Nov 26, 2012

MATHEMATICAL MODEL_Documented by Marsigit


A mathematical model for an axiomatic system is a well-defined set, which assigns meaning for the undefined terms presented in the system, in a manner that is correct with the relations defined in the system. The existence of a concrete model* proves the consistency of a system. 

Models can also be used to show the independence of an axiom in the system. By constructing a valid model for a subsystem without a specific axiom, we show that the omitted axiom is independent if its correctness does not necessarily follow from the subsystem. 

Two models are said to be isomorphic if one-to-one correspondence can be found between their elements, in a manner that preserves their relationship. An axiomatic system for which every model is isomorphic to another is called categorial, and the property of categoriallity ensures the completeness of a system. 

* A model is called concrete if the meanings assigned are objects and relations from the real world, as opposed to an abstract model which is based on other axiomatic systems.
The first axiomatic system was Euclidean geometry.

1 comment:

  1. Syahrial
    S2 PEP kelas B 2016
    sedikit saya ambil kata-kata dari artikel di atas ialah sebuah model matematika untuk sistem aksiomatik adalah satu set yang didefinisikan dengan baik, yang memberikan makna bagi istilah terdefinisi disajikan dalam sistem, dengan cara yang benar dengan hubungan didefinisikan dalam sistem. artinya model matematika itu sudah berada pada suatu sistem dan sistem inilah yang mengarah kepada pembuktian matematika tersebut, model matematika juga dapat memberikan dan mempermudah dalam penerapannya dan pemahamannya.


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