Ubungqina abufunwayo: umzekelo we-axiom

Yintoni efihlakeleyo emva kwegama elingaqondakaliyo elithi "axiom", livela phi na kwaye lithetha ntoni? Umfundi wesikolo esikolweni wesi-7 uya kuphendula ngokukhawuleza lo mbuzo, ukususela nje ngoku, xa eqonda i-planimetry course, sele sele ejongene nomsebenzi: "Ziziphi iingxelo ezibizwa ngokuba yi-axioms, zinika imizekelo." Umbuzo ofanayo kumntu omdala, mhlawumbi, uya kukhokelela ekuhlazweni. Ixesha elidlulayo liphuma kumzuzu wokufunda, kunzima ngakumbi ukukhumbula iziseko zesayensi. Nangona kunjalo, igama elithi "axiom" lisetyenziswe rhoqo kwimpilo yemihla ngemihla.

Inkcazo yekota

Ngoko zithini iinkcazo ezibizwa ngokuba yi-axioms? Imizekelo ye-axioms ihluke kakhulu kwaye ayigcini nakweyiphi indawo yenzululwazi. Eli gama lavela kwiilwimi zakudala zesiGrike kwaye ngokuguqulela kwangempela kuthetha ukuba "indawo eyamkelekileyo".

Inkcazo engqongqo yeli gama ithi i-axiom yintsikelelo eyisiseko kwanoma yimuphi umxholo ongenakufunwa ubungqina. Le ngcamango isasazeka ngokubanzi kwimathematika (kwaye ngokukodwa kwiJometri), ingqiqo, ifilosofi.

Nangona u-Aristotle wamaGrike wasendulo wathi ubungqina obonakalayo abufunayo. Umzekelo, akukho mntu unokungabaza ukuba ukukhanya kwelanga kubonakala kuphela emini. Omnye wezibalo, u-Euclid, wavelisa le ngcamango. Umzekelo we-axiom malunga neendlela eziqhelekileyo ezingaqhelekanga zizo.

Emva kwexesha, inkcazo yegama itshintshile. Ngoku i-axiom ayibonakali nje kuphela njengesiqalo senzululwazi, kodwa kwakhona njengokuba kukho umphumo ophakathi, osebenza njengendawo yokuqala yombono oqhubekayo.

Iimvume ezivela kwiklasi yesikolo

Abafundi besikolo baqhelana nezikhundla ezingafuneki ukuqinisekiswa kwizifundo zemathematika. Ngoko ke, xa abagqibeleleyo bezikolo zamabanga aphezulu banikwe umsebenzi: "Nika imizekelo ye-axioms", bahlala bekhumbula izifundo zejometri ne-algebra. Nazi imimiselo yeempendulo ezifumaneka rhoqo:

• Ngomgca kukho iingongoma ezibhekise kuyo (oko kukuthi, ulala kumgca) kwaye awuyiyo (ungalala emgceni);
• Umgca ochanekileyo unokutsalwa kuwo nawaphi na amanqaku amabini;
• Ukwahlula indiza zibe ziiplani ezimbini, enye kufuneka ibonise umgca ochanekileyo.

I-algebra kunye ne-arithmetic ayifaki ukuvelisa ezo nkcazo, kodwa umzekelo we-axiom ingafumaneka nakwiziko lezenzululwazi:

• Naliphi na inani lilingana nalo;
• Icandelo lilandele zonke iinombolo zemvelo;
• Ukuba k = 1, kwakhona l = k.

Ngaloo ndlela, iingcamango ezilukhuni ngakumbi zenziwa ngeengxaki ezilula, i-corollaries zenziwe, kwaye iiforms zivela.

Ukwakhiwa kweengcali zenzululwazi ezisekelwe kwi-axioms

Ukwakha inzululwazi yenzululwazi (ayinandaba nokuba yintoni inzululwazi esithetha ngayo), sifuna isiseko - izitena eziza kubumba. Inqobo yendlela yokwenza i-axiomatic: isichazizwi semigqaliselo yenziwe, umzekelo we-axiom yenziwe, ngesiseko apho ezinye izikhundla zithathwa.

I-glossary yesayensi kufuneka ibe neengqungquthela zephondo, oko kukuthi, ezo ezingenakuzimisela ngabanye:

• Ukuchaza ngokucacileyo ikota nganye, ukuchaza intsingiselo yayo, ukufikelela kwisiseko senzululwazi.
• Isinyathelo esilandelayo kukufumanisa isethi esisiseko seengxelo, okumele kube ngokwaneleyo ukubonisa ubungqina beengxelo ezikhoyo. Izithuba ezisisiseko ngokwazo zamukelwa ngaphandle kokulungiswa.
• Isinyathelo sokugqibela sisakhiwo kunye nesiphetho esinengqiqo semibandela.

Izikhundla ezivela kwiisayensi ezahlukeneyo

Iintetho ngaphandle kobu bungqina abukho kuphela kwizenzululwazi ezichanekileyo, kodwa nakwazo ziqhelekileyo zibhekiswa njengabantu abancedisayo. Umzekelo ocacileyo yifilosofi echaza i-axiom njengento yokuqinisekisa, into enokukwaziwa ngaphandle kolwazi olusebenzayo.

Umzekelo we-axiom uphantsi kwenzululwazi yezomthetho: "umntu akanako ukugweba umsebenzi wakhe". Ukuqhubela phambili kwesi siqinisekiso, imigangatho yomthetho wezomthetho iyanqunyulwa - ukungakhethi kwamanyathelo omthetho, okokuba, ijaji ayikwazi ukuqwalasela ityala ukuba unomdla ngqo okanye ngokungathandabuzekiyo kuyo.

Akusiyo yonke into ethathwa ngokungenakunikwa

Ukuqonda umahluko phakathi kwama-axioms enyaniso kunye namazwi alula achazwa inyaniso, umntu kufuneka ahlaziye isimo sengqondo kubo. Ngokomzekelo, ukuba sithetha ngenkolo, apho yonke into ithathwa ngokungenanto, kukho umgaqo wokuqiniseka ngokupheleleyo ukuba into yinyaniso, kuba akunakwenzeka ukubonisa. Kwaye kwiindawo zenzululwazi zithi akunakwenzeka ukujonga indawo ethile, ngokufanelekileyo, kuya kuba yinto ecacileyo. Ukulungela ukungathandabuzeki, ukuhlaziya - yilokho ekwahlula usosayensi oyinyaniso.