Axioms vs Postulates
Raws li kev xav, ib qho axiom lossis postulate yog ib nqe lus uas suav tias yog qhov tseeb ntawm tus kheej. Ob qho tib si axioms thiab postulates yog suav tias yog qhov tseeb yam tsis muaj pov thawj lossis ua qauv qhia. Yeej, ib yam dab tsi uas pom tseeb lossis tshaj tawm tias muaj tseeb thiab lees txais tab sis tsis muaj pov thawj rau qhov ntawd, hu ua axiom lossis postulate. Axioms thiab postulate ua lub hauv paus rau kev txiav tawm lwm qhov tseeb.
Cov neeg Greek thaum ub tau lees paub qhov sib txawv ntawm ob lub ntsiab lus no. Axioms yog qhov kev xav ntawm tus kheej, uas muaj rau txhua ceg ntawm kev tshawb fawb, thaum postulates muaj feem xyuam nrog kev tshawb fawb tshwj xeeb.
Axioms
Aristotle los ntawm nws tus kheej siv lo lus "axiom", uas los ntawm Greek "axioma", uas txhais tau hais tias "kom muaj nqis", tab sis kuj "yuav tsum tau". Aristotle muaj lwm lub npe rau axioms. Nws siv los hu lawv ua "cov khoom sib xws" lossis "kev xav zoo ib yam". Hauv Kev Ua lej, Axioms tuaj yeem muab faib ua "Logical axioms" thiab "Non-logical axioms". Logical axioms yog propositions los yog nqe lus, uas yog xam raws li universally tseeb. Tsis yog-logical axioms qee zaum hu ua postulates, txhais cov khoom rau lub npe ntawm kev ua lej tshwj xeeb, lossis cov lus qhia kev xav, uas yog siv los txiav tawm los tsim kev ua lej. "Tej yam uas sib npaug rau ib yam, sib npaug rau ib leeg" yog ib qho piv txwv rau qhov paub zoo axiom nteg los ntawm Euclid.
Postulates
Lo lus "postulate" yog los ntawm Latin "postular", ib qho lus qhia uas txhais tau tias "xav tau". Tus tswv thov nws cov tub kawm kom lawv sib cav txog tej nqe lus uas nws tsim tau. Tsis zoo li axioms, postulates tsom mus ntes dab tsi tshwj xeeb ntawm ib qho qauv. "Nws muaj peev xwm kos ib txoj kab ncaj nraim los ntawm ib qho taw tes mus rau lwm qhov", "Nws muaj peev xwm tsim tau ib qho ncaj ncaj tsis tu ncua nyob rau hauv txoj kab ncaj nraim", thiab "Nws muaj peev xwm piav qhia lub voj voog nrog txhua qhov chaw thiab txhua lub vojvoog" yog ob peb yam piv txwv rau postulates illustrated los ntawm Euclid.
Dab tsi yog qhov txawv ntawm Axioms thiab Postulates?
• Ib qho axiom feem ntau muaj tseeb rau txhua qhov hauv kev tshawb fawb, thaum lub postulate tuaj yeem ua tau tshwj xeeb ntawm ib qho chaw tshwj xeeb.
• Nws tsis tuaj yeem ua pov thawj los ntawm lwm cov axioms, thaum postulates yog provable rau axioms.
