Ibimenyetso bishya byerekana ko Cantor yibye Dedekind?

Irushanwa ryashizeho imibare igezweho

Mu mateka yamateka yimibare, umubano muto wagaragaye nkuburumbuke bwubwenge - cyangwa nkimpaka - nkubwa hagati ya Georg Cantor na Richard Dedekind. Kwandikirana kwabo mu myaka ya 1870 na 1880 byabyaye bimwe mubitekerezo byimpinduramatwara mu mfatiro z’imibare, uhereye ku iyubakwa rikomeye ry’imibare nyayo kugeza guhishurwa gutangaje ko ubuziraherezo buza mu bunini butandukanye. Ariko ikibazo kimaze igihe kinini mu mateka y’imibare mu binyejana byashize giherutse kugira imbaraga: Cantor yaba yarahawe inguzanyo irenze iyo yari akwiye, kandi Dedekind yahawe make cyane? Isesengura rishya ryabahanga ryandikirana ryabo bwite, inyandiko zandikishijwe intoki, hamwe nigihe gikurikiranye n’ibitabo byabo ni uguhatira umuryango w’imibare kongera gusuzuma uwatanze ibitekerezo ubu tuvuga ko byoroshye kuri Cantor wenyine.

Ibi ntabwo ari ugutongana gusa mumashuri yerekeye ibisobanuro. Ikibazo cyo kumenya niba Cantor yariganye - cyangwa byibuze ashimwa bidahagije - Dedekind yibasiye intandaro yukuntu dushyira nyirubwite ubwenge, uburyo ubufatanye buvanga no kugenerwa, n'impamvu ibyangombwa nibisabwa muri buri gice, uhereye kumibare itanduye kugeza mubucuruzi bugezweho.

Ibyo amateka yamateka yamaze kutubwira

Umubano uri hagati ya Cantor na Dedekind wanditswe neza binyuze mumabaruwa yagiye ahana hagati ya 1872 na 1899. Inzandiko zabo, zasohowe bwa mbere mu gitabo cyegeranijwe na Emmy Noether na Jean Cavaillès mu 1937, zigaragaza kungurana ibitekerezo mu bwenge. Mu 1872, abo bagabo bombi batangaje ubwigenge bwubatswe bwimibare nyayo - Cantor ukoresheje icyo bita ubu buryo bwa Cauchy, na Dedekind bakoresheje "gukata". Ariko amabaruwa yerekana ko Dedekind yateje imbere imyubakire ye kuva mu 1858, imyaka 14 yuzuye mbere yuko itangazwa, ubwo yigishaga kubara muri Polytechnic i Zürich.

Icyo abahanga mu by'amateka bamenye kuva kera ni uko Cantor yishingikirije cyane kuri Dedekind mu myaka yashinzwe yo gushyiraho ibitekerezo. Mu ibaruwa 1873 yandikiye Dedekind niho Cantor yabanje gutanga ikibazo cyo kumenya niba imibare nyayo ishobora gushyirwa mu nzandiko imwe kuri imwe hamwe n’imibare isanzwe. Dedekind ntabwo yashishikarije iperereza gusa ahubwo yagize uruhare runini mu koroshya ibimenyetso bya mbere bya Cantor byerekana ko ibintu bitabarika. Nyamara igihe Cantor yasohoraga ibisubizo byingenzi mu kinyamakuru cya Crelle mu 1874, uruhare rwa Dedekind ntirwigeze ruvugwa.

Uku gusiba ntabwo kwabaye inshuro imwe. Mu bitabo byinshi mu mpera za 1870 na 1880, Cantor yateje imbere ibitekerezo byerekana ibimenyetso bidashidikanywaho byo kungurana ibitekerezo kwe na Dedekind - harimo no gutangira hakiri kare ubukaridinali, igitekerezo cyo guhakana, ndetse n'imiterere ya topologiya yashizweho - adatanga uburyo bwo kwemeza ko amahame ya kijyambere azakenera.

Ibimenyetso bishya: Igihe cyandikishijwe intoki n'imishinga idashyizwe ahagaragara

Bourse iherutse, gushushanya ku bikoresho byububiko muri kaminuza ya Göttingen ndetse na marginalia mbere yirengagijwe muri Dedekind ya Nachlass (umutungo w’ubuvanganzo), yongereye uburemere muri uru rubanza. Abahanga mu by'amateka bagaragaje inyandiko zandikishijwe intoki ziri mu ntoki za Dedekind zigaragaza ibitekerezo by'ingenzi byashyizweho - harimo na verisiyo yo hambere y'ibyahinduka theorem ko seti itagira iherezo niba kandi iyo ishobora gushyirwa muri bijection hamwe na sisitemu ikwiye - bijyanye n'ibihe mbere yuko Cantor atangaza ibisubizo bisa.

