Humbowo hutsva hwekuti Cantor akateedzera Dedekind?

Kukwikwidzana Kwakaumba Masvomhu Azvino

Muzvinyorwa zvenhoroondo yemasvomhu, hukama hushoma hwakaratidza sehungwaru hunoorera - kana kuti hune nharo - sehuya huri pakati paGeorg Cantor naRichard Dedekind. Tsamba dzavo muma1870 nema1880 dzakaburitsa dzimwe pfungwa dzechimurenga muhwaro hwemasvomhu, kubva pakuvakwa kwakasimba kwenhamba chaidzo kusvika pazaruro inokatyamadza yekuti kusaguma kunouya muhukuru hwakasiyana. Asi mubvunzo wanetsa pakati pevanyori venhoroondo dzemasvomhu kweanopfuura zana wakawana simba idzva nguva pfupi yadarika: Cantor akawana chikwereti chakawanda kupfuura chaaifanirwa here, uye Dedekind akawana zvishoma here? Ongororo itsva yenyanzvi dzetsamba dzavo dzepachivande, zvinyorwa zvemanyoro, uye kutevedzana kwenguva kwezvinyorwa zvavo kuri kumanikidza nzanga yemasvomhu kuti iongororezve kuti ndiani akabereka zvechokwadi pfungwa dzatinoti zvino dzinoita seCantor chete.

Iyi haisiriyo nyaya yedzidzo pamusoro pezvinyorwa. Mubvunzo wekuti Cantor akanyengerwa — kana kuti haana kupihwa zvikwereti zvakakwana — Dedekind unobaya pamoyo wekuti tinopa sei muridzi wepfungwa, kuti kubatana kunokanganisa sei kugovera, uye nei zvinyorwa uye zvirevo zvine chekuita nendima yega yega, kubva kumasvomhu chaiwo kuenda kune bhizinesi razvino.

Zvatakatoudzwa Nenhoroondo Yenhoroondo

Ukama huri pakati peCantor naDedekind hunonyorwa zvakanaka kuburikidza netsamba dzetsamba dzakatsinhaniswa pakati pe1872 ne1899. Tsamba yavo, yakatanga kubudiswa mumagazini yakaunganidzwa naEmmy Noether naJean Cavailles muna 1937, inoratidza kuchinjana kwenjere kwakanyanya. Muna 1872, varume vaviri vakazvimiririra vakaburitsa zvivakwa zvenhamba chaidzo - Cantor achishandisa izvo zvave kunzi Cauchy sequences, uye Dedekind achishandisa "kucheka" kwake kwakakurumbira. Asi mabhii anoratidza kuti Dedekind akagadzira kuvaka kwake kwakachekwa kare muna 1858, makore gumi nemana akazara isati yaburitswa, achidzidzisa kuverenga paPolytechnic muZürich.

Zvagara zvichizivikanwa nevanyori venhoroondo ndezvekuti Cantor aitsamira zvakanyanya paDedekind mukati memakore ekugadzira edzidziso. Yakanga iri mutsamba ya1873 kuna Dedekind kuti Cantor akatanga kubvunza mubvunzo wekuti nhamba chaidzo dzaigona kuiswa mutsamba imwe-kune-imwe nenhamba dzechisikigo. Dedekind haana kungokurudzira kubvunza chete asi akapa kurerutsa kwakakosha kuchiratidzo chekutanga cheCantor chekuti izvo chaizvo hazviverengeki. Asi Cantor paakaburitsa mhedzisiro iyi inokosha muCrelle's Journal muna 1874, mupiro waDedekind hauna kutaurwa.

Kusiiwa uku kwanga kusiri kuitika kamwe chete. Mukati mezvinyorwa zvakawanda mukupera kwema1870 nema1880s, Cantor akagadzira mazano airatidza kujeka kwekutsinhana kwake naDedekind - kusanganisira kuumbwa kwekare kwekadhinari, pfungwa yekusaverengeka, uye chimiro che-point-set topology - pasina kupa rudzi rwekubvuma iyo yazvino miitiro yedzidzo yaizoda.

