endless loop; infinite loop

In this paper,all the metahomomorphisms on the infinite cyclic group Z are given.

给出了无限循环群上的全体亚同态映射。

This paper tries to give a definition of the sum and the product of infinite infinitesimal,and it also tries to give some examples to illustrate the sum and the product of infinite infinitesimal being or not being infinitesimal.

给出了无限个无穷小的和、积的一种定义，并用例子指出无限个无穷小的和、积既可能是无穷小，也可能不是无穷小。

The notion of the subshift of infinite type on noncompact symbolic space was introduced,and the chaotic behave of the subshift was discussed.

引入了非紧致符号空间上的无限子移位的概念，讨论了无限型子移位映射的混沌性质，给出了三个分别与Ｌｉ－Ｙｏｒｋｅ意义下混沌等价的条件。

Plato tried his best to argue that the infinite could be verified by the finite things, but he failed, and so did Kant.

我们认为这个问题源出自柏拉图相论的分离问题,柏拉图试图从有限的感性世界逻辑地上升到无限的理性世界,康德在《判断力批判》里也试图从有限过渡到无限,但他们都以失败告终。

G.W.F.Hegel s thought about quantity and mathematical infinity;

黑格尔关于量与数学的无限性思想

This article analyzed the basis of limit establishment-the thought in infinity and limit,discussed several deep stage problems in the limit definition,to deepen the understanding in limit concept and to comprehend the essence of limit correctly.

分析了极限建立的基础——无限的引入和极限的思想,讨论了极限定义中的一些深层次问题,以期加深对极限概念的理解,正确认识其本质。

Epistemologically,infinity would produce paradox.

芝诺悖论与无限概念密切相关。