Nyu pruf se Cantor bin tif Dedekind?

"Di layn bitwin intɛlektual inflɔɛns ɛn intɛlektual tif nɔto di aydyɔ dɛnsɛf de drɔ am, bɔt na di dɔkyumentri trel we de rawnd dɛn. If klia rɛkɔd nɔ de, prɔyoritɛd dispyut kin bi tin fɔ intaprit — ɛn di pɔblisha we gɛt maynd kin win di istri kredit bɔku tɛm."

Di wan dɛn we de difend Kantor de agyu se i transfɔm di raw matirial we Dedekind bin si am to wan sistamɛtik tiori — se Dedekind bin gi sid, bɔt Kantɔ bin bil di gadin. Trut de fɔ dis: Cantor in 1895–1897 Beiträge zur Begründung der transfiniten Mengenlehre ripresent wan monumental sɛntesis we go fa pas ɛnitin we Dedekind bin dɔn rayt. Bɔt di nyu pruf sho se di sid dɛn bin ful-ɔp fɔm pas aw dɛn bin no bifo, ɛn di we aw Kantɔ nɔ bin gri se dɛn nɔ bin gri wit dɛn, na bin, at minimum, wan impɔtant ɛtikul laps bay ɛni ɛra in standad.

Wetin Mek Dedekind Stay Silent

Wan pan di tin dɛn we rili fayn fɔ dis stori na di we aw Dedekind insɛf bin ansa — ɔ fɔ se, i nɔ bin gɛt wan. Pan ɔl we i bin gɛt bɔku pruf fɔ se in yon prɔyoritɛd, Dedekind nɔ ɛva aks Kantɔ na pɔblik fɔ tif. Bɔku tin dɛn kin ɛp fɔ ɛksplen dis rεstrεshɔn:

we dɛn kɔl
• Difrɛns pan tɛmpracha: Dedekind bin rɛzɛv, metikul, ɛn dip prayvet. Cantor bin want fɔ gɛt bɔku prɔpati, i bin de du bɔku tin dɛn, ɛn i bin rili want fɔ mek pipul dɛn no am na wan matematiks establishmɛnt we bin de rijek in wok bɔku tɛm.
• Prɔfɛshɔnal vulnerability: Cantor bin spɛn bɔku pan in wok na di Yunivasiti ɔf Hale, we na sɛkɔn-taya institiushɔn, ɛn i bin gɛt bad bad ɔpɔzishɔn frɔm Liɔpɔld Krɔnɛka. Dedekind, we bin kɔmfyut fɔ establish na di Brunswick Politeknik, kin dɔn fil se wan prɔyoritɛd dispyut go de ɔnda am.
• Mutual dependence: Pan ɔl we di kredit nɔ bin balans, dɛn tu man ya bin valyu di rileshɔnship. Dedekind in 1888 masta wok Was sind und was sollen die Zahlen? bil pan aydia dɛm we dɛn bin dɔn divɛlɔp togɛda, ɛn wan pɔblik dispyut bin fɔ dɔn dɔti ɔl tu di lɛgsi dɛm.
• Pɔblikeshɔn filɔsofi: Dedekind bin biliv se dɛn fɔ jɔs pablish aydia dɛn we dɛn dɔn rich wan stet we rili klia ɛn kɔmplit. I bin disayd klia wan fɔ nɔ pablish bɔku rizɔlt dɛn, we i bin si se na fɔ sɔm tɛm. Insay in yon we, wan aidia we dɛn nɔ bin dɔn pablish nɔ bin rɛdi yet fɔ di wɔl.

Dis las pɔynt na sɔntɛm di wan we de tɔch wi at pas ɔl. Dedekind in yon pafɛkt pɔsin bin mek di vaykum we Kantɔ bin ful-ɔp. Di nyu pruf nɔ de sho se wan wikɛd pɔsin as i de layt wan strɔkchɔral prɔblɛm: if transparent dɔkyumentri sistɛm nɔ de, di mɔ pɔblisha we de prolific de kapchɔ di kredit, ilɛksɛf udat bin gɛt di aidia fɔs.