Humbowo Hutsva: Manyorero eNguva uye Zvisina Kudhindwa Zvisina Kudhindwa

Chidzidzo chenguva pfupi yapfuura, kudhirowa pazvinhu zvakachengetwa paYunivhesiti yeGöttingen uye zvakambotariswa marginalia muDedekind's Nachlass (literary estate), yakawedzera huremu hunokosha kunyaya iyi. Vanyori venhoroondo vakaona zvinyorwa zvekunyora muruvoko rwaDedekind zvinodonongodza makiyi e-set-theoretic concepts - kusanganisira yekutanga vhezheni yeingava iyo theorem yekuti seti haina magumo kana uye chete kana ichigona kuiswa mubijection nechikamu chayo chayo - kufambidzana nenguva pamberi Cantor yakaburitsa zvakaenzana mhedzisiro.

Chinonyanyo shamisa ndeye seti yezvinyorwa kubva 1874 kusvika 1877 umo Dedekind anodhiza pfungwa nezve mepu pakati pemaseti e "masimba" akasiyana (atinodaidza zvino kuti makadhidhi). Aya manotsi akatangira basa raCantor rakatsikiswa papfungwa dzakafanana nemakore akati wandei. Nepo Dedekind akasarudza kuramba kudhindwa - chimwe chikonzero nekuda kwenyaya yake yekuda kukwana uye pamwe nekuti akanzwa pfungwa dzisati dzave muchimiro chinogutsa - Cantor, uyo aikwanisa kuwana pfungwa idzi kuburikidza netsamba yavo, akakurumidza kubudisa.

Mutsara wenguva uri kunetsa mune zvawo chaiwo. Nyanzvi dzakaronga kanokwana zviitiko zvinomwe zvakasiyana pakati pa 1873 na 1885 apo pfungwa inotanga kubuda muzvinyorwa zvepachivande zveDedekind kana mabhii kuCantor, uyezve inowanikwa mumapepa akadhindwa eCantor mukati memwedzi mitanhatu kusvika ku18 - pasina kutaurwa.

Kunyepa kana Hute hweKudyidzana?

Usati wamhanyira kupa mhosva Cantor, zvakakosha kuti unzwisise tsika yehungwaru ye19th-century mathematics. Zvimiro zvechitubu uye zvirevo zvaive zvishoma zviri pamutemo sezvazviri nhasi. Pakanga pasina mafomati ereferensi, pasina maitiro ekuongorora-vezera sezvatinoaziva, uye muganho pakati pe "kufemerwa nehurukuro" uye "kukwereta pfungwa" waive usina kujeka. Nyanzvi dzemasvomhu dzaigarogovana mazano mutsamba nekunzwisisa kwakazara kuti kodzero dzekuburitsa ndedzemunhu anonyora bepa.

"Mutsara uripo pakati pepesvedzero yenjere nehumbavha hwenjere unotorwa kwete nepfungwa pachadzo, asi negwaro remagwaro rakaapoteredza. Kana pasina marekodhi akajeka, kusawirirana kwekutanga kunova nyaya yekududzira - uye muparidzi ane ushingi anowanzo kuhwina nhoroondo yenhoroondo."

Vadziviriri vaCantor vanopokana kuti akashandura zvakaonekwa naDedekind kuita dzidziso yakarongeka - kuti Dedekind akapa mbeu, asi Cantor akavaka bindu. Pane chokwadi kune izvi: Cantor's 1895–1897 Beiträge zur Begründung der transfiniten Mengenlehreinomiririra kuumbwa kukuru kunoenda kure kupfuura chero chinhu chakanyorwa naDedekind. Asi humbowo hutsva hunoratidza kuti mbeu idzi dzakaumbwa zvizere kupfuura zvaimbozivikanwa, uye kutadza kwaCantor kuzvibvuma kwaive, padiki, kuparara kwetsika nemaitiro enguva ipi zvayo.