By'umwihariko igitangaza ni urutonde rw'inoti kuva 1874 kugeza 1877 aho Dedekind ashushanya ibitekerezo bijyanye no gushushanya hagati y "imbaraga" zitandukanye (icyo twita abakaridinali). Izi nyandiko ziteganya ibikorwa bya Cantor byasohotse kumyumvire imwe mumyaka myinshi. Mu gihe Dedekind yahisemo guhagarika ibitabo - igice kubera ko yari afite imigani itunganijwe kandi ikindi kubera ko yumvaga ibitekerezo bitaragera ku buryo bushimishije - Cantor, wageraga kuri ibyo bitekerezo akoresheje inzandiko zabo, yahise yihutira gutangaza.

Ingengabihe iragayitse muburyo bwihariye. Intiti zashushanyije byibuze ingero ndwi zitandukanye hagati ya 1873 na 1885 aho igitekerezo kibanza kugaragara mu nyandiko bwite ya Dedekind cyangwa amabaruwa yandikiwe Cantor, hanyuma kigaragara mu mpapuro zasohowe na Cantor mu mezi 6 kugeza kuri 18 - nta magambo yatanzwe.

Kwiba cyangwa igihu cy'ubufatanye?

Mbere yo kwihutira kwamagana Cantor, ni ngombwa gusobanukirwa umuco wubwenge wimibare yo mu kinyejana cya 19. Amahame ya citation na attribution yari make cyane kurenza uko bimeze muri iki gihe. Nta miterere isanzwe yerekana, nta sisitemu yo gusuzuma-urungano nkuko tubizi, kandi imipaka iri hagati "yatewe inkunga n'ikiganiro" na "yatijwe igitekerezo" yari itoroshye. Abahanga mu mibare bakunze gusangira ibitekerezo mumabaruwa bumva neza ko uburenganzira bwo gutangaza ari ubw'uwanditse impapuro.

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Abunganira Cantor bavuga ko yahinduye ibikoresho fatizo by'ibyo Dedekind yabonye mu buryo bwa gahunda - ko Dedekind yatanze imbuto, ariko Cantor yubaka ubusitani. Hariho ukuri kuri ibi: Cantor's 1895–1897 Beiträge zur Begründung der transfiniten Mengenlehre igereranya synthesis yibintu birenze kure ibyo Dedekind yari yanditse. Ariko ibimenyetso bishya byerekana ko imbuto zakozwe neza kuruta uko byari bisanzwe bizwi, kandi kuba Cantor yarananiwe kubyemera, byibuze, ni imyitwarire idahwitse ukurikije ibihe byose.

Kuki Dedekind Yacecetse

Kimwe mu bintu bishimishije muriyi nkuru ni igisubizo cya Dedekind - cyangwa, kubura kimwe. Nubwo afite ibimenyetso byinshi byerekana ko ashyira imbere, Dedekind ntabwo yigeze ashinja kumugaragaro Cantor ko yibye. Ibintu byinshi bifasha gusobanura uku kubuza:

• Itandukaniro ry'ubushyuhe: Dedekind yari abitswe, yitonze, kandi yiherereye. Cantor yari umuntu ukomeye, yororoka, kandi yifuzaga cyane kumenyekana mu mibare yakunze kwanga akazi ke.
• Intege nke zumwuga: Cantor yamaze igihe kinini mu mwuga we muri kaminuza ya Halle, ikigo cyo mu cyiciro cya kabiri, maze ahura n’abatavuga rumwe na Leopold Kronecker. Dedekind, washinzwe neza muri Brunswick Polytechnic, ashobora kuba yarumvaga ko amakimbirane yibanze yaba munsi ye.
• Kwishingikiriza: Nubwo ubusumbane mu nguzanyo, abagabo bombi bahaye agaciro umubano. Ibikorwa bya Dedekind 1888 Ese sind und yari sollen apfa Zahlen? yubakiye kubitekerezo bari batezimbere hamwe, kandi amakimbirane rusange yaba yaranduye umurage yombi.
• Filozofiya yo gutangaza: Dedekind yizeraga ko ibitekerezo bigomba gutangazwa gusa iyo bigeze kumurongo wuzuye kandi wuzuye. Yahisemo yeruye kudatangaza ibisubizo byinshi, yabonaga by'agateganyo. Kuri we, igitekerezo kitaratangazwa cyari kitariteguye ku isi.

