数学模型有别于其他模型的重要一点就是：数学通过定义公理来创造属于自己的世界。
Mathematical models differ in an important aspect from other models: mathematics create, by defining axioms, a universe of their own.
数学公理或真理是永远不会错的。
既然它是个公理，我们可以用它来解这个数学题目了。
Since it is an axiom, we can use it to solve this maths problem.
这是一些数学家不喜欢选择公理的理由之一。
This is one of the reasons why some mathematicians dislike the axiom of choice.
本文介绍了泛布尔代数的数学模型、公理体系和化简方法；
This paper introduces the mathematics model, axiom system and simplified method of the Panboolean alegara.
数学归纳法推理是典型的三段论，而不是完全归纳法，其基础是自然数列的性质，而不是逻辑公理。
Mathematic induction is a typical syllogism, it is not complete induction, its base is the property of natural sequence, but not logic axioms.
以《几何原本》为代表的欧氏几何是古希腊文明的一个火车头，是古代数学公理化方法的一个辉煌成就。
Euclidean geometry is not only the leader of the civilization of ancient Greek but also the brilliant achievements of axiomatic approach in mathematics.
公理方法是一种源于几何的数学方法。其突出的特点，使之很快就成为一种运用广泛的科学方法。
The axiomatic method is a mathematics method from geometry, owing to the outstanding characteristic, it is getting a scientific method used extensively.
不过我认为这就像在数学中，我们得先承认接受一些公理才能开始演算。
But I felt that it was like in mathematics, one has to accept certain formulas in advance in order to start calculations.
到了十九世纪末，数学家开始从众多不同的具体研究对象中抽象出它们的共同特征进行公理化研究。
By the late nineteenth century, mathematicians began to conduct axiomatic study through abstracting the common features of a number of different concrete objects.
到了十九世纪末，数学家开始从众多不同的具体研究对象中抽象出它们的共同特征进行公理化研究。
By the late nineteenth century, mathematicians began to conduct axiomatic study through abstracting the common features of a number of different concrete objects.
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