Wetin Dis Min fɔ Intɛlektual Atribiushɔn Tide

Di Cantor-Dedekind kes de resɔn fa fawe pas di istri bɔt matematiks. Insay ɛvri kɔlabɔraytiv fil — frɔm sayɛns risach to sɔftwɛl divɛlɔpmɛnt to biznɛs strateji — di kwɛshɔn bɔt udat ɔriginate wan aydia ɛn udat jɔs ɛksɛkutiv am stil vexingly at fɔ sɔlv. Di mɔdan akademik sistɛm dɔn ansa wit ikɔnishɔnal rigorous norms arawnd saytayshɔn, kɔ-ɔdaship, ɛn opin-akses prɛprint. Bɔt na di wɔl fɔ biznɛs, usay tim dɛn de wok togɛda ɛvride pan shered prɔjek dɛm, di prɔblɛm de kɔntinyu.

Tink bɔt aw bɔku impɔtant biznɛs disizhɔn dɛn, prɔdak inovashɔn dɛn, ɛn stratejik pivot dɛn de kɔmɔt frɔm infɔmal tɔk-tɔk — wan Slak mɛsej ya, wan waytbɔd sɛshɔn de, wan ɔfhand kɔmɛnt na mitin. If dɛn nɔ gɛt di rayt fɔ du di wok, bɔku tɛm di pɔsin we rayt di las ripɔt ɔ gi di las prɛzɛntɛnshɔn kin gɛt di kredit, ɛn di pɔsin we mek di aidia nɔ de igen. Dis na di Dedekind prɔblɛm insay kɔpɔt fɔm.

Mɔdan pletfɔm dɛn lɛk Mewayz de adrɛs dis chalenj bay we dɛn de sɛntralayz tim kɔlabɔreshɔn, prɔjek dɔkyumentri, ɛn wokflɔ trakin insay wan sistɛm. Wit 207 intagreted modules we span CRM, projɛkt manejmɛnt, tim kɔmyunikeshɔn, ɛn analitiks, ɛvri kɔntribyushɔn na log, taymstamp, ɛn atribyut. We wan tim mɛmba prɔpos wan strateji na wan prɔjek not, da rɛkɔd de kin kɔntinyu. We dɛn chenj wan wokflɔ, di chenj istri de sho udat mek di ajɔstmɛnt ɛn ustɛm. Di kayn atribiushɔn gap we bin de mɔna Dedekind fɔ pas wan sɛntiwɔd, kin bi strɔkchɔral wan we nɔ pɔsibul we dɛn bil di dɔkyumentri infrastukchɔ insay di pletfɔm sɛf.

Rɛasɛs Kantɔ in Lɛgsi

Nɔn pan dis nɔ de stɔp di tru tru brilians we Georg Cantor gɛt. In dayagɔnal argumɛnt fɔ 1891, in divɛlɔpmɛnt fɔ transfinit ɔrdinal ɛn kadinal nɔmba dɛn, ɛn in kɔntinyuɔm haypɔtɛsis stil de ɔp ay ay achivmɛnt dɛn we de bia in difrɛn kriyaytiv sayn. Di kwɛshɔn we di nyu pruf dɔn rayz nɔto if Kantɔ na bin bigman pan matematiks — i nɔ gɛt wan dawt fɔ se i bin bi — bɔt if di istri narativ nɔ bin fayn fɔ lopsayd.

