选择公理

This is one of the reasons why some mathematicians dislike the axiom of choice.

这是一些数学家不喜欢选择公理的理由之一。

Any time it is possible to specify such an explicit choice, the axiom of choice is unnecessary.

在任何有可能指定这种明确选择的时候，选择公理都是没有必要的。

People's attitude is suspicion of axiom of choice and axiom of parallelism.

人们对平行公理和选择公理的态度都表现为：怀疑。

For certain infinite sets ''X'', it is also possible to avoid the axiom of choice.

对于特定的无限集合''X''，也有可能避免选择公理。

Yet, the BPI is strictly weaker than the axiom of choice, though the proof of this statement is rather non-trivial.

但是 BPI 严格的弱于选择公理，尽管这个陈述的证明是非常不平凡的。

It is known that all of these statements are consequences of the axiom of choice ( the easy proof makes use of

已知所有这些陈述都是选择公理的推论

We love their loved ones, friends, but not because of personal feelings rather give up their choice of conscience, objective judgments, in the face Xunqing, we chose selfless; the face of a dispute, we have the axiom of choice.

我们爱自己的亲人，朋友，但是不能因为个人的感情的而放弃自己良心的选择，客观的判断，面对徇情，我们选择无私；面对争执，我们选择公理。

The problem then becomes constructing such an ordering, and it turns out that every set can be well-ordered if and only if the axiom of choice is true.

问题就变成构造这样一个排序，而它使得所有集合可以是良序的，当且仅当选择公理为真。

Countable and uncountable sets , the axiom of choice , Zorn's lemma.

集合论。可数和不可数集，选择公理，佐恩引理。

On the base of Frege's study, Russell put forward the theory of types to settle Russell's paradox. On the base of non-set, Russell brought forward axiom of infinity and axiom of option as the premises and built a system. He tried to defined the non-negative integer in logic terms and derive the theorems of arithmetic from the laws of logic by deductive method.

罗素在弗雷格研究的基础上，提出逻辑类型论来解决罗素悖论，以非集合论理论为基础，以无穷公理和选择公理为前提，利用逻辑概念定义数学概念，并构造系统，通过逻辑演绎法从逻辑公理推导数学定理。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。