Someone once said that the rationals -- the fractions -- are like the stars in the night sky.

有人曾这样比喻：有理数，或者说分数，就像天空的星星；

To avoid circularity in the definition, we must be able to characterize the sets of rationals obtainable in this way…

为了避免循环定义，我们需要刻划通过这种方法得出的有理数集合的特征…

This is one kind of shape which is different from esthetics theory , rationals and tools are the character of the latter .

这是一种与工具化理性化为特征的哲学美学明显不同的美学理论形态。

Forward-thinking, wise and knowledgeable, rationals have shaped our world by developing the latest gadgets and technology.

理性者有远见、聪明、知识渊博，他们通过开发最新的小玩意和技术塑造我们的世界。

So, can we make a one-to-one match between the whole numbers and the set of all the decimals, both the rationals and the irrationals?

那么，我们可以将正整数和所有无理、有理的小数“一对一”对应吗？