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11.
Given the old conception of the relation greater than, the proposition that the whole is greater than the part is an immediate consequence. But being greater in this sense is not incompatible with being equal in the sense of one-one correspondence. Some who failed to recognize this formulated invalid arguments against the possibility of infinite quantities. Others who did realize that the relations of equal and greater when so defined are compatible, concluded that such relations are not appropriately taken as quantitative relations, at least, not in general. If suitable quantitative relations were to be defined, there was a possibility of retaining either the traditional definition of greater and finding another concept of equality, or of retaining the concept of equality as one-one correspondence and defining greater than so that it is incompatible with equality in this sense. The former alternative was implicitly taken by Bolzano, who never succeeded in defining suitable quantitative relations. The latter alternative was taken by Cantor, and is the basis of his great success in constructing a mathematical theory of the transfinite.  相似文献   
12.
再看冷聚变     
因为原子核和电子不仅在能量大小而且在能量的释放时间上都有着巨大的差别,所以核物理和化学占领着两个不同的世界。但彭斯(Pons)、弗莱希曼(Fleischmann)和霍金斯(Hawkins)的观测结果以及琼斯(Jones)等人的独立工作表明在这两个世界中存在一座桥梁。因此而诞生的学科人们习惯称之为“冷聚变”,这是一个不幸的名字。因为没有已知的理论可适当地支持这些结果,而且许多实验数据表述很差并且难于重复,使得多数科学家一直反对这种观念。这些实验所揭示的现象本质与人们固守的传统观念间存在的矛盾也增加了人们接受它的困难。尽管…  相似文献   
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