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I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

  • -- Georg Cantor 康托

我意识到，在这项事业中，我把自己置身于一种与广泛持有的有关数学无限大的观点和经常为数字的本质辩护的观点相反的立场。

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Mathematical concerning

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Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

从整体上看，纯数学明显比应用数学更有用。因为最重要的是技术，而数学技术主要是通过纯数学来教授的。

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Anyone who acquires more than the usual amount of knowledge concerning a subject is bound to leave it as his contribution to the knowledge of the world.

任何一个人，如果他在某一方面获得的知识超过了通常的水平，他就一定会把它作为他对世界知识的贡献而离开。

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Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

欧几里得告诉我，没有假设就没有证据。因此，在任何论证中，都要检验假设。

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We are least open to precise knowledge concerning the things we are most vehement about.

对于那些我们最热衷的事情，我们最不愿意接受精确的知识。

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