka hōʻoia 'ana i kona mau manaʻo i maopopo maliuia mai, wehewehe i nā complexities o ka revaluation o ka ninau kahiko o ka mea i ka helu. Kantor hōʻike ana i ka lākou o nā kumu ma luna o ka laina mai ka oi aku nona iho ma mua o Aleph-Aʻohe. Ua alakai aku ai i ka luawai-ike pilikia o ka hoʻomaumau kuhiakau -ʻaʻohe cardinals ma waena o aleph-Aʻohe aʻaʻohe mana helu ma ka laina. Kēia pilikia i loko o ka mua a me ka lua o ka hapalua o ka 20th kenekulia mea o ka nui hoihoi a me ka ua, ua aʻoʻia he nui mathematicians, ma ka Vol. H. Kurt Gödel a me Paul Cohen.

kaumaha

Kawaihae Georga Kantora 1884,ʻino ihola ma kona mau incipient noʻonoʻo maʻi, akā, ua mau nō e hana 'Imi. I ka 1897, ua kokua mai, e hoopaa i ka mua International Ahaolelo Lahui o Mathematicians ma Zurich. Kekahi kumu, no ka mea, kū'ē i ka Kronecker, ua make pinepine a makemake me ka bipi i opuu ae mathematicians, a ho'āʻo e imi i ke ala, e hoola ia lakou mai ka ino ma na kumu i haha aku hooweliweli e hou i ka manaʻo nui.

iaia

Ma ka huli ana o ke kenekulia i kana hana, ua akoakoa ike i ke kumu no ka kumumanaʻo o ka mana, Ka Ikepili a me ka topology. Eia hou kekahi, Kantora Georga puke i mālama ai i ka impetus no ka hou 'ana o ka formalist a me ka intuitionist kula o Logical kumu o ka makemakika. Kēia i me ka nui loa loli i ka'ōnaehana o ke ao ana, a ua pinepine pili me ka "hou makemakika."

I ka 1911, Cantor i waena o ka poe i kono ai i ka hookahakaha o ka 500th lā hoʻomanaʻo o ke Kulanui o St Andrews i loko o Kekokia. Hele aku la ia malaila me ka manao e halawai me Bertrand Russell, ka mea i loko o kona mau nei i paʻi hana He Mathematica pinepine haawiia i ka German mathematician, akā, i ka i hiki mai. University i hookoia Cantor i honorary degere, akā, ma muli o ka maʻi ka mea, ua hikiʻole eʻae i ka ia nā kumu kāki i loko o kanaka.

Cantor hoʻomaha i ka 1913, a noho ma kaʻilihune, a starving iloko o ka First World War. Hang ma ka hanohano o kona 70th lā hānau i loko o 1915 i hōʻoki aku no o ke kaua, akā, ua mālama 'ia he uuku ka lawelaweʻia ma kona wahi. He make ma 06.01.1918, ma Galle, i loko o ka psychiatric haukapila, kahi ana i hoolilo ai ka makahiki hope o kona ola.

Georg Cantor: A Kawaihae. ohana

August 9, 1874, i ka Kelemānia mathematician mare Valli Gutman. Ka hui, he 4 keikikane a me na kaikamahine 2. Ke keiki hope i hanau ia ma 1886 ma Cantor kuai i ka hou i ka hale. Kākoʻo i ka ohana, ua kokua mai o kona makua kāne hoʻoilina. Ke ola kino o Cantor nui loli i ka make ana o kana keiki muli iho i loko o 1899 - no ka mea, aole loa ia i haalele ai ia i ke kaumaha.