Georg Cantor: dhigay aragti, Biography iyo xisaabta qoyska

Georg Cantor (photo waxay muujinaysaa dambe ee maqaalka) - xisaab Jarmal kaas oo horumariyey aragtida ah ee nooc oo soo bandhigay fikradda ah tirada transfinite, Rowan weyn, laakiin kala duwan oo midba midka kale ka. Waxa uu sidoo kale siiyey qeexidda dhabta ah ee tirada horsanaanta iyo jiifoo iyo aasaasay ay xisaabta.

Georg Cantor: Biography gaaban

Wuxuu ku dhashay St. Petersburg 03.03.1845. Aabbihiisna wuxuu ahaa deenish Protestant Georg Waldemar Cantor, ayaa waxaa ku hawlan ganacsiga, in H. Vol. Oo sarrifka saamiyada. Oo hooyadiis, Mary, Bem ahaa Catholic ah iyo ka qoyskaaga ka mid ah fanaaniinta caanka yimid. Marka in 1856 aabbihiis George xanuunsan noqday, qoyska in search of jawi fudud ugu horeysay u dhaqaaqay Wiesbaden ka dibna si Frankfurt. talanti Xisaabeed, wiilka u muuqday hor dhalashadiisii 15aad, halka waxbarashada ee dugsiyada gaarka loo leeyahay iyo dugsiyada dadweynaha ee Darmstadt iyo Wiesbaden. In dhamaadka, Georg Cantor aabbihiis in go'aanka uu ku adkeeyey inay noqon xisaabyahan ah halkii injineer.

tababar kooban oo ka tirsan jaamacadda Zurich ee 1863. Ka dib markii Cantor lagu wareejiyay University Berlin inaad wax ka barato physics, falsafada iyo xisaabta. Waxaa uu wax ku baray;

• Karl Theodor Weierstrass, takhasuska, kuwaas oo in falanqaynta, malaha saameyn ugu weyn ee George;
• Ernst Kummer, kaas oo baray xisaabta ugu sareeya;
• Leopold Kronecker, tirada takhasus aragti, oo markii danbe ka soo horjeeda Cantor.

Isagoo muddo hal xilli dugsiyeed ee Jaamacadda Göttingen ee 1866, sannadka soo socda George qoray sha phD hoos horyaalka "In xisaabta, farshaxanka waydiinaya su'aalo waa ka qiimo badan xalinta dhibaatooyinka" ku saabsan dhibaatada in Carl Friedrich Gauss tagay la xallin uu Disquisitiones Arithmeticae (1801) . Ka dib markii barayay kooban at School Berlin ee gabdhaha Kantor shaqada ee jaamacadda Halle, halkaas oo uu ku sugnaa ilaa dhamaadka naftiisa bilaabay, marka hore sida oo bare ka ah, tan iyo 1872 kaaliye professor ah, oo tan iyo 1879 ugu horeysay sida professor ah.

cilmi

Bilowga taxane ah oo 10 shuqullada ka 1869 si ay u 1873, Georg Cantor loo arkaa aragtida ah tirooyinka. Shaqada ka tarjumaysaa hamiday ee mawduuca uu daraasad iyo saamaynta Gauss Kronecker. At soo jeedinaya of Heinrich Heine Eduard, asxaabta Cantor ee Halle, kuwaas oo loo aqoonsan yahay tayadiisa xisaabta, ayuu u soo jeestay in aragtida ah ee taxanaha trigonometric, kaasoo balaariyay fikradda guud ee tirada dhabta ah.

Iyada oo ku saleysan shaqada shaqada ee variable ah oo adag oo xisaab ah Jarmal Bernhard Riemann ee 1854, in 1870 Cantor ayaa muujisay in shaqada noocan oo kale ah loo soo bandhigi karo in hal hab oo kaliya - by taxane trigonometric. Tixgelinta la ballamay lambarada (dhibcood), taas oo aysan ka horimaan lahaa view this, isaga, in meesha ugu horeysa, in 1872, si ay u qeexida tirooyinka aan buuxin marka la eego isku xigxigta, is-tirooyinka buuxa (jajabyada abyooneyaasha) ka dibna si bilowgii shaqadii on shuqulkiisii uu nolosha, aragti set iyo fikradda guud ee tirada transfinite.

