无穷小是有多小？
中英文连载
Are You Ready for Happiness? (24)
Perhaps one might ask how matter can be ultimately empty when the more it is divided, the more matter is produced.
或许有人会问：物质的个体只会越分越多,怎么最后会变空呢?
In philosophy and mathematics, we refer to things sometimes as infinitely large or infinitely small. However, this is an incorrect concept, since an infinitely small particle simply doesn’t exist in this world. For instance, a minute can be divided into sixty seconds; a second can be divided into one hundred even smaller units; if we continue in this way, we end up with something we call infinitely small.
我们知道，在哲学和数学中，有无限大和无限小的概念。但所谓的无限小，应该是一个存在着很大漏洞的错误观念，因为世上根本不存在无限小的东西。比如说，一分钟，我们可以分为六十个一秒钟；一秒钟，又可以再分为一百个更小的单位，然后一直这样无边无际地分下去，最后的结果，叫做无限小。
In fact, if a second can be divided indefinitely, time will stop permanently on that second, unable to get past it. Yet we all know, in the objective world, there is a time limit to a second. The two obviously contradict each other.
但实际上，如果一秒钟可以无穷无尽地分下去，永远都分不完，则时间将永远停留在这一秒钟上面，再也过不去。然而，众所周知，在客观世界中，一秒钟的时间却是有限的。二者显然有了矛盾。
Similarly, if a molecule or electron can be divided indefinitely, then a building and a grain of rice will be equal in weight and mass. However, we know from experience a grain of rice hardly carries any weight or mass because it is comprised of very few molecules and atoms; a building, on the other hand, is massive and heavy because it is made up of a lot of molecules and atoms.
再比如，如果一个分子或一个电子永远都分不完，则一栋房子的重量和体积，就会与一粒米的重量和体积毫无分别，因为它们都一样无穷无尽。但现实生活已经告诉我们，一粒米之所以重量很轻、体积很小，那是因为它的结构当中的分子、原子没有那么多。反之，一栋楼的体积之所以那么大，重量那么重，也是因为它的结构当中有很多的分子或原子。
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