Iyi ngingo yanyuma birashoboka cyane. Dedekind wenyine gutungana byateje icyuho Cantor yujuje. Ibimenyetso bishya ntibigaragaza cyane umugome kuko bimurika ikibazo cyimiterere: mugihe hatabayeho sisitemu yinyandiko iboneye, abamamaji benshi bafata inguzanyo, batitaye kubari bafite igitekerezo mbere.

Icyo Ibi Bisobanura Kumutungo Wubwenge Uyu munsi

Urubanza rwa Cantor-Dedekind rwumvikana cyane kurenza amateka yimibare. Muri buri gice gikorana - kuva mubushakashatsi bwa siyansi kugeza iterambere rya software kugeza ku ngamba z'ubucuruzi - ikibazo cyo kumenya uwatangije igitekerezo ninde wabishyize mu bikorwa bikomeje kugorana gukemura. Sisitemu yubumenyi igezweho yashubije hamwe ningingo zikaze zijyanye no kuvuga, gufatanya kwandika, hamwe no gufungura ibyapa. Ariko mwisi yubucuruzi, aho amakipe akorana burimunsi mumishinga isangiwe, ikibazo kirakomeza.

. Hatariho inyandiko zifatika, umuntu wanditse raporo yanyuma cyangwa atanga ikiganiro cya nyuma akenshi ahabwa inguzanyo, mugihe uwatangije igitekerezo acika inyuma. Iki nikibazo cya Dedekind muburyo bwibigo.

Amahuriro agezweho nka Mewayz akemura iki kibazo muguhuza ubufatanye bwitsinda, inyandiko zumushinga, hamwe nakazi gakurikirana muri sisitemu imwe. Hamwe na 207 modules ihuriweho na CRM, imicungire yimishinga, itumanaho ryamakipe, hamwe nisesengura, buri musanzu wanditse, igihe cyagenwe, kandi kiranga. Iyo umwe mu bagize itsinda atanze ingamba mu nyandiko y'umushinga, iyo nyandiko irakomeza. Iyo akazi kahinduwe, amateka yo guhindura yerekana uwagize ibyo ahindura nigihe. Ubwoko bw'itandukanyirizo bwibasiye Dedekind mu binyejana birenga ibinyejana biba bidashoboka muburyo bwubaka mugihe ibikorwa remezo byubatswe byubatswe.

Gusuzuma Umurage wa Cantor

Nta na kimwe muri ibyo kigabanya ubwiza nyabwo bwa Georg Cantor. Igitekerezo cye cya diagonal cyo mu 1891, iterambere rye ryimibare itondekanya nimero ya karidinari, hamwe na hypothesis ye ikomeza kuba ibintu byiza bimaze kugerwaho n'umukono we wo guhanga udasanzwe. Ikibazo cyatanzwe nibimenyetso bishya ntabwo ari ukumenya niba Cantor yari umuhanga mu mibare - nta gushidikanya ko yari - ariko niba amateka yaranze akarengane.

Umusanzu wa Dedekind mu rufatiro rwimibare ugenda urushaho kumenyekana nkishingiro muburyo busanzwe. Kubaka imibare nyayo akoresheje gukata bikomeje kuba inzira isanzwe mubitabo byisesengura bigezweho. Igitekerezo cye cya algebraic cyagize ingaruka ku bisekuruza by'imibare kuva Emmy Noether kugeza André Weil. Kandi ubushishozi bwe bushingiye ku bumenyi, ubu bwanditswe neza binyuze mu bimenyetso bifatika, bugaragaza umuntu utekereza utari umunyamakuru wa Cantor gusa ahubwo ko yari umunyabwenge we - kandi rimwe na rimwe, uwamubanjirije.

Isubiramo ntabwo ari ugusenya umurage umwe kugirango wubake undi. Nibijyanye no kugera ku gusobanukirwa neza nuburyo ibitekerezo byimpinduramatwara bitera imbere: atari mugihe cyihariye cyubwenge, ahubwo binyuze mubiganiro birambye, bigira uruhare runini, no kunonosora buhoro buhoro ibitekerezo bisangiwe. Amahano nuko inyandiko zerekana inyandiko zabaye nkeya, kandi amahame yo gutangaza ntagabanuka, kugirango abashe kumenya ukuri gufatanije mugihe nyacyo.

