Imfundo:, Sayensi
Iyiphi inombolo yendalo? Imbali, ububanzi, iipropati
IMathematika yahluke kwifilosofi jikelele malunga nekhulu lesithandathu BC. Kwaye kwaqala ngaloo mzuzu ulandelelwano lwayo olunqabileyo kwihlabathi. Icandelo ngalinye lophuhliso liqalise into entsha - i-akhawunti yeprayimari yashintsha, yaguqulwa yaba yintlukwano kunye nokubala, i-calculus, ithatha indawo emininzi, iifomula zaba nzima kakhulu, kwaye kwafika ixesha lokuba "iimathematika eziyinkimbinkimbi zaqala - zonke iinombolo zaphela." Kodwa yayiyintoni isiseko?
Qala ekuqaleni
Inombolo yemvelo ibonakala kwimeko yokuqala yokusebenza kwemathematika. Emva komgudu, ezimbini iingcambu, iingcambu ezintathu ... Ziyabonga ngenxa yezinzululwazi zaseNdiya ezithathele inkqubo yokuqala yenombolo yesithuba.
Ngamaxesha amandulo, amanani anikezwa intsingiselo eyimfihlelo, inkulu yemathematika uPythagoras ikholelwa ukuba inani eliphantsi kokudala umhlaba kunye nezinto eziphambili - umlilo, amanzi, umhlaba, umoya. Ukuba sicinga yonke into ukusuka kwicala leemathematika, ngoko yintoni inamba yemvelo? Intsimi yamanani engokwemvelo ichazwe ngu-N kwaye imela uluhlu olungapheliyo lweenombolo ezipheleleyo kunye ezilungileyo: 1, 2, 3, ... + ∞. I-Zero ingabandakanywa. Isetyenziselwa ngokuyinhloko ukubala izinto nokuyalela.
Yintoni inamba yemvelo kwimathematika? Axioms Peano
Intsimi N yintsimi yesiseko apho imathematika yeprayimari isekelwe khona. Ngethuba lexesha, iindawo zeenombolo ezipheleleyo, ezinengqiqo, ezinobunzima bezihlukeneyo .
Imisebenzi ye-mathematikhi yase-Italy uGiuseppe Peano yenza ukuba kubekho ukulungiswa kwesithethi, kufezekiswe izimo zayo kwaye kulungiselelwe umgangatho wokufumana izigqibo ezithe zagqitha ngaphaya kwintsimi yentsimi N.
- Iyunithi ithathwa njengenombolo yendalo.
- Inombolo elandela inombolo yendalo yendalo.
- Ngaphambi kokubambisana akukho namba yemvelo.
- Ukuba inombolo b ilandela inomboro c nombolo d, ke c = d.
- I-axia of theduction, ebonisa ukuba inombolo enjalo yemvelo: ukuba kukho ingxelo ethile exhomekeke kwiparameter yinyaniso kwinani 1, ngoko sicinga ukuba isebenza kwinombolo n ukusuka kwintsimi yamanani N. = 1 ukusuka kwintsimi yamanani engokwemvelo N.
Imisebenzi eyisiseko kwintsimi yemvelo
Ekubeni i-N yayingowokuqala yokubala kweemathematika, yinto yokuba zombini idibansi yenkcazo kunye nohla lwexabiso leenombolo zenkqubo zithunyelwa ngezantsi. Zivaliwe kwaye akukho. Uhlobo oluphambili kukuba imisebenzi evaliweyo iqinisekisiwe ukushiya isiqhamo kwisithuba se-N, kungakhathaliseki ukuba yeyiphi inamba echaphazelekayo. Kwanele ukuba zendalo. Isiphumo sendlela yokusebenzisana yamanani esele asisayixhamla kwaye ixhomekeke ngokuthe ngqo kumanani amanani abandakanyekayo kwintetho, kuba ingangqubana nencazelo engundoqo. Ngoko, imisebenzi evuliwe:
- Ukongeza - x + y = z, apho x, y, z zifakwe kwintsimi N;
- Ukuphindaphinda - x * y = z, apho x, y, z zifakwe kwintsimi N;
- Exponentiation - x y , apho x, y ifakiwe kwintsimi N.
