Qhov Tseem Ceeb Qhov txawv - Postulate vs Theorem
Postulates thiab theorems yog ob nqe lus uas feem ntau siv hauv lej. Ib qho postulate yog ib nqe lus uas xav tias muaj tseeb, tsis muaj pov thawj. Lub theorem yog ib nqe lus uas tuaj yeem ua pov thawj tseeb. Qhov no yog qhov sib txawv tseem ceeb ntawm postulate thiab theorem. Theorems feem ntau ua raws li cov lus qhia.
Postulate yog dab tsi?
Ib lus tshaj tawm yog ib nqe lus uas xav tias muaj tseeb yam tsis muaj pov thawj. Postulate yog txhais los ntawm Oxford phau ntawv txhais lus raws li "qhov uas tau hais los yog xav tias muaj tseeb raws li lub hauv paus rau kev xav, kev sib tham, lossis kev ntseeg" thiab los ntawm American Heritage phau ntawv txhais lus yog "ib yam dab tsi xav tias tsis muaj pov thawj tias nws tus kheej yog qhov tseeb lossis feem ntau lees txais, tshwj xeeb tshaj yog thaum siv. raws li lub hauv paus rau kev sib cav."
Postulates tseem hu ua axioms. Postulates tsis tas yuav muaj pov thawj vim tias lawv pom tseeb. Piv txwv li, cov lus hais tias ob lub ntsiab lus ua ib kab yog ib qho postulate. Postulates yog lub hauv paus los ntawm cov theorems thiab lemmas tsim. Lub theorem tuaj yeem muab tau los ntawm ib lossis ntau qhov postulates.
Muab hauv qab no yog qee yam yam ntxwv tseem ceeb uas txhua tus postulates muaj:
- Postulates yuav tsum yooj yim to taub - lawv yuav tsum tsis txhob muaj ntau lo lus uas nyuaj to taub.
- Lawv yuav tsum ua kom zoo ib yam thaum ua ke nrog lwm cov postulates.
- Lawv yuav tsum muaj peev xwm siv nws tus kheej.
Txawm li cas los xij, qee qhov postulates - xws li Einstein tus postulate tias lub ntiaj teb yog homogenous - tsis yog ib txwm muaj tseeb. Ib qho postulate yuav dhau los ua qhov tsis raug tom qab qhov kev tshawb pom tshiab.
Yog tias qhov sib npaug ntawm cov ces kaum sab hauv α thiab β tsawg dua 180 °, ob txoj kab ncaj nraim, tsim los tsis tu ncua, ntsib ntawm sab ntawd.
Dab tsi yog Theorem?
Ib txoj kev xav yog ib nqe lus uas tuaj yeem ua pov thawj tias muaj tseeb. Oxford phau ntawv txhais lus txhais lub theorem yog "cov lus qhia dav dav tsis yog nws tus kheej tab sis ua pov thawj los ntawm cov saw hlau ntawm kev xav; ib qho tseeb tsim los ntawm kev lees paub qhov tseeb" thiab Merriam-Webster txhais nws tias "ib qho qauv, qhov lus pom zoo, lossis nqe lus hauv lej lossis logic deduced los yog txiav tawm los ntawm lwm cov qauv lossis cov lus qhia".
Theorems tuaj yeem ua pov thawj los ntawm lub laj thawj laj thawj lossis los ntawm kev siv lwm cov theorems uas twb tau ua pov thawj tseeb. Ib qho theorem uas yuav tsum tau ua pov thawj txhawm rau ua pov thawj lwm qhov theorem yog hu ua lemma. Ob leeg lemmas thiab theorems yog nyob ntawm postulates. Ib qho theorem feem ntau muaj ob ntu hu ua hypothesis thiab xaus. Pythagorean theorem, plaub xim theorem, thiab Fermat's Last Theorem yog qee qhov piv txwv ntawm theorems.
Visualization ntawm Pythagorean theorem
Qhov txawv ntawm Postulate thiab Theorem yog dab tsi?
Definition:
Postulate: Postulate txhais tau tias "ib nqe lus lees paub tseeb raws li lub hauv paus rau kev sib cav lossis kev xav."
Theorem: Theorem txhais tau tias cov lus qhia dav dav tsis yog qhov tseeb tab sis ua pov thawj los ntawm cov saw hlau ntawm kev xav; qhov tseeb tsim los ntawm kev lees paub qhov tseeb”.
Pov thawj:
Postulate: Ib nqe lus yog ib nqe lus uas xav tias muaj tseeb yam tsis muaj pov thawj.
Theorem: Ib txoj kev xav yog ib nqe lus uas tuaj yeem ua pov thawj tias muaj tseeb.
Relation:
Postulate: Postulates yog lub hauv paus rau theorems thiab lemmas.
Theorem: Theorems yog raws li cov lus qhia.
Yuav tsum ua pov thawj:
Postulate: Postulates tsis tas yuav tsum tau ua pov thawj vim lawv hais qhov tseeb.
Theorem: Theorems tuaj yeem ua pov thawj los ntawm kev xav txog kev xav lossis siv lwm cov theorems uas tau ua pov thawj tseeb.
