Ubufakazi obusha bokuthi uCantor wenze i-Dedekind?

Kungani u-Dedekind Ahlala Ethule

Enye yezinto ezithakazelisa kakhulu zale ndaba impendulo ka-Dedekind - noma kunalokho, ukuntula kwakhe eyodwa. Yize enobufakazi obanele bokuthi ubalulekile kuye, u-Dedekind akakaze asole uCantor esidlangalaleni ngokukopela. Izinto ezimbalwa zisiza ukuchaza lesi sivimbelo:

• Umehluko wesimo sezulu: I-Dedekind ibigodliwe, icophelela, futhi iyimfihlo ngokujulile. UCantor wayenesifiso sokuvelela, echuma, futhi efuna ukuqashelwa esikhungweni sezibalo esasivame ukwenqaba umsebenzi wakhe.
• Ukuba sengozini kochwepheshe: U-Cantor uchithe ingxenye enkulu yomsebenzi wakhe e-University of Halle, isikhungo sesigaba sesibili, futhi wabhekana nokuphikiswa okunonya okuvela ku-Leopold Kronecker. U-Dedekind, owasungulwa ngokunethezeka e-Brunswick Polytechnic, kungenzeka ukuthi waba nomuzwa wokuthi impikiswano ebalulekile izoba ngaphansi kwakhe.
• Ukuncika okufanayo: Naphezu kokungalingani kwezikweletu, womabili amadoda ayebazisa ubudlelwano. Umsebenzi wobuciko ka-Dedekind wango-1888 Ingabe u-sind und was sollen die Zahlen? wakhelwe phezu kwemibono ababeyithuthukisile ndawonye, futhi ingxabano yomphakathi yayiyongcolisa womabili amafa.
• Ifilosofi yokushicilela: U-Dedekind wayekholelwa ukuthi imibono kufanele ishicilelwe kuphela lapho isifinyelele esimweni sokucaca okuphelele nokuphelela. Ukhethe ukungayishicileli imiphumela eminingi, ayithatha njengeyesikhashana. Ngokubona kwakhe umbono ongakashicilelwa wawungakalungeli umhlaba.

Leli phuzu lokugcina mhlawumbe libuhlungu kakhulu. Ukufuna ukuphelela kuka-Dedekind kwadala isikhala esagcwaliswa nguCantor. Ubufakazi obusha abuvezi kangako umuntu okhohlakele njengoba bukhanyisa inkinga yesakhiwo: uma zingekho izinhlelo zemibhalo esobala, umshicileli osebenza kakhulu uthwebula isikweletu, kungakhathaliseki ukuthi ubani owayenombono kuqala.

Lokhu Kusho Ukuthini Ngesibaluli Sobuhlakani Namuhla

Icala le-Cantor-Dedekind lisebenza ngalé komlando wezibalo. Kuyo yonke imikhakha yokusebenzisana - kusukela ocwaningweni lwesayensi kuye ekuthuthukisweni kwesoftware kuya kumasu ebhizinisi - umbuzo wokuthi ubani owasungula umbono nokuthi ubani omane owenze usalokhu unzima kakhulu ukuwuxazulula. Isistimu yezemfundo yesimanje iphendule ngezinkambiso eziqinile ezithinta ukucaphuna, ukubhalwa ngokubambisana, kanye nokunyathelisa kwangaphambili kokufinyelela okuvulekile. Kodwa emhlabeni webhizinisi, lapho amaqembu abambisana nsuku zonke kumaphrojekthi abiwe, inkinga iyaqhubeka.

Cabangela ukuthi zingaki izinqumo zebhizinisi ezibucayi, ukusungulwa kwemikhiqizo emisha, kanye namasu abalulekile avela ezingxoxweni ezingakahleleki — umlayezo we-Slack lapha, iseshini yebhodi elimhlophe lapho, ukuphawula okuphambene nomhlangano. Ngaphandle kwemibhalo ehlelekile, umuntu obhala umbiko wokugcina noma owethula isethulo sokugcina ngokuvamile uthola ikhredithi, kuyilapho umuntu obangele umbono efiphele ngemuva. Lena inkinga ye-Dedekind ngendlela yebhizinisi.