aragti set

Georg Cantor, aragtida ah kaas oo dhigaya asalkiisu ka soo jeedo ee waraaqaha la Machadka Farsamada ee xisaab Braunschweig Richard Dedekind, ahaa saaxiibada isaga la lahayd tan iyo yaraantaadii. Waxay soo gabagabeeyey in ay qaybood, uguna ama aan la koobi karayn, waa hannaanka ka mid ah xubno ka (, tirada tus {0, ± 1, 2 ± ...}) kuwee leedahay guri gaar ah, halka xafidaada ay shaqsi. Laakiin marka Georg Cantor codsatay in ay bartaan sifooyinka ay ka mid warqadihiisa (tusaale ahaan, {A, B, C} si {1, 2, 3}), si deg deg ah uu ogaaday in ay ku kala duwan yihiin heerka raacsan yahay, xitaa haddii ay ahaayeen nooc aan la koobi karayn , gabal set t. e. ama hoosaad ah oo ay ku jiraan tiro la mid ah waxyaabaha sida laftiisa waa. Uu hab ugu dhakhsaha badan siiyey natiijo la yaab leh.

In 1873, Georg Cantor (xisaab) muujisay in tirooyinka buuxa, inkasta oo aan la koobi karayn, waa la tirin karo, maxaa yeelay, iyagu la gelin karaa fool-ka-fool ah waraaqo la dabiiciga ah (ie. E. 1, 2, 3 ,. D.). Waxa uu muujiyay in la ballamay ee tirada dhabta ah oo ka kooban koobi karayn a buuxa iyo kuwa aan buuxin, iyo xoomey. Waa maxay isku liddiga ah, Cantor caddeeyeen in set oo dhan lambarada aljebrada ka kooban xubno ka badan intii set oo dhan abyoonayaasha, iyo in tirada dhaafsiisantahay oo aan aljabrada, kuwaas oo iyaduna ka mid ah tiro aan buuxin waa xoomey iyo halkan tiradoodu waa ka weyn yahay abyoonayaasha ah iyo waa in la tixgeliyaa sida aan la koobi karayn.

Dadka ka soo horjeeda iyo taageerayaasha

Laakiin shaqada Cantor, taas oo marka hore uu horey natiijada, lama daabacay "Krell" magazine sida mid ka mid ah faallada ah, Kronecker waxaa ka soo horjeeda. Laakiin ka dib markii fara gelin ku sameeyeen Dedekind waxaa la daabacay sanadkii 1874kii iyagoo hoos horyaalka "Sifooyinka oo dhan lambarada aljabrada dhab ah."

Sayniska iyo nolashiisa qaaska ah

Isla sanadkaas, inta lagu guda jiro Malabka waa inuu naagtiisa, Valli Gutman in Interlaken, Switzerland leh, Cantor kulmay Dedekind kuwaas oo si raxmad leh uga hadashay uu aragti cusub. mushaar George yaraa, laakiin lacagta aabbihiis, kuwaas oo ku dhintay 1863, ayuu u dhisay isaga, xaaskiisa iyo shan caruur ah guriga. Qaar badan oo ka shuqulladiisa ayaa lagu daabacay in Sweden weriyey cusub ACTA Mathematica, tafatiraha iyo aasaasaha ah taas oo ahayd Gösta Mittag-Leffler, ka mid ah kii ugu horeeyay ee la aqoonsado talantigii ka mid ah xisaab Jarmalka.

Isgaarsiinta la metaphysics ah

Aragtida Cantor ahaa mawduuca cusub oo cilmi baaris la xiriira koobi karayn xisaabta (tus, xigaan 1, 2, 3 ,. D., Oo nooc dheeraad ah oo ku adag), taas oo inta badan ku tiirsan tahay mid-ka-mid ah waraaqaha. Cantor Development of hababka cusub ee dejinta su'aalo ku saabsan sii wadida iyo xad sare ah waxbarashada uu isku qasan.

Markii uu ku dooday in tiro aan la koobi karayn run ahaantii jira, ayuu si falsafadda qadiimiga ah iyo Dr Makumbe jeestay oo la xiriira xad dhabta ah iyo ka iman kara, iyo sidoo kale in ay waxbarashada diineed ee hore, kaas oo waalidka isaga siiyey. In 1883kii, in uu buugga "Fundamentals of aragtida guud ee qaybood" Kantor isku daro uu fikradda ah metaphysics ee Plato.

Kronecker sidoo kale, kuwaas oo uu sheegay in "waxaa jira" abyoonayaasha kaliya ( "Ilaah wuxuu abuuray abyoonayaasha, inta kale - shuqulka nin"), oo sannado badan si adag u diiday dood iyo hortagi uu magacaabayo Jaamacadda Berlin.

lambarada transfinite

In 1895-97 GG. Georg Cantor si buuxda u sameeyay uu fikrad oo joogtada ah iyo xad la'aan, ay ka mid yihiin tiro ah isku xigxiga oo jiifoo aan dhammaadka lahayn, ee uu shaqada ugu caansan, la daabacay ka yar title "waxa kaloy aragtida ah ee tirada transfinite" ee (1915). shaqada waxaa ka mid ah inuu fikrad, kaas oo uu hoggaaminayay mudaaharaad in set ah aan la koobi karayn waa la samatabbixin karaa waraaqo ah fool-ka-fool ah kula mid ka mid ah subsets ay.