Sei Dedekind Akaramba Akanyarara

Chimwe chezvinhu zvinonyanya kunakidza zvenyaya iyi mhinduro yaDedekind - kana kuti, kushaya kwake imwe. Kunyangwe aine humbowo hwakakwana hwezvaaikoshesa, Dedekind haana kumbobvira apomera Cantor pachena. Zvinhu zvakawanda zvinobatsira kutsanangura kuzvidzora uku:

• Musiyano wehutsinye: Dedekind yakanga yakachengetwa, yakanyatsojeka, uye yakavanzika zvakadzama. Cantor aiva neshungu, akabudirira, uye aida chaizvo kuzivikanwa mune imwe sangano remasvomhu raiwanzoramba basa rake.
• Professional vulnerability: Cantor akapedza nguva yakawanda yebasa rake paYunivhesiti yeHalle, chikoro chechipiri, uye akatarisana nekupikiswa kunotyisa kubva kuna Leopold Kronecker. Dedekind, akagadzwa zvakanaka paBrunswick Polytechnic, anogona kunge akanzwa kuti gakava rekutanga raizova pasi pake.
• Mutual dependence: Pasinei nekusaenzana kwechikwereti, varume vose vaikoshesa hukama. Dedekind's 1888 masterwork Was sind und was sollen die Zahlen? yakavakirwa pamazano avakange vagadzira pamwechete, uye gakava reruzhinji raizosvibisa mbiri mbiri.
• Publication philosophy: Dedekind aidavira pfungwa dzinofanira kuburitswa chete kana dzasvika pakujeka nekukwana. Akanyatsosarudza kusaburitsa mibairo mizhinji, yaaiona seyenguva. Sekuona kwake, imwe pfungwa isina kudhindwa yakanga isati yagadzirira nyika.

Iyi poindi yekupedzisira ndiyo inonyanya kurwadza. Dedekind's own perfectionism yakagadzira vacuum iyo Cantor yakazadza. Humbowo hutsva hahunyanyo ratidza munhu akaipa sezvahunojekesa dambudziko remugadzirirwo: pakashaikwa magadzirirwo emagwaro akajeka, muparidzi ane ruzivo anowedzera kutora chikwereti, zvisinei nekuti ndiani akatanga kufunga.

Zvinorevei Izvi kune Intellectual Attribution Nhasi

Mhosva yeCantor-Dedekind inoenderera mberi kupfuura nhoroondo yemasvomhu. Mundima yese yekubatana - kubva pakutsvagisa kwesainzi kusvika pakuvandudza software kusvika kune bhizinesi zano - mubvunzo wekuti ndiani akatanga zano uye ndiani akangozviita unoramba uchinetsa kugadzirisa. Iyo yemazuva ano yedzidzo sisitimu yapindura nemaitiro akawedzera kuomarara akatenderedza citation, co-authorship, uye yakavhurika-yekuwana preprints. Asi munyika yebhizimisi, umo zvikwata zvinodyidzana zuva nezuva pamapurojekiti akagoverana, dambudziko rinoramba riripo.

Funga kuti ingani sarudzo dzakakosha dzebhizinesi, kuvandudzwa kwechigadzirwa, uye hunyanzvi pivots dzinobuda muhurukuro dzisina kurongwa - meseji yeSlack pano, musangano webhodhi chena ipapo, kutaura kwekunze mumusangano. Pasina magwaro akarongeka, munhu anonyora mushumo wekupedzisira kana kupa mharidzo yekupedzisira kazhinji anogashira kiredhiti, nepo munhu aita kuti pfungwa yacho iende kumashure. Iri ndiro dambudziko reDedekind muchimiro chekambani.