Izinkundla zesimanje ezifana ne-Mewayz zibhekana nale nselele ngokuhlanganisa ukubambisana kweqembu, imibhalo yephrojekthi, nokulandelela ukuhamba komsebenzi kube yisistimu eyodwa. Ngamamojula ahlanganisiwe angu-207 ahlanganisa i-CRM, ukuphathwa kwephrojekthi, ukuxhumana kweqembu, nezibalo, yonke iminikelo ifakiwe, igxivizwe isikhathi, futhi ibangelwa. Uma ilungu leqembu liphakamisa isu kunothi lephrojekthi, lelo rekhodi liyaqhubeka. Uma ukugeleza komsebenzi kulungiswa, umlando woshintsho ubonisa ukuthi ubani owenze ukulungisa nokuthi nini. Uhlobo lwegebe lokuchayeka elikhungethe i-Dedekind isikhathi esingaphezu kwekhulu liba yinto engenakwenzeka ngesakhiwo uma ingqalasizinda yemibhalo yakhiwe endaweni yesikhulumi ngokwayo.

Ukuhlola kabusha Ifa leCantor

Akukho kulokhu okwehlisa ukukhalipha kwangempela kuka-Georg Cantor. Ukuphikisana kwakhe kwe-diagonal ka-1891, ukuthuthukiswa kwakhe kwezinombolo ze-ordinal ne-cardinal transfinite, kanye ne-hypothesis yakhe eqhubekayo kusalokhu kuyimpumelelo ephakeme ephethe isiginesha yakhe yokudala ehlukile. Umbuzo ophakanyiswe ubufakazi obusha akukona ukuthi uCantor ubeyisazi sezibalo esisezingeni eliphezulu - ngokungangabazeki wayenguye yini - kodwa ukuthi ukulandisa okungokomlando kulahlekile ngokungafanele.

Amagalelo ka-Dedekind ezisekelweni zezibalo aya ngokuya aqashelwa njengesisekelo ngomqondo ongokoqobo. Ukwakha kwakhe izinombolo zangempela ngokusebenzisa ukusikeka kuseyindlela evamile ezincwadini zokuhlaziya zesimanje. Ithiyori yakhe yezinombolo ze-algebra yaba nomthelela ezizukulwaneni zezibalo kusukela ku-Emmy Noether kuya ku-André Weil. Futhi imininingwane yakhe ye-set-theoretic, manje ebhalwe ngokugcwele ngobufakazi benqolobane, yembula umuntu ocabangayo owayengeyena nje umlobeli kaCantor kodwa owayelingana nobuhlakani bakhe - futhi, kwezinye izimo, nomanduleli wakhe.

Ukuhlola kabusha akukhona ukudiliza ifa elilodwa ukuze kwakhiwe elinye. Kumayelana nokuzuza ukuqonda okunembe kakhudlwana kokuthi imibono eguquguqukayo ikhula kanjani ngempela: hhayi ezikhathini ezihlukene zobuhlakani, kodwa ngezingxoxo eziqhubekayo, ukuthonyana, kanye nokuthuthukiswa kancane kancane kwemiqondo eyabiwe. Okudabukisayo ukuthi irekhodi ledokhumentari belincane kakhulu, futhi izinkambiso zokushicilelwa zixega kakhulu, ukuthwebula leli qiniso lokusebenzisana ngesikhathi sangempela.

Izifundo Zomhlaba Wokubhaliwe-Wokuqala

Ingxabano ye-Cantor-Dedekind inikeza isifundo esinamandla esidlulela ngale kwezemfundo. Enkathini lapho izingxabano zempahla eqanjiwe zinganquma isiphetho sezinkampani nemisebenzi, ukubaluleka kokuqina, amadokhumenti esikhathi sangempela ngeke kugcizelelwe. Konke ukusebenzisana kuveza imibono, futhi yonke imibono inesiqalo. Izinhlangano ezithuthukayo kuzoba yilezo ezithatha leso sizindalwazi - hhayi njengokucatshangelwa kwakamuva, kodwa njengesici esishumekiwe sendlela umsebenzi owenziwa ngayo.

Kumabhizinisi angu-138,000 asevele asebenzisa i-Mewayz ukuphatha imisebenzi yawo, lo mgomo wakhelwe ekuhambeni komsebenzi kwansuku zonke. Konke ukusebenzelana kweklayenti okungene ku-CRM, yonke i-invoyisi ekhiqizwayo, yonke ingqophamlando yephrojekthi elandelwayo idala irekhodi elingunaphakade, eliseshekayo lokuthi ubani onikele ngani futhi nini. Ngandlela thize, ingqalasizinda u-Dedekind angakaze abe nayo — uhlelo oluqinisekisa ukuthi iminikelo ekhaliphile ayishabalali ibe ezincwadini eziyimfihlo, ilinde iminyaka engaphezu kwekhulu ukuthi ibonwe.

