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。

Behold! By appealing to the Axiom of Choice, I can claim that I can dissect the very moon into but five parts, then put it back together and pop it into my mouth—like this fly!

听着！利用公理选择的方法，我可以把天上月亮分割成五个部分，然后再把它装起来放进我的嘴里，就像那只苍蝇那样！

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。

The others problems discussed are nested interval method, Cantor theorem, C del incompleteness theorem and Axiom of choice etc.

同时对区间套法，康托定理，哥德尔定理，选择公理等与之密切相关的一些问题，作了深入讨论并得出创新性结论。

Although the axiom of constructibility does resolve CH, it is not generally considered to be intuitively true any more than CH is generally considered to be false.

要反对这一观点，要是能展示一条既能被直观所支持、又能从证明或证否面解决连续统假设的新公理，那就很足够了。

To take just one example, consider the set theorist's axiom of extensionality : For any sets A and B , if A and B have the same members, then A is the same set as B .

举例说，考虑集合论的外延公理：对任何集合A和B，如果A和B有相同的成员，那么A作为集合和B同一。

All the problems that Russell's 'axiom of infinity' brings with it can be solved at this point.

至此，罗素的"无穷公理"所带来的一切问题都已获致解决。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。