Mapuratifomu emazuvano akaita seMewayz anogadzirisa dambudziko iri nekuisa pakati pekubatana kwechikwata, zvinyorwa zvepurojekiti, nekuronda mafambiro ebasa muhurongwa humwe. Iine mazana maviri nenomwe akasanganiswa mamodule anotora CRM, manejimendi epurojekiti, kutaurirana kwechikwata, uye analytics, mupiro wega wega unodhindwa, wakadhindwa nguva, uye unoenderana. Kana nhengo yechikwata ikaronga zano mune chinyorwa cheprojekiti, rekodhi iyoyo inoenderera. Kana kufambiswa kwebasa kuchigadziriswa, nhoroondo yekuchinja inoratidza kuti ndiani akagadzirisa uye riinhi. Rudzi rwegepu rekutaura iro rakatambudza Dedekind kweanopfuura zana rinove risingagoneke muchimiro kana zvinyorwa zvezvinyorwa zvivakwa mupuratifomu pachayo.

Kuongororazve Nhaka yeCantor

Hapana chimwe cheizvi chinodzikisira kupenya chaiko kwaGeorg Cantor. Nharo yake ye diagonal ya 1891, kukura kwake kwenhamba dze transfinite ordinal ne cardinal, uye fungidziro yake yekuenderera mberi inoramba iine budiriro yakakura inotakura siginicha yake yekugadzira inosiyanisa. Mubvunzo wakamutswa nehumbowo hutsva hausi wekuti Cantor aive nyanzvi yemasvomhu here - hapana mubvunzo kuti aive - asi kuti nhoroondo yenhoroondo yakaraswa zvisina kunaka.

Mipiro yaDedekind kunheyo dzemasvomhu iri kuramba ichizivikanwa sehwaro mupfungwa chaiyo. Kuvaka kwake nhamba chaidzo kuburikidza nekucheka kunoramba kuri nzira yakajairwa mumabhuku ekuongorora emazuva ano. Dzidziso yake yenhamba yealgebra yakapesvedzera zvizvarwa zvemasvomhu kubva kuna Emmy Noether kusvika kuna André Weil. Uye maonero ake edzidziso, zvino akanyatso kunyorwa kuburikidza neuchapupu hwemudura, anoratidza munhu anofunga anga asiri mutori wenhau waCantor chete asi akaenzana nenjere dzake - uye, mune dzimwe nguva, akamutangira.

Kuongorora zvakare hakusi kuputsa nhaka imwe kuti ivake imwe. Ndezvekuwana kunzwisisa kwakanyatsojeka kwekuti pfungwa dzechimurenga dzinokura sei: kwete munguva dzega dzeunyanzvi, asi kuburikidza nenhaurirano inoenderera, kurudziro, uye kukwenenzvera zvishoma nezvishoma kwepfungwa dzinogovana. Dambudziko nderekuti rekodhi rekodhi rakanga rishoma, uye tsika dzechinyorwa dzakarembesa, kutora chokwadi chekubatana uku munguva chaiyo.

Zvidzidzo zveKunyorwa-Nyika Yekutanga

Kukakavadzana kweCantor-Dedekind kunopa chidzidzo chine simba chinopfuurira kupfuura dzidzo. Muzera umo kukakavara kwepfuma yepfungwa kunogona kuona magumo emakambani nemabasa, kukosha kwekuomarara, kwechokwadi-nguva zvinyorwa hazvigone kuwedzeredzwa. Kubatana kwese kunogadzira mazano, uye zano rega rega rine mavambo. Masangano achabudirira ndeaya anotora mavambo acho sechinhu chaicho - kwete sekufunga kwekupedzisira, asi sechinhu chakabatanidzwa chekuti basa rinoitwa sei.

Kune 138,000 mabhizinesi ari kutoshandisa Mewayz kubata mashandiro avo, musimboti uyu wakavakirwa mukufambiswa kwezuva nezuva. Kudyidzana kwese kwevatengi kwakaiswa muCRM, invoice yega yega inogadzirwa, chiitiko chega chega chakatevedzwa chinogadzira rekodhi risingaperi, rinotsvakwa rekuti ndiani akapa chii uye rinhi. Ndiwo, neimwe nzira, zvivakwa zvisina kumbobvira zvave naDedekind - hurongwa hunoita kuti mipiro yakanaka irege kupera mumabhuku ekunyora ega, ichimirira makore anopfuura zana kuti izivikanwe.