The tirada jiifoo transfinite yar uu ula jeedo xoogga set kasta, taas oo la gelin karaa fool-ka-fool ah waraaqo la tirooyinka caadiga ah. Kantor tilmaamay aleph-eber. hannaanka transfinite Large Alef-qoondeeyey mid ka mid ah, laba ama Aleph-t. D. Waxaa sii horumariyo ordinals xisaabta, taas oo ahayd mid ah xisaabta ku uguna. Sidaas darteed, waxa uu ku hodanaynta fikirka ah xad la'aan.

Mucaaradka uu la kulmay, iyo wakhtiga ay qaadatay si loo hubiyo in fikradaha uu si buuxda u aqbalay, sharxay badnida revaluation ee su'aasha hore ee waa maxay tirada. Kantor muujisay in tiro dhibcood on line ee uu leeyahay awood ka saraysa Aleph-eber. Tani waxay keentay in dhibaatada si fiican u yaqaan ee la xiqiijiyay in sii socodka - ma cardinals dhexeeya aleph-eber iyo ma dhibcood awood on line ah. Tani waxay dhibaato qeybtii koowaad iyo labaad ee qarnigii 20aad waa dan weyn ayaa bartay by xisaabyahannada badan, in H. Vol. Kurt Gödel iyo Paul Cohen.

niyad-jabka

Biography Georga Kantora 1884 markii weelkii uu cudurka dhimirka sidoo kale, laakiin waxa uu sii waday in ay si firfircoon uga shaqeeyaan. In 1897 uu ka caawiyay in ay qabtaan International Congress koowaad ee xisaabyahannada ee Zurich. Qayb ahaan sababtoo ah waxa uu ka soo horjeeda Kronecker ah, oo marar badan wuxuu u naxariisateen kuwii la xisaabyahannada dhallinyarada gaysashada iyo isku dayeen in ay helaan hab iyaga badbaadiya ka dhibaatayn macalimiinta dareemaya hanjabay by fikrado cusub.

aqoonsi

At Warega of qarnigii uu shaqada waxaa si buuxda u aqoonsan yahay in ay sal u ah aragtida ah ee hawlaha, falanqaynta iyo topology. Intaa waxaa dheer, buugga Kantora Georga adeegay sidii wadadii loogu talagalay horumarinta dheeraad ah ee dugsiga formalist iyo intuitionist ee aasaaska macquul ah ee xisaabta. Tani waxa ay si weyn u bedelay habka waxbaridda iyo inta badan la xidhiidha ee "xisaabta cusub."

In 1911, Cantor ka mid ah kuwa lagu martiqaaday in ay dabaal-guuradii 500aad ee Jaamacadda St Andrews ee Scotland ahaa. Markaasuu halkaas ka tegey ayaa rajeynaya inuu la kulmo Bertrand Russell, kuwaas oo in shaqada uu dhawaan la daabacay Principia Mathematica si joogta ah loo gudbiyo xisaab Jarmalka, laakiin taasi ma dhicin. University abaal Cantor shahaado sharaf, laakiin ay sabab u tahay cudur ayuu waxa uu awoodi waayay inuu aqbalo abaalmarinta qof.

Cantor ka fariistay 1913 oo ku noolaa saboolnimada iyo macaluul lagu jiro dagaalkii koowaad ee aduunka. Dabaaldegyada lagu sharfayo dhalashadiisii 70aad ee 1915 ayaa la baajiyay sababo la xiriira dagaalka, laakiin xaflad yar oo lagu qabtay guriga uu ka. Wuxuu on 06.01.1918 dhintay, ee Galle, isbitaalka dhimirka, halkaas oo uu ka sano ee la soo dhaafay ee uu noloshiisa ku qaatay.

Georg Cantor: Biography A. qoyska

August 9, 1874tii, xisaabyahan Jarmalka guursaday Valli Gutman. Lamaanahan ayaa lahaa 4 wiil iyo 2 gabdhood. ilmaha ee la soo dhaafay waxa uu ku dhashay 1886 in Cantor iibsatay guri cusub. Taageer qoyska uu ka caawiyay dhaxalka aabbihiis. caafimaadka ee Cantor si weyn u saamaysay dhimashada wiilkiisa yaru ku 1899 - tan iyo markii ay ma ka niyad-jabka.