Khawufane ucinge ukuba infinity ibonakala ngathi ayinakwenzeka. Nangona kunjalo, abathi beMathematics bathi le senzulu inika indoda ithuba lokuba ne-infinity "kuwe." Ke, iMathematicarian Alexei Savvateye inika iMathematics nge-infinity. "Ukuphuhliswa kweMathematics," ubhala kwincwadi yakhe, "Kulapho waba sisifo" kuwe. " Kwaye kokukhona "kuwe" nge-infinity, ngcono uyaqonda imathematics. " Ukuqonda indlela izazinzulu ezicinga ngayo infinitity yemathematics, masiqwalasele ukulandelelana kweNumeri yeNdalo 1, 2, 3, 4, ... nto leyo enokuthi iqhubeke ngokukhululeka. Iinkqubo eziqhubekayo zihlala yimizekelo yokuqala yengcinga enzima njengelize. Okwangoku, kwiMathematics, iinkqubo ezingenamda okanye inqaku lesiphelo lifunyanwa rhoqo, kwaye umbuzo wokungazuzeni ngokwayo uhamba neengcambu zawo kwimathematics ye-Greece.
Imbali ye-infinity
Eyona nto iphambili yokuqalisa malunga nokunganyaniseki lwezibalo mhlawumbi i-fanorilopher yesithandi semibuzo yamaGrike yakwaZenon. Enye yazo (ibhaliwe ngenkulungwane yesihlanu ukuya kwixesha lethu) kwaye ikhathaza i-achilles, ezona zikhawulezayo kuwo onke amaGrike, ekufuneka ziqhubene ne-turtle. Ngokutsho kwe-paradox, i-achilles elinemilenze ekhawulezayo ayisoze ibambe i-turtle yokuzonwabisa ukuba ifudo liphambi kwe-achilles.
I-Aristotle yayikhathazekile yile nto kunye nezinye izinto eziphathelele ukungabi nako ukwenziwa okungapheliyo. Indalo iphela, wacinga ukuba, ingekhe inkulu kakhulu. Ukuba ibinjalo, isiqingatha sakhe siya kuba engenasiphelo. Kodwa yintoni eyenza yonke into engaphezulu kwesiqingatha somsebenzi wakhe? Kuyabonakala ukuba, akukho nto; Zombini zingenasiphelo, ke kufuneka kubekho ubungakanani. Kodwa azinakuba lukhulu, njengoko isiqingatha esinye sahlukile. U-Aristotle ubeka phambili inani lezinye izichaso kwaye uza kwisigqibo sokuba indalo iphela kufuneka isokugqibela. Ukujonga iinkwenkwezi ngaphezulu, Uza kwisigqibo sokuba i-cosmos iqulethe inqanaba elikhulu (kodwa lagqitywa) inqanaba elivela kumbindi.
Nangona kunjalo, ixabisa i-Aristotle ukucebisa indlela umntu obuza ukuba ngubani kwelinye icala lendawo. Nangona kunjalo, le mbono yathanda abantu kangangeminyaka elingaphezu kwewaka leminyaka, engabi kakubi. Kwinkulungwane yesithathu i-BC, i-Afriemeda ibalwa ukuba ingakanani i-sands ezokuzalisa indalo i-Aristotle, kwaye kwiXesha Eliphakathi, i-St. Thomas Aquinsky ixhaswa yicawe.
Yonke into itshintshile xa uNikolai Coornicus wathi umhlaba ayisosiseko sendalo iphela. Emva kwenkulungwane yeshumi elinesixhenxe, iGalileo Gallile yamkelwa njengomcinga oyingozi, njengoko yayibonakalalisiwe kangako kwi-infinity. Umhlaba awunasiphelo, wawuthathela ingqalelo, kwaye umcimbi ungonaphakade. Uninzi emva koko, ngeminyaka yee-1920, umcimbi wezibalo waseJamani uDavide uHillbert weza novavanyo lwengqondo oludumileyo ukubonisa indlela ekunzima ngayo ukufezekisa umxholo we-infinity.