Eminye imisebenzi, isiphumo esingenakho kwimeko yencazelo "yintoni inamba yendalo", ilandelayo:
- Ukukhupha - x - y = z. Intsimi yamanani emvelo iyavuma kuphela kwimeko apho x mkhulu kuno-y;
- ICandelo - x / y = z. Intsimi yamanani emvelo iyavuma kuphela kwimeko xa ihlukaniswa ngu y ngaphandle kwayo, oko kukuthi, ngokupheleleyo.
Iipropati zamanani ezisensimini N
Zonke iziphakamiso zeemathematika ezongezelelweyo ziya kusekelwe kwiipropati ezilandelayo, ezincinci kakhulu, kodwa ezi zinto zingabalulekanga.
- Ipropati yokuhambisa indawo yongezwa ngu x + y = y + x, apho iinombolo x, y zifakiwe kwintsimi N. Okanye bonke abaziwa "isishintshi ayitshintshi ekutshintsheni kweendawo zentsimi".
- Ipropati yokuthutha ngokuphindaphinda x x y y y y y x, apho iinombolo x, y zifakiwe kwintsimi N.
- Ukuhlanganiswa kwepropati yokongeza (x + y) + z = x + (y + z), apho x, y, z zifakwe kwintsimi N.
- Ukuhlanganiswa kwepropati yokuphindaphinda (x * y) * z = x * (y * z), apho iinombolo x, y, z zifakwe kwintsimi N.
- Ipropati yokuhambisa ngu x (y + z) = x * y + x * z, apho iinombolo x, y, z zifakiwe kwintsimi N.
Itheyibhile yePythagoras
Olunye lwamanyathelo okuqala ngolwazi lwabafundi malunga nesakhiwo sonke seemathematika zaseprayimari emva kokuba baziqonde ngokwabo ukuba amanani amabizwa yindalo yiPythagoras itafile. Ingabonwa nje kuphela kwindlela yokujonga isayensi, kodwa kwakhona njengesikhumbuzo esisigxina sezesayensi.
Itheyibhile yokuphindaphinda yaba neenguqu ezininzi kwixesha: ukusuka kuyo, isuswe isuswe, kwaye iinombolo ukusuka ku-1 ukuya ku-10 zichaza ngokwazo, ngaphandle kokuqwalasela i-oda (amakhulu, amawaka ...). Yitheyibhile apho iintloko zemiqolo kunye neikholomu zinamanani, kwaye iziqulatho zeeseli zendlela yazo zilingana nemveliso yazo.
Kwimiqathango yokufundisa kwiminyaka edlulileyo, kwakudingeka ukuba ikhumbule itafile yePythagorean "ngokulandelelana", okokuqala, okokuqala kwakukho ukukhumbula. Ukuphindaphindwa ngo-1 kwagqitywa, kuba isiphumo sasi-1 okanye ngaphezulu. Okwangoku, etafileni ngamehlo abukhali ungabona ukuhamba rhoqo: imveliso yamanani ikhula ngesinyathelo esinye, esilingana nesihloko somgca. Ngaloo ndlela, into yesibini ibonisa ukuba mangaphi amaxesha ukuthatha okokuqala, ukuze ufumane umkhiqizo oyifunayo. Le nkqubo ayilungelekanga kunokuba yenziwa kwi-Middle Ages: kwanokuqonda ukuba yintoni inombolo yendalo kunye nokuba yinto encinci kangakanani, abantu bakwazi ukunyanzelisa i-akhawunti yabo yemihla ngemihla kusetyenziswa amandla asetyenziswayo.
I-subset efana nokuzalwa kweemathematika
Okwangoku, intsimi yeenombolo zemvelo N ibonwa nje ngokuba enye yee-subset zeenombolo eziyinkimbinkimbi, kodwa oku kungenzi nto ibaluleke kakhulu kwisayensi. Inombolo yemvelo yinto yokuqala umntwana efunda ngokuzifunda ngokwakhe kunye nehlabathi elikujikelezayo. Umnwe omnye, iminwe emibini ... Ngombulelo kuye, umntu uhlakulela ukucinga, kunye nokukwazi ukuqonda isizathu kunye nokuvelisa umphumo, ukulungiselela umhlaba ukufumanisa izinto ezinkulu.
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