Cabanga nje ukuthi infinity kubonakala kungenzeki. Kodwa-ke, ama-mathematiciatiants athi le sayensi inika umuntu ithuba lokuba yi-infinity "kuwe." Ngakho-ke, isazi sezibalo u-Alexei Savvateyev ubiza izibalo ngokusebenzisa infinity. "Ukuthuthukiswa kwezibalo," kubhala encwadini yakhe, "Yilokhu lapho uba infinity of" kuwe. " Futhi lapho wena "kuwe" nge-infinity, okungcono uqonda izibalo. " Ukuze uqonde ukuthi ososayensi bacabanga kanjani ngendlela indlela acabanga ngayo ukulandelana kwezibalo, ake sicabangele ukulandelana kwezinombolo zemvelo 1, 2, 3, 4, ... Yikuphi okungenzeka kungaqhubeka ngokungapheli. Izinqubo eziqhubekayo ezinjalo zivame ukuba yizibonelo zokuqala zomqondo onjalo oyinkimbinkimbi njenge-infinity. Okwamanje, kwiMathematics, izinqubo ezingenamkhawulo noma indawo yokugcina zitholakala kaningi, futhi umbuzo we-infinity uqobo uhambisana nezimpande zawo kuma-matheematics weGrisi yasendulo.
Umlando we-infinity
Ukuzindla okuqala kokucabanga kwe-mathematical infinity cishe kungenzeka kuyizeluleko zefilosofi yamaGrikhi kaZenon. Enye yazo (ebhalwe ngekhulu lesihlanu kule ndalo yethu) futhi iphathelene nama-Achilles, ngokushesha okukhulu kwawo wonke amaGrikhi, okufanele asebenze emcimbini. Ngokusho kwe-achilles esheshayo, ama-achilles anemilenze egqoke angeke athole ufudu lokuzijabulisa uma ufudu luphambi kwe-achilles.
U-Aristotle naye wakhathalela ngalezi ezinye izimfumbe mayelana nokuhlukahluka okungapheli. Umkhathi, wacabanga, akakwazanga ukuba mkhulu ngokungapheli. Ukube bekunjalo, khona-ke ingxenye yakhe yayiyoba nakapheli. Kepha yini eyenza konke infinity ngaphezu kwengxenye yesigamu sakhe? Ngokusobala, akukho lutho; Zombili zingenamkhawulo, ngakho-ke kufanele kube nosayizi owodwa. Kepha abakwazi ukuba ngosayizi ofanayo, njengoba ingxenye eyodwa ihlukile ngokwengeziwe. U-Aristotle ubeka ezinye izinto eziningi eziphikisanayo futhi eza esiphethweni sokuthi indawo yonke kufanele ibe yokugcina. Ubheka izinkanyezi phezu kwakhe, ufika esiphethweni sokuthi ama-cosmos aqukethe indawo enkulu (kodwa enomqondo) emhlabathini enkabeni.
Kodwa-ke, kubiza u-Aristotle ukuphakamisa ukuthi othile ubuze kanjani ngakolunye uhlangothi lwe-sphere. Noma kunjalo, lo mbono wakuthanda abantu iminyaka engaphezu kwenkulungwane, ngokuvamile akukubi. Ekhulwini lesithathu BC, u-Archimeda wabalwa ukuthi mangaki ama-sands azodinga ukugcwalisa indawo yonke ye-aristotle, futhi ngeNkathi Ephakathi, uSt.
Konke sekuguqukile lapho uNikolai Copernicus ethi izwe akusona isikhungo sendawo yonke. Kamuva ngekhulu leshumi nesikhombisa, uGalileo Galalee waqashelwa njengomcabangi oyingozi, njengoba kwaboniswa obala nge-infinity. Umhlaba awunamkhawulo, wakubheka, futhi kubalulekile ukuthi kungukuphakade. Eziningi kamuva, ngawo-1920s, isazi sezibalo saseJalimane uDavid Hilbert saqhamuka nokuhlolwa kwengqondo okudumile ukukhombisa ukuthi kunzima kangakanani ukubona umqondo we-infinity.