Amasomo yinyandiko-Isi Yambere

Impaka za Cantor-Dedekind zitanga isomo rikomeye rirenze amasomo. Mubihe aho amakimbirane yumutungo wubwenge ashobora kugena iherezo ryamasosiyete nakazi, akamaro kinyandiko zikomeye, igihe-ntigishobora kuvugwa. Ubufatanye bwose butanga ibitekerezo, kandi igitekerezo cyose gifite gihamye. Amashyirahamwe atera imbere azaba ayo gufata ibyo byemezo nkibisanzwe - ntabwo ari ibitekerezo, ahubwo ni ibintu byashizwemo byerekana uko akazi gakorwa.

Kubucuruzi 138.000 bumaze gukoresha Mewayz gucunga ibikorwa byabo, iri hame ryubatswe mubikorwa bya buri munsi. Buri mikoranire yabakiriya yinjiye muri CRM, inyemezabuguzi yatanzwe, buri mushinga wibanze ukurikiranwa ukora inyandiko ihoraho, ishakishwa ninde watanze icyo nigihe. Ni mu buryo bumwe, ibikorwa remezo Dedekind atigeze agira - sisitemu yemeza ko imisanzu itangaje idacika mu ikaye yigenga, itegereje ikinyejana kimenyekana.

Amateka ntashobora na rimwe gutanga umwanzuro utajenjetse niba Cantor yibye Dedekind. Ibimenyetso bishya bigoramye umunzani, ariko ukuri kuzuye kuribitse muburyo bworoshye bwubucuti bwikinyejana cya 19 bwakozwe binyuze mumabaruwa yandikishijwe intoki no kuganira imbona nkubone nta archive ishobora kwiyubaka. Ibyo dushobora kwiga, ariko, ntibisobanutse: andika ibintu byose, inguzanyo cyane, kandi wubake sisitemu zitanga inshingano zikora. Ubutaha Dedekind akwiye ibyiza.

Ibibazo bikunze kubazwa

Ni ibihe bimenyetso byerekana ko Cantor ashobora kuba yaribye Dedekind?

Bourse iherutse gusuzuma inzandiko zabo zandikirwa kuva mu myaka ya za 1870 na 1880, zigaragaza ko ibitekerezo byinshi byashingiweho na Cantor ku nyigisho zashyizweho ndetse n'imiterere y'urudaca ibitekerezo bya Dedekind yari yarabisangiye wenyine. Abahanga mu by'amateka berekana itandukaniro riri hagati y’inyandiko zandikishijwe intoki za Dedekind zidasohotse n’ibitabo bya Cantor byakurikiyeho, hamwe n’ibice biri mu mabaruwa yabo aho Dedekind yagaragaje ibitekerezo by'ingenzi byagaragaye nyuma mu mirimo ya Cantor nta nyito iboneye.

Nigute umubano wa Cantor-Dedekind wagize ingaruka kumibare igezweho?

Ubufatanye bwabo no guhangana kwabo byashizeho urufatiro rwimibare igezweho. Ubwubatsi bwa Dedekind bwubaka bwimibare nyayo binyuze mukugabanya no guteza imbere Cantor gutezimbere ibitekerezo byashizwe hamwe byashyizeho urwego rushingiye kumibare yose yiki gihe. Kungurana ibitekerezo kwabo kutagira iherezo, gukomeza, na kamere yibintu byimibare byakuruye impaka zikomeje gutwara ubushakashatsi muri logique, filozofiya yimibare, nubushakashatsi bwibanze.

Kuki impaka zo kwiba zongeye kugaragara ubu?

Ibikoresho bishya byububiko byabitswe, harimo inzandiko zidashobora kugerwaho hamwe nimbonerahamwe yandikishijwe intoki, byatumye abahanga mu by'amateka bongera kubaka igihe nyacyo cyo guteza imbere ibitekerezo. Ibikoresho byifashishwa mu gusesengura inyandiko hamwe nuburyo bwambukiranya imipaka nabyo byorohereje gukurikirana imigendekere yibitekerezo hagati yimibare yombi. Ubu buvumbuzi bushya bwashimangiye amasomo kandi bituma ibitabo byinshi byasuzumwe n’urungano byongera gusuzuma umwimerere w’intererano ya Cantor.

Ni he nshobora kubona izindi ngingo zimbitse ku mibare n'amateka y'ubwenge?

Ibinyamakuru byigisha, ububiko bwa kaminuza, hamwe namasomero yatunganijwe neza ni intangiriro nziza kubushakashatsi bwimbitse. Kubanyamwuga nabashinzwe gukora ibintu bashaka gutangaza no gucunga neza ibyabo byuburezi neza, Mewayz itanga OS yubucuruzi 207-module itangirwa $ 19 / mo ikubiyemo blog, ibikoresho bya SEO, hamwe nubuyobozi bwabumva - byose bikenewe kugirango hubakwe urubuga rwubumenyi rwemewe.