Nhoroondo inogona kusambopa mutongo wakajeka wekuti Cantor akanyengedza Dedekind. Humbowo hutsva hunorereka chikero, asi chokwadi chakazara chakavigwa muhunyengeri hweushamwari hwemuzana ramakore rechi 19 hwaiitwa kuburikidza netsamba dzakanyorwa nemaoko uye nekurukurirano dzechiso nechiso izvo pasina anochengeterwa anogona kugadzira patsva. Zvatingadzidza, zvisinei, hazvina kujeka: nyora zvese, kiredhiti nerupo, uye kuvaka masisitimu anoita kuti kupihwa kuve nyore. Dedekind inotevera inofanirwa nani.

Mibvunzo Inowanzo bvunzwa

Ndeupi humbowo hunoratidza kuti Cantor anogona kunge akateedzera Dedekind?

Chidzidzo chenguva pfupi yapfuura chinoongorora tsamba dzavo dzakakura kubva ku1870s na1880s, zvichiratidza kuti mazhinji epfungwa dzeCantor dzekutanga padzidziso yetiyeti uye chimiro cheinfinity padhuze negirazi pfungwa Dedekind akange agovana zvakavanzika zvisati zvaitika. Vanyori venhoroondo vanonongedzera kumutsauko wenguva pakati pezvinyorwa zvisina kudhindwa zveDedekind uye zvinyorwa zvakazotevera zvaCantor, pamwe nendima mutsamba dzavo apo Dedekind akadonongodza pfungwa huru dzakazobuda mubasa raCantor pasina kunyorwa kwakakodzera.

Hukama hweCantor-Dedekind hwakakanganisa sei masvomhu emazuvano?

Kushandira pamwe nekukwikwidzana kwavo kwakaumba hwaro hwemasvomhu azvino. Kuvaka kwaDedekind kwakaomarara kwenhamba chaidzo kuburikidza nekucheka uye kuvandudza kwaCantor kweshanduko seti dzidziso pamwe chete kwakagadzira dhizaini iyo inenge yese yemazuva ano masvomhu yakamira. Kutsinhana kwavo pamusoro pepfungwa yekusaguma, kuenderera mberi, uye chimiro chezvinhu zvemasvomhu zvakamutsa nharo dzinoramba dzichikurudzira tsvakiridzo yepfungwa, huzivi hwemasvomhu, uye zvidzidzo zvehwaro nhasi.

Sei gakava rekunyepa richitanga zvakare?

Zvitsva zvakaiswa mudura, kusanganisira mavara aisasvikika kare uye zvinyorwa zvemanyoro, zvakabvumira vanyori venhoroondo kuti vagadzirezve nguva chaiyo yekuvandudzwa kwepfungwa. Maturusi ekuongorora manyorerwo epamusoro uye nzira dzekuchinjisa-referensi zvaitawo kuti zvive nyore kuronda mafambiro epfungwa pakati pevaviri vesvomhu. Zvitsva zvakawanikwa izvi zvakadzora kufarira mune zvedzidzo uye zvakurudzira kuti mabhuku akaongororwa nevezera akati wandei kuti vaongorore zvekare nezvekwakabva kwaCantor.

Ndokupi kwandingawane zvimwe zvinyorwa zvakadzama nezvemasvomhu nenhoroondo yenjere?

Majenari ezvidzidzo, dura remayunivhesiti, uye maraibhurari edhijitari akachengetedzwa zvakanaka zvekutanga zvekutsvagisa zvakadzama. Kune nyanzvi nevagadziri vezvemukati vari kutsvaga kuburitsa uye kutonga zvedzidzo zvavo nemazvo, Mewayz inopa 207-module bhizinesi OS inotangira pa$19/mo inosanganisira blogging, SEO maturusi, uye manejimendi evateereri - zvese zvinodiwa kuvaka chikuva cheruzivo chine chiremera.