Ufuna ukuhlala wazi izindaba zakamuva ezivela emhlabeni wesayensi edumile nobuchwepheshe obuphakeme? Bhalisela isiteshi sethu se-telegraph ukuze ungaphuthelwa izimemezelo zezindaba ezintsha!
Indikimba yehhotela elingapheli
Ngakho-ke, ake sithi ungumnikazi wehhotela ehhotela ngaphansi kwegama elingokomfanekiso "infinity". Onke amakamelo ehhotela, angenamkhawulo abaningi, agcwele, kepha kungazelelwe kuvela isivakashi esisha. Akudingeki ukuthi uyihambise? Cha, konke okudingayo ukuhambisa isivakashi kusuka egumbini 1 kuya egumbini 2, futhi isivakashi esivela egumbini 2 sisegumbini 3 njalonjalo. I-Voila - Igumbi lokuqala manje selikhululekile isivakashi esisha. Kepha kuthiwani uma kuzoba nezivakashi ezintsha ezingapheli?
Kuyavela ukuthi usengaba nomusa. Abaqashi abavela egumbini lokuqala bangena egumbini lezinombolo 2, futhi abaqashi basendlini yesibili bangena egumbini labathathu naku-infinity. Njengoba amakamelo esenamakamelo aphindwe kabili, futhi ngenxa yalokho waba nezinombolo, manje usungabeka izivakashi eziningi ezintsha (manje ezikhululekile) izinombolo ezingathandeki. Ngisho nezinombolo kufanele zibe njengezinombolo eziningi, ngoba kunenombolo engapheli yamakamelo, kungakhathalekile ukuthi ngabe bayinqaba noma eyinqaba. Ngenxa yalokhu, singabeka zonke izinombolo ngaphandle kwebhalansi kuphela kuma- "Rooms", ahlalwa izinombolo. Lokhu kuhlolwa kwengqondo kwaziwa njenge-paradox yehhotela elingapheli, elibonisa ngokuphelele izakhiwo zamasethi angenamkhawulo.
Ngokusho koMdali we-Theory of Set, Mathematics Georg Kantor, kunezinombolo eziningi, futhi leli nani elingenamkhawulo lezinombolo lichaza izinhlobo eziningi zezinombolo. Isibonelo, nge-paradox inani lezinombolo lalifana nenombolo yezinombolo (nezinombolo ezingathandeki, nezinombolo ezilula, kanye nezigidigidi eziningi, njll.). Namuhla kubonakala kusobala, kepha bekungabonakali ku-aristotle nabalandeli bakhe, ababecabanga ukuthi kungabonakali komqondo wesayensi ongamukeleki.
Setha i-Theory - Ingxenye Yezibalo, ezifundela izakhiwo ezijwayelekile zamasethi - amasethi wezakhi zemvelo yokuphikisana, enayo impahla evamile.
UCantor waphinde wafakazela ukuthi inani lama-fress lilingana naleli nani elingapheli alibiza ngalo u-Aleph zero. Into ephawuleka kakhulu akufakazele (ngosizo lwengxabano okuthiwa yi-diagonal), ekhona ngaphezu kwenombolo engaphezu kweyodwa engapheli.
Uzoba nentshisekelo: Yini efakazela i-theorem ye-poincare mayelana nokubuya
Umsebenzi kaKantor wahlangana nokumelana okukhulu, kepha ekugcineni wanqoba futhi manje wamukele cishe yonke indawo. Kukhona okuncane okuncane kwezibalo ezibizwa ngokuthi ama-intuioli noma abakwaCorkerculivists abangakholelwa ukuthi singawuqonda ngempela umqondo we-toility ye-infinite. Ekhulwini lamashumi amabili, amafelosofi ajoyinwa, ezazibule ukuthi ukubukeka kwe-cantorsky kungaqondwa ku-infinity. Ucabangani ngalokhu? Izimpendulo zizolinda lapha, kanye nasekuphawulani kwale ndatshana.