The proof is by contradiction. Suppose each real number could be given its own room.
这样的论证是自相矛盾的。
The proof by contradiction is one of the most important methods of proving propositions in mathematics.
如何有效地提高和改进反证法的教学，是摆在中学数学教师面前的一个重要课题。
Motion sickness : Sickness caused by contradiction between external data from the eyes and Internal cues from the balance centre In the Inner ear.
晕动病：从眼睛传入的讯息和内耳平衡器官传入的讯息不一致而导致的疾病。
This isn't in contradiction with my advice actually - it's learning that you can control bad situations by getting help from others.
事实上，这与我的坚毅并不矛盾——你能够通过他人的帮助来控制恶劣的处境。
Let me offer a few more related observations, by way of extension and refinement, not contradiction.
在这里我并不想反驳什么，只是和大家分享一些经拓展和提炼后的相关观点。
These images of contradiction are understood by the artist as a metaphor for modern times.
这些矛盾的意向可以被艺术家作为现代的暗喻来理解。
But in seeming contradiction, the unemployment rate also rose by two percentage points, from 9.7% to 9.9%.
不过，单从表面数据看来，彼此矛盾的是，失业率同时也提高了0.2个百分点，由9.7%上升到了9.9%。
Until March 23rd, that is, when he intervened by phone in a popular RAI breakfast TV programme and aired his views—without contradiction.
直到3月23日，当他在RAI早餐时间段的一档受欢迎的电视节目中出现时受到了电话干扰，方才毫无矛盾地曝出了他的观点。
Creative reflections: Hidden by old and new urban construction in the contradiction between things, to trigger the real world of people.
创作感言：通过城市建设中隐藏的新旧事物之间的矛盾，来引发人们对现实社会的思考。
The third chapter points out the contradiction of the present naturalization laws by analyzing the lack and the practical problems.
第三章主要通过对现行国籍法的不足及在实际操作中产生的问题进行分析，指出矛盾。
It solves the contradiction between the individual rationality and that of collective by putting the contradiction of the collective rationality on the basis of that of the individual.
它通过把集体理性的矛盾建立在个人理性的基础上，来解决个人理性与集体理性的矛盾。
Vie may to find a new breach to think and analyze the contradiction by the view of acculturation.
从文化适应的角度来看待和分析这些矛盾，也许可以找到新的突破口，当然，这只是一种尝试而已。
An effective comprehensively broken down works have been implemented aimed to increasing production and decreasing pressure to the contradiction caused by dual high water injection in Erlian oilfield.
二连油田针对“双高注水”产生的一系列矛盾有效开展了以“提液降压”为主的油田综合治理工作。
Finally, a numerical example shows that the modified RLS algorithm result in faster convergence speed by solving the contradiction between speed and accuracy.
算例表明：改进的RLS算法能解决收敛速度与收敛精度之间的矛盾，有效地加快了收敛速度。
The explanation offered by Kant alleges that the contradiction does not affect the object in its own proper essence, but attaches only to the Reason which seeks to comprehend it.
康德所提出的解答认为这矛盾并不是对象自己本身所固有，而仅是属于认识这对象的理性。
The small contradiction can be enlarged by the uncivilized words and someone will be criticized by the public.
小小的矛盾可以被不文明的用语放大，一些人会被大众批评。
By analysis, we mean analyzing the contradiction in things.
通过分析，我们指对事物矛盾的分析。
But water resource amount what can offer in the basin is limited; the contradiction among the demand and supply will be sharp day by day.
而流域内所能提供的可用水资源量是有一定限度的，需求与供给间的矛盾将日趋尖锐。
Culture Exchange and among the main investors, the text submitted by the contradiction between the agent and the upgrade is center stage contradictory gathering.
文交所和主力投资人之间，文交所和代理商之间的矛盾升级是现阶段矛盾的中心聚集地。
The solving of shortage demand contradiction is in final analysis decided by people's demand increase.
解决需求不足矛盾，归根到底取决于消费需求特别是居民消费需求的增长。
The method which creating question situation is inspiring interest, inducement, guiding-deep, inspiring doubt, going forward one by one, compare, contradiction, suspense, query.
创设问题情境的方法有：激趣法、诱导法、引深法、激疑法、递进法、比较法、矛盾法、悬念法、质疑法。
The anxiety of ZHANG Wei was formed by the contradiction between nature and society, nationalism and globalism, and the paradox between initiation and morality.
自然与人事的对峙，启蒙者的困境与道德审美化的文化选择，本土与西化的冲突，是形成张炜深层焦虑的重要原因。
An Oxford University scholar killed a woman by mistake when he practised shooting, which activated the contradiction between townsfolk and scholars existing for a long time.
牛津大学的一位学者在练习射箭的时候误杀了一名妇女，从而激化了牛津市民与学者之间早已存在的矛盾。
This dissertation attempts to solve the contradiction by conceptual construction.
本文以概念建构化解矛盾。
Analyzing the hardship of undergraduate employment, in the authors opinion, it isn t caused by the enlargement of colleges, but the contradiction between supply and demand.
通过对大学生就业难现象进行分析，认为其原因并非由高校扩招引起，而是由供求矛盾所致。
It has caused mainly by the contradiction between the rising commercial housing price.
其产生原因主要归咎为商品房房价的持续走高与大众的购买力之间的矛盾。
At present, massive contradiction in China is characterized by interests and massiveness. The main aspect of contradiction is management.
当前我国的群体矛盾具有利益性、群体性，矛盾的主要方面是管理层。
By analysing the exterior contradiction of things, we can know interior essence.
矛盾是对立的统一，通过分析外在的矛盾现象，可以看到事物内在的本质。
By analysing the exterior contradiction of things, we can know interior essence.
矛盾是对立的统一，通过分析外在的矛盾现象，可以看到事物内在的本质。
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