Umlando ungase ungalokothi ulethe isinqumo esiqondile sokuthi u-Cantor ukhohliwe yini i-Dedekind. Ubufakazi obusha butshekisa isikali, kodwa iqiniso eligcwele licashwe emfihlakalweni yobungane bangekhulu le-19 obaqhutshwa ngezincwadi ezibhalwe ngesandla nezingxoxo zobuso nobuso okungekho zingobo zomlando ezingazakha kabusha. Esingakwazi ukukufunda, nokho, akucaci: bhala yonke into, faka isikweletu ngesandla esivulekile, futhi wakhe amasistimu enza ukuba kube khona okuzenzakalelayo. I-Dedekind elandelayo ifanelwe okungcono.

Imibuzo Evame Ukubuzwa

Yibuphi ubufakazi obuphakamisa ukuthi uCantor kungenzeka wenze u-Dedekind?

Umfundaze wakamuva uhlola ukuxhumana kwawo okubanzi kusukela ngawo-1870 nawo-1880, okuveza ukuthi imibono eminingi eyisisekelo kaCantor kuthiyori emisiwe kanye nemvelo ye-infinity efana nemibono eyizibuko u-Dedekind abelane ngayo ngasese ngaphambili. Izazi-mlando zikhomba ukungezwani komugqa wesikhathi phakathi kwemibhalo yesandla ye-Dedekind engashicilelwe kanye nokushicilelwa okwalandela kukaCantor, kanye nezindima ezincwadini zabo lapho u-Dedekind aveza khona imiqondo eyinhloko eyavela kamuva emsebenzini kaCantor ngaphandle kokuchazwa okufanele.

Ubudlelwano beCantor-Dedekind bube nomthelela kanjani kuzibalo zesimanje?

Ukubambisana kwabo nokubangisana kwabo kulolonga izisekelo zezibalo zesimanje. Ukwakhiwa okuqinile kuka-Dedekind kwezinombolo zangempela ngokusikeka kanye nokuthuthukiswa kwe-Cantor yesethi yetiyori eguquguqukayo ndawonye kwasungula uhlaka cishe zonke izibalo zesimanje ezisekelwe kulo. Ukushintshana kwabo ngomqondo wokungapheli, ukuqhubeka, kanye nemvelo yezinto zezibalo kwaqubula izimpikiswano eziqhubeka nokuqhuba ucwaningo kungqondongqondo, ifilosofi yezibalo, nezifundo eziyisisekelo namuhla.

Kungani impikiswano yokukopela iqala kabusha manje?

Izinto zokulondoloza umlando ezifakwe kwidijithali, okuhlanganisa nezinhlamvu ebezingafinyeleleki ngaphambilini nokusalungiswa kwemibhalo yesandla, kuvumele osomlando ukuthi bakhe kabusha imigqa yesikhathi enembe kakhudlwana yokuthuthukiswa kombono. Amathuluzi athuthukisiwe okuhlaziya umbhalo kanye nezindlela zokuphambana nazo zenze kwaba lula ukulandelela ukugeleza kwemiqondo phakathi kwezazi zezibalo ezimbili. Lokhu okutholakele okusha kuvuselele intshisekelo yezemfundo futhi kwenze ukuthi ukushicilelwa okumbalwa okubuyekezwe ontanga ukuthi kuphinde kuhlole ubuqiniso beminikelo kaCantor.

Ngingazithola kuphi izindatshana ezijulile zezibalo nomlando wobuhlakani?

Amajenali ezemfundo, izingobo zomlando zasenyuvesi, nemitapo yolwazi yedijithali ekhethiwe yizindawo ezinhle kakhulu zokuqala zocwaningo lokujula. Kochwepheshe nabadali bokuqukethwe abafuna ukushicilela nokuphatha okuqukethwe kwabo kwezemfundo ngendlela efanele, Mewayz inikeza i-OS yebhizinisi engamamojula angu-207 eqala ku-$19/mo ehlanganisa ukubhuloga, amathuluzi e-SEO, nokuphathwa kwezithameli — konke okudingekayo ukuze kwakhiwe inkundla yolwazi enegunya.