Dedekind in kɔntribyushɔn to di fawndeshɔn dɛm fɔ matematiks de rɛkɔgnayz mɔ ɛn mɔ as fawndeshɔn insay di mɔs litral sɛns. In kɔnstrɔkshɔn fɔ di rial nɔmba dɛn via kɔt stil bi di standad we fɔ du tin na di mɔdan analisis tɛksbuk dɛn. In aljɛbrik nɔmba tiori bin afɛkt bɔku jɛnɛreshɔn dɛn we sabi bɔt matematiks frɔm Ɛmi Nɔta to Andrɛ Wayl. Ɛn in sɛt-tiori insayt dɛm, we naw dɛn dɔn mɔ ful-ful dɔkyumɛnt tru di arkival pruf, de sho wan tinka we nɔ bin jɔs bi Kantɔ in kɔrɛspɔndɛnt bɔt in intɛlektual ikwal — ɛn, insay sɔm kes dɛm, in prɛdisɔs.

Di riasesmɛnt nɔto fɔ pwɛl wan lɛgsi fɔ bil ɔda wan. I de bɔt fɔ gɛt mɔ kɔrɛkt ɔndastandin bɔt aw rivɔlɔshɔnari aydia dɛn kin rili divɛlɔp: nɔto insay isol mɔnt dɛn we gɛt sɛns, bɔt tru sɔstayn dayalɔg, inflɔwɛns pan dɛnsɛf, ɛn di rifinmɛnt smɔl smɔl fɔ di kɔnsɛpt dɛn we dɛn sheb. Di trayji na dat di dokyumɛnti rɛkɔd bin tu spays, ɛn di pɔblikeshɔn norm dɛn tu laks, fɔ kapchɔ dis kɔlabɔraytiv rialiti insay rial tɛm.

Lɛsin fɔ wan Dokumɛnt-Fɔs Wɔl

Di Cantor-Dedekind kɔntroversi de gi pawaful lɛsin we de go fa fawe pas akademi. Insay dis tɛm we intɛlekchual prɔpati dispyut kin disayd wetin go apin to kɔmni ɛn wok, wi nɔ go ebul fɔ tɔk bɔt di impɔtant tin we strɔng, rial-taym dɔkyumɛnt. Ɛvri kolaboreshɔn de mek aydia, ɛn ɛvri aydia gɛt usay i kɔmɔt. Di ɔganayzeshɔn dɛn we go go bifo go bi di wan dɛn we de kapchɔ da provenans de as sɔntin we de apin — nɔto as afta-tɔk, bɔt as ɛmbaded ficha fɔ aw wok de du.

Fɔ di 138,000 biznɛs dɛn we dɔn ɔlrɛdi de yuz Mewayz fɔ manej dɛn opareshɔn, dɛn bil dis prinsipul insay di wokflɔ we dɛn de du ɛvride. Ɛvri klaynt intarakshɔn we dɛn log insay di CRM, ɛvri invɔys we dɛn jenarayz, ɛvri prɔjek maylston we dɛn trak de mek wan pɔrmanent, sɔch rɛkɛd fɔ udat kɔntribyut wetin ɛn ustɛm. Na, insay wan we, di infrastukchɔ we Dedekind nɔ ɛva gɛt — wan sistɛm we de mek shɔ se briliant kɔntribyushɔn dɛn nɔ de vanish insay prayvet notbuk dɛn, we de wet fɔ pas wan ɔndrɛd ia fɔ mek dɛn no am.

Istri nɔ kin ɛva gi difinitiv jɔjmɛnt fɔ no if Kantɔ bin tif Dedekind. Di nyu pruf de tilt di skel, bɔt di ful trut de bɛr insay di subtleties fɔ wan 19th sɛntinari padi biznɛs we dɛn bin kɔndɔkt tru lɛta dɛn we dɛn rayt wit an ɛn tɔk-tɔk fes-to-fes we no arkiv nɔ go ebul fɔ bil bak. Bɔt wetin wi kin lan nɔ gɛt wan dawt: rayt ɔltin, gi kredit to fri-an, ɛn bil sistɛm dɛn we de mek atribiushɔn ɔtomɛtik. Di nɛks Dedekind fɔ gɛt bɛtɛ.

