完备

By 25 he had produced what many consider the most important result of 20th century mathematics: his famous "incompleteness theorem."

到了二十五岁，他提出著名的不完备定理，被许多人认为是二十世纪最伟大的数学成果。

The Incompleteness Theorem states that any consistent mathematical theory must contain one or more premises that cannot be proved within the theory.

哥德尔不完备定理是说：当一个演绎系统是自足的，总有至少一个或几个前提是在系统内不能证明的。

But the third mathematical crisis and Godel's Incompleteness Theorem provide obvious philosophical significance: It proclaims and proves that human mind is not infinite and we must maintain a humble attitude in front of the mysterious nature.

但第三次数学危机和哥德尔不完备定理，在哲学的意义上是明显的：它宣告并且证明人的理性、理智不是无限的，人类必须在大自然的秘密面前保持谦逊的态度。

Gdel's first incompleteness theorem states that:Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete.

第一，他证明了，对于任意的数学系统，如果其中包含了算术系统的话，那么这个系统不可能同时是完备的和一致的。

It is not my intention to introduce a mathematical crisis into religious arguments, although an American mathematician, when speaking of Godel's Incompleteness Theorem, did call mathematics a branch of theology.

我并不想把数学的危机问题引入宗教问题的争论中来，尽管一个美国数学史家，在谈到哥德尔不完备定理时，乾脆称"数学，神学的一个分支。"

In this paper, the author queried a few conclusions in [1] , and elaborated different views on several problems, such as relations between non-Euclidean geometry and real space, relations between mathematical logic and thinking, the significance of Godel s second incompleteness theorem, and so on.

本文对文〔1〕的几个论断提出一些疑问，并在"非欧几何与现实空间"、"数理逻辑与思维"、"哥德尔不完备性定理的意义"等若干问题上表述了与《数学是什么》一文中不同的观点。

It was not until Godel, the great mathematician who proposed the famous Incompleteness Theorem, that the philosophical significance more fully revealed itself in fundamental mathematical research.

直到再后来，大数学家哥德尔发现了著名的"哥德尔不完备定理"，将数学基础研究的哲学意义，揭示得更加明显。

Del's incompleteness theorem , the availability of complete information that omics data potentially represents might not be sufficient to understand all the underlying principles that govern the functions of biological systems.

拿歌德尔不完备定理作个类比，就算获得了完整的"组学"数据信息也并不意味着我们就可以理解生命系统中所有的潜在法则。

The reasoning of human being is limited,which leads to the incompleteness of legislation.

人类的理性是有限度的，这就必然导致有限理性下的立法具有不完备性。

The denial of more than one will in Christ by the heretics necessarily involved the incompleteness of His human nature.

剥夺一个以上的将在基督里所涉及的异端一定的不完备性，他的人性。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