Umehluko phakathi kwe-theorem ne-axiom

Isibuyekezo sokugcina: 22/05/2023

Isingeniso

Ezweni Kwizibalo, amagama amabili avame ukudideka yilawa ithiyemu y i-axioma. Nakuba zombili zibalulekile ekwakhiweni kolwazi lwezibalo, zinomehluko omkhulu ngokwencazelo nokusetshenziswa kwazo. Kulesi sihloko sizoxoxa ngalo mehluko futhi sibone ukuthi usebenza kanjani ezimweni ezihlukahlukene zezibalo.

Incazelo yethiyori

Ithiyori isiphakamiso sezibalo esifakazelwe ukuthi siyiqiniso. Ngamanye amazwi, ithiyori isitatimende esifakazelwe nge-logic kanye nezibalo. Amathiyori asebenzisa ama-axiom njengesisekelo sawo, kodwa ahlanganisa lezi zakhiwo nezinye izimpikiswano nokucabanga ukuze akhiqize isiphetho esisha nesibalulekile.

Isibonelo se-Theorem:

Enye yetiyoremu eyaziwa kakhulu kwizibalo i-theorem ye-Pythagorean, ethi kunxantathu ongakwesokudla, isikwele se-hypotenuse silingana nesamba sezikwele zabanye onxantathu. izinhlangothi ezimbili. Le theorem yafakazelwa okokuqala nguPythagoras ngekhulu lesi-5 BC futhi kusukela ngaleso sikhathi uye wasetshenziswa emagatsheni amaningi ezibalo ne-physics. ukuxazulula izinkinga okuyinkimbinkimbi.

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Incazelo ye-axiom

I-axiom isiphakamiso sezibalo esamukelwa njengeqiniso ngaphandle kokudinga ukuqinisekiswa. Kuyiqiniso eliyisisekelo lokho kuyasetshenziswa ukwakha ezinye izimiso zezibalo kanye namathiyori. Ama-axiom ayisisekelo sezibalo futhi noma yibuphi ubufakazi kufanele busekelwe kuwo.

Isibonelo se-Axiom:

Esinye sezibonelo ezivame kakhulu ze-axiom yi-axiom yokuzikhethela. Le axiom ithi, uma kubhekwa iqoqo lamasethi angenalutho, kukhona indlela yokukhetha i-elementi kusethi ngayinye eqoqweni. Le-axiom isetshenziswa emikhakheni eminingi yezibalo futhi inemithelela ebalulekile kuthiyori emisiwe kanye ne-topology.

Umehluko phakathi kwe-theorem ne-axiom

Umehluko omkhulu phakathi kwe-theorem kanye ne-axiom ukuthi i-theorem ifakazelwa ukuthi iyiqiniso, kuyilapho i-axiom yamukelwa njengeyiqiniso ngaphandle kobufakazi. Ama-axioms ayisisekelo sanoma yiluphi uhlelo lwezibalo, kuyilapho ama-theorems kuyizakhiwo ezithathwe kuzo.

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Omunye umehluko obalulekile ukuthi ama-theorems ayiziphakamiso ezintsha ezithathwe kwezinye izimiso, kanti ama-axiom angamaqiniso ayisisekelo avumela ukuthi konke okunye kwakhiwe. Ngakho-ke, ama-theorems ngokuvamile ayinkimbinkimbi futhi athuthukile kunama-axiom, ngoba asekelwe kwezinye izindlela zokucabanga kanye nezibalo.

Isiphetho

Kafushane, i-theorem ne-axiom ngamagama abalulekile kwizibalo. Ama-axiom angamaqiniso ayisisekelo amukelwayo ngaphandle kwesidingo sokuboniswa, kuyilapho amathiyori ayiziphakamiso ezithathwe kuwo ngokunengqondo nokucabanga. Ukuqonda umehluko phakathi kwala magama kubalulekile kunoma ubani ofuna ukwakha ulwazi lwakhe lwezibalo futhi alusebenzise ekuxazululeni izinkinga nokucwaninga kule ndawo.

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