Kwɛshɔn dɛn we dɛn kin aks bɔku tɛm

Us pruf sho se Cantor kin dɔn tif Dedekind?

Skɔlaship we dɛn jɔs dɔn du de ɛgzamin dɛn bɔku bɔku kɔrɛspɔndɛns frɔm di 1870 ɛn 1880 dɛm, we sho se bɔku pan di fawndeshɔn aydia dɛm we Kantɔ gɛt pan sɛt tiori ɛn di kayn we aw infiniti de klos wan de mirɔ kɔnsɛpt dɛm we Dedekind bin dɔn sheb prayvet wan bifo. Di wan dɛn we de rayt bɔt istri de tɔk bɔt di difrɛns we de bitwin di tɛmlayn we Dedekind in manuskrip dɛn we nɔ bin dɔn pablish ɛn di buk dɛn we Cantor bin pul afta dat, wit sɔm pat dɛn na dɛn lɛta dɛn usay Dedekind bin tɔk bɔt di men aidia dɛn we leta bin apia na Cantor in wok we nɔ bin gɛt di rayt atribiushɔn.

Aw di Cantor-Dedekind rilayshɔn bin inflɔws di mɔdan matematiks?

Dɛn kolaboreshɔn ɛn rivalri bin fundamɛntli shep di fawndeshɔn dɛm fɔ di mɔdan matematiks. Dedekind in strɔng kɔnstrɔkshɔn fɔ rial nɔmba dɛn tru kɔt ɛn Cantor in divɛlɔpmɛnt fɔ transfinit sɛt tiori togɛda bin establish di fremwɔk we ɔl di kɔntempɔral matematiks de pan. Dɛn ɛkshɛnj pan di kɔnsɛpt fɔ infiniti, kɔntinyuiti, ɛn di kayn we aw tin dɛn we gɛt fɔ du wit matematiks de, bin mek pipul dɛn bigin fɔ agyu bɔt we de kɔntinyu fɔ drɛb risach pan lɔjik, filɔsofi fɔ matematiks, ɛn fawndeshɔn stɔdi tide.

Wetin mek di plagiarism dibat de kam bak naw?

Nyu dijital arkival matirial dɛm, inklud lɛta dɛm we dɛn nɔ bin de akses bifo ɛn manuskrip draft dɛm, dɔn alaw istri pipul dɛm fɔ rikostrɔk mɔ prɛsis tɛmlayn dɛm fɔ divɛlɔp aydia. Advans tɛkstual analisis tul ɛn krɔs-rɛfrɛns we dɛn de yuz dɔn mek am izi bak fɔ tray fɔ no aw di kɔnsɛpt dɛn de flɔ bitwin di tu matematiks dɛn. Dɛn fresh tin ya we dɛn dɔn fɛn dɔn mek pipul dɛn gɛt intres bak pan di akademik ɛn dɛn dɔn mek sɔm buk dɛn we dɛn kɔmpin dɛn dɔn rivyu fɔ ri-evalyu di ɔrijinal we di kɔntribyushɔn dɛn we Kantɔ bin gi.

Usay a go fɛn mɔ dip atikul dɛn bɔt matematiks ɛn intɛlekchual istri?

Akademik jɔnal dɛm, yunivasiti arkiv dɛm, ɛn dijital laybri dɛm we dɛn dɔn kɔrɛkt na fayn fayn statin pɔynt dɛm fɔ dip-dayv risach. Fɔ pɔblisha ɛn kɔntinyu krieta dɛn we de luk fɔ pablish ɛn manej dɛn yon ɛdyukeshɔn kɔntinyu fayn fayn wan, Mewayz de gi 207-mɔdyul biznɛs OS we de stat na $19/mo we inklud blɔk, SEO tul, ɛn ɔdiɛns manejmɛnt — ɔltin we dɛn nid fɔ bil wan ɔtoriti no pletfɔm.