Ngaba ufuna ukuhlala nazi iindaba zamva nje kwihlabathi lenzululwazi elidumileyo kunye netekhnoloji ephezulu? Bhalisa kwitshaneli yethu ye-telegraph ukuze ungaphoswa izibhengezo ezintsha zeendaba!
I-paradox yehotele engapheliyo
Ke, masithi usiyamkela ihotele phantsi kwegama lemfuziselo "infinity". Onke amagumbi ehotele, angenasiphelo ezininzi, agcwele, kodwa ngequbuliso indwendwe entsha liyavela. Akunyanzelekanga ukuba uyiqhubele? Hayi, yonke into oyifunayo kukuhambisa indwendwe ukusuka kwigumbi loku-1 ukuya kwigumbi le-2, kwaye iindwendwe ezivela egumbini 2 zisegumbini lesithathu lisegumbini lesithathu. IVoila-igumbi lokuqala ngoku likhululekile kwindwendwe entsha. Kodwa kuthekani ukuba kuya kubakho iindwendwe eziphindiweyo?
Kuyavela ukuba usenokuba nobubele. Abaqeshi begumbi lokuqala baya kwigumbi elinamagumbi 2, kwaye abalimi beli gumbi lesibini bangena kwigumbi lesithathu kwaye kunjalo ... ukuya kwi-infinity. Kuba amagumbi anegumbi eliphindwe kabini, kwaye ke anamanani, ngoku unokwenza iindwendwe ezininzi ezitsha kwi (ngoku zisimahla) amanani angaqhelekanga. Kwanamanani kufuneka abe ngamanani, kuba kukho inani elingenasiphelo lamagumbi, nokuba zingabalulekanga. Ngenxa yoko, singawabeka onke amanani ngaphandle kwebhalansi kuphela "kuphela, ehlala namanani. Olu vavanyo lwengqondo lwaziwa njenge-paradox yehotele engapheliyo, ebonisa ngokugqibeleleyo iipropathi zeseti ezingenasiphelo.
Ngokutsho kuMdali wemithi yeeseti, iMathematics Georg I-Ingor, kukho amanani amaninzi, kwaye eli nani lingenasiphelo lichaza iintlobo ezininzi zamanani. Umzekelo, kwi-paradox inani lamanani lalingafana nenani leenombolo zenani (kunye neenombolo ezingathandekiyo, kunye neenombolo ezilula, kunye neebhiliyoni ezininzi, njl. Njl.). Namhlanje kubonakala kucacile, kodwa kwakungabonakali ukuba i-Aristotle kunye nabalandeli bakhe, ababeqwalasele inzuzo yomxholo wesayensi ongamkelekanga.
Cwangcisa ithiyori - Icandelo leMathematics leMathematics, elisebenzisa iipropathi ngokubanzi zeseti - iiseti zezinto ezingekho mthethweni, ezinepropathi eqhelekileyo.
I-Cantotor ikwangqina ukuba inani lamaqhezu lilingana neli nani lingenasiphelo kangangokuba wabiza i-Alephro. Eyona nto imangalisayo ayibonakalisileyo (ngoncedo lwempikiswano ebizwa ngokuba yi-diagonal), ekhoyo ngaphezu kwenani elinye elingapheliyo.
Uya kuba nomdla: Yintoni engqina i-theorem ye-pointere malunga nokubuya
Umsebenzi wase-Kantor wadibana nokunganyangeki, kodwa ekugqibeleni waphumelela kwaye ngoku wamkela phantse phantse kuyo yonke indawo. Kukho incinci encinci yezibalo ezibizwa ngokuba zii-Intuioists okanye ii-constrivists ezingakholelwa ukuba singayiqonda kakuhle imbono ye-toinecrite. Kwinkulungwane yamashumi amabini, intanda-bulumko yajoyina, ezazibuza ukuba ingaba iicartorky zibonakala zinokuqondwa zinfinity. Ucinga ntoni ngale nto? Iimpendulo ziya kulinda apha, kunye namagqabaza